Gr 11 Math Lit: November Mix P(2)
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Questions and Answers

What is the main purpose of using a national road map?

  • To plan a route between destinations and estimate traveling costs and times (correct)
  • To find the positions of houses within a small housing complex
  • To determine the exact location of a specific street
  • To identify points of interest on a specific route

    • What is the primary function of a strip chart?

  • To show the location of streets and other locations within a city
  • To show the positions of houses within a small housing complex
  • To provide detailed information about a specific route, including locations of towns and points of interest (correct)
  • To provide an overview of major routes and roads in a country

    • What is the main difference between a national road map and a street map?

  • Grid reference system
  • Content (correct)
  • Scale
  • Symbol usage

    • When using a housing complex map, what is the most important skill to possess?

    <p>Ability to work with a map that shows a small area with limited detail</p> Signup and view all the answers

    What is the formula to calculate the actual distance from a map measurement?

    <p>Actual distance = Map measurement × Scale factor</p> Signup and view all the answers

    Why is it essential to use the given scale when using a map?

    <p>To determine the actual distance when a distance table or distance markers are not provided</p> Signup and view all the answers

    What is the primary purpose of using a distance table or distance markers on a map?

    <p>To calculate the actual distance when a scale is not provided</p> Signup and view all the answers

    What is the main difference between Calculation Type 1 and Calculation Type 2 when using scales?

    <p>The direction of the calculation</p> Signup and view all the answers

    What is the first step in assembling the components?

    <p>Interpret Instructions</p> Signup and view all the answers

    What is the purpose of drawing 2D plans or nets?

    <p>To represent each face of the model in its proper arrangement</p> Signup and view all the answers

    What is the formula to calculate the probability of a simple event?

    <p>P(event) = number of ways in which an event can happen / total number of possible outcomes</p> Signup and view all the answers

    Why is it important to follow the assembly steps in the correct sequence?

    <p>To ensure that the components fit together properly</p> Signup and view all the answers

    What is the purpose of estimating the time required for each step of the assembly process?

    <p>To determine the total time needed for the entire assembly</p> Signup and view all the answers

    What is the definition of a simple event?

    <p>An event that involves a single occurrence or trial</p> Signup and view all the answers

    What is the purpose of regularly checking the assembled parts against the instructions or plans?

    <p>To ensure accuracy and make adjustments as needed</p> Signup and view all the answers

    What is the original form of probability value resulting from the calculation?

    <p>Fraction Format</p> Signup and view all the answers

    What is the purpose of using mathematical tools and techniques in assembly?

    <p>To measure and cut materials accurately</p> Signup and view all the answers

    What is the importance of understanding instructions in assembly?

    <p>To ensure correct assembly and identify all components and tools required</p> Signup and view all the answers

    Which of the following is a characteristic of a tree diagram?

    <p>Each branch represents different possible outcomes</p> Signup and view all the answers

    What is the purpose of determining probability values?

    <p>To make predictions about future events</p> Signup and view all the answers

    What is the purpose of gathering all necessary materials and tools before starting the assembly?

    <p>To ensure that everything is in the correct size, quantity, and type</p> Signup and view all the answers

    What is the formula for calculating the probability of a simple event?

    <p>P(event) = number of ways in which an event can happen / total number of possible outcomes</p> Signup and view all the answers

    What is the main difference between simple and compound events?

    <p>Simple events involve a single occurrence or trial, while compound events involve more than one occurrence or trial</p> Signup and view all the answers

    What is the purpose of two-way tables in probability calculations?

    <p>To compare two different variables and determine probability values</p> Signup and view all the answers

    What is the percentage format of probability values obtained by?

    <p>Multiplying the fraction by 100</p> Signup and view all the answers

    What is the main application of probability values in advertisements?

    <p>To determine car insurance rates for different genders and age groups</p> Signup and view all the answers

    What is the main limitation of probability values?

    <p>They predict the likelihood of an event, but do not guarantee the outcome</p> Signup and view all the answers

    What is the main characteristic of compound events?

    <p>They involve more than one occurrence or trial</p> Signup and view all the answers

    What is the primary purpose of a floor plan?

    <p>To show the design and dimensions of the inside of a building or structure</p> Signup and view all the answers

    What is the function of an elevation plan?

    <p>To show the design and dimensions of the outside of a building or structure</p> Signup and view all the answers

    What is the purpose of a design drawing?

    <p>To show the design, layout, and components of an item to be constructed or manufactured</p> Signup and view all the answers

    What is the key concept for describing features of a building or structure?

    <p>Describe features of a building or structure</p> Signup and view all the answers

    What is the purpose of using a scale to determine dimensions?

    <p>To accurately measure and determine the actual dimensions of features shown on the plan</p> Signup and view all the answers

    What is the formula for calculating plan measure from actual dimension?

    <p>Plan Measure = Actual Dimension / Scale Factor</p> Signup and view all the answers

    What is the primary purpose of building 3D models from 2D plans?

    <p>To facilitate the movement between 2D and 3D representations of objects</p> Signup and view all the answers

    What is the process of creating a 2D net from a 3D object?

    <p>Drawing 2D plans/nets of 3D models</p> Signup and view all the answers

    What is the purpose of creating a 2D net?

    <p>To facilitate the movement between 2D and 3D representations of objects</p> Signup and view all the answers

    What is the process of creating a 3D object from a 2D net?

    <p>Building 3D models from 2D plans</p> Signup and view all the answers

    What is the formula to convert an actual distance to a map measurement?

    <p>Map measurement = Actual distance / Scale factor</p> Signup and view all the answers

    What type of scale is expressed in the format 1:50,000?

    <p>Number Scale</p> Signup and view all the answers

    What is the purpose of a floor plan?

    <p>To show a 2-dimensional perspective of a building as seen from above, without the roof</p> Signup and view all the answers

    What is the formula to determine the actual distance from a map measurement?

    <p>Actual distance = Map measurement × Scale factor</p> Signup and view all the answers

    What is the main difference between a number scale and a bar scale?

    <p>A number scale shows the relationship between the size of the area on the map and the actual size, while a bar scale shows the relationship between measured length and actual distance</p> Signup and view all the answers

    What happens to a number scale if the size of the map is changed?

    <p>The number scale becomes invalid, and a new number scale must be determined</p> Signup and view all the answers

    Why is it only possible to estimate distances on a map using a scale and not to determine distances accurately?

    <p>Because many factors can affect the accuracy of a distance calculation on a map</p> Signup and view all the answers

    What is the purpose of a scale on a map?

    <p>To enable users to estimate traveling distances</p> Signup and view all the answers

    What is the advantage of a bar scale over a number scale?

    <p>A bar scale remains valid even if the size of the map is changed</p> Signup and view all the answers

    What is the formula to convert a map measurement to an actual distance?

    <p>Actual distance = Map measurement / Scale factor</p> Signup and view all the answers

    What is the term used to describe the point where two graphs intersect?

    <p>Point of Intersection</p> Signup and view all the answers

    What is the purpose of drawing graphs in unfamiliar situations?

    <p>To make sense of the situation and reveal patterns and trends</p> Signup and view all the answers

    What is the method of estimating the point of intersection from a graph?

    <p>Identify the Two Graphs, Locate the Intersection Point, Read Horizontal Value, and Read Vertical Value</p> Signup and view all the answers

    What is the importance of understanding intersection points?

    <p>For analyzing and interpreting data</p> Signup and view all the answers

    What is the conversion factor to convert weight from kilograms to pounds?

    <p>2.206</p> Signup and view all the answers

    What is the formula to convert temperature from Celsius to Fahrenheit?

    <p>°F = (1.8 × °C) + 32</p> Signup and view all the answers

    What is the term used to describe numerical values used to switch between different units of measurement?

    <p>Conversion Factors</p> Signup and view all the answers

    What is the purpose of the Trial and Improvement Method?

    <p>To determine the values at which two relationships are equal</p> Signup and view all the answers

    What is the importance of conversions between solid and liquid quantities?

    <p>Essential in various contexts such as baking and construction</p> Signup and view all the answers

    What is the term used to describe moving from one interval to another with a completely different fee?

    <p>Non-Joined Segments</p> Signup and view all the answers

    What is the purpose of converting minutes to seconds?

    <p>To calculate time differences accurately</p> Signup and view all the answers

    What is the formula to convert hours to seconds?

    <p>Seconds = Hours x 3600</p> Signup and view all the answers

    What is the purpose of measuring time in seconds?

    <p>To calculate time differences</p> Signup and view all the answers

    What is the formula to convert minutes to hours?

    <p>Hours = Minutes / 60</p> Signup and view all the answers

    What is the surface area of a rectangular box?

    <p>2lw + 2lh + 2wh</p> Signup and view all the answers

    What is the purpose of using a stopwatch?

    <p>To measure time</p> Signup and view all the answers

    What is the purpose of converting units of measurement?

    <p>To change units within the same system or between different systems</p> Signup and view all the answers

    What is the formula to calculate the volume of a rectangular box?

    <p>l × w × h</p> Signup and view all the answers

    What is the purpose of estimation techniques?

    <p>To make reasonable estimates of quantities when exact measurement is not possible</p> Signup and view all the answers

    What unit is used to express surface area?

    <p>Square units</p> Signup and view all the answers

    What is the conversion ratio between cubic meters and liters?

    <p>1 cubic meter = 1000 liters</p> Signup and view all the answers

    What is the purpose of using significant figures?

    <p>To reflect the precision of the data</p> Signup and view all the answers

    What is the formula to calculate the surface area of a cylinder?

    <p>2πr^2 + 2πrh</p> Signup and view all the answers

    What is the purpose of measuring length, area, and volume?

    <p>To understand the properties of geometric figures</p> Signup and view all the answers

    What is the first step in measuring and estimating?

    <p>Identify the quantity to be measured or estimated</p> Signup and view all the answers

    What is the conversion ratio between cubic centimeters and milliliters?

    <p>1 cubic centimeter = 1 milliliter</p> Signup and view all the answers

    What is the main difference between simple and compound events?

    <p>Simple events involve a single occurrence or trial</p> Signup and view all the answers

    What is the purpose of converting between units in surface area and volume calculations?

    <p>To convert between different units of measurement</p> Signup and view all the answers

    What is the volume of a cylindrical container?

    <p>πr^2 × h</p> Signup and view all the answers

    What is the formula for calculating the probability of a simple event?

    <p>P(event) = number of ways in which an event can happen / total number of possible outcomes</p> Signup and view all the answers

    What is the purpose of a tree diagram in compound events?

    <p>To visualize the outcomes of a compound event</p> Signup and view all the answers

    What happens when you convert 1 cubic meter to cubic centimeters?

    <p>It becomes 1,000,000 cubic centimeters</p> Signup and view all the answers

    What is the importance of understanding conversion between units in surface area and volume calculations?

    <p>It is necessary for accurate calculations</p> Signup and view all the answers

    What is the meaning of a probability value?

    <p>A value that describes the likelihood of an event</p> Signup and view all the answers

    What is the characteristic of a graph that represents a constant ratio relationship?

    <p>A graph that becomes steeper at an increasing rate</p> Signup and view all the answers

    What is the purpose of a two-way table in compound events?

    <p>To compare two different variables and determine probability values</p> Signup and view all the answers

    What type of relationship is characterized by a graph that becomes steeper at an increasing rate?

    <p>Constant ratio relationship</p> Signup and view all the answers

    What is an example of a simple event?

    <p>Calculating the probability of a weather forecast</p> Signup and view all the answers

    What is the name of the portion of the graph that represents a fixed fee that does not change with usage?

    <p>Flat Portion</p> Signup and view all the answers

    What is the uncertainty in prediction?

    <p>The fact that probability values do not guarantee outcomes</p> Signup and view all the answers

    What is the name of the relationship that occurs when different fees or values are charged for different time intervals?

    <p>Step-function relationship</p> Signup and view all the answers

    What is the main difference between a flat portion and an increasing portion in a graph?

    <p>A flat portion represents a fixed fee, while an increasing portion represents a variable rate</p> Signup and view all the answers

    What is the purpose of drawing graphs of unfamiliar situations?

    <p>To make sense of the situation and reveal patterns and trends</p> Signup and view all the answers

    What is the name of the portion of the graph that represents additional charges that increase linearly with usage?

    <p>Increasing Portion</p> Signup and view all the answers

    What is the format of probability values that is obtained by multiplying the fraction by 100?

    <p>Percentage format</p> Signup and view all the answers

    What is the name of the relationship that occurs when a value is increased by a factor and then this new increased value is again increased by the factor?

    <p>Constant ratio relationship</p> Signup and view all the answers

    What is the name of the skills that learners need to develop to draw and interpret graphs?

    <p>Drawing and interpreting graphs skills</p> Signup and view all the answers

    What is the characteristic of a step-function relationship?

    <p>A graph that looks like a series of steps</p> Signup and view all the answers

    What is the purpose of recognizing and understanding the implications of constant ratio relationships, combination relationships, and step-function relationships?

    <p>To recognize and understand the implications of the relationships in real-world situations</p> Signup and view all the answers

    What type of graph is made up of a combination of different types of relationships?

    <p>Combination graph</p> Signup and view all the answers

    What is the first step in performing conversions from grams to milliliters?

    <p>Identify the weight in grams</p> Signup and view all the answers

    What is the formula to convert from cubic units to liters?

    <p>Volume (l) = Volume (m³) × 1000</p> Signup and view all the answers

    What is the formula to calculate the total liters of paint needed?

    <p>Paint Needed (liters) = Surface Area (m²) / Spread Rate (m²/liter)</p> Signup and view all the answers

    What is the purpose of converting time recording values into a single unit?

    <p>To make it easier to perform calculations</p> Signup and view all the answers

    What is the formula to convert minutes to seconds?

    <p>Seconds = Minutes × 60</p> Signup and view all the answers

    What is the purpose of identifying the week and dates of the events in a timetable?

    <p>To locate the specific week and date of the event</p> Signup and view all the answers

    What is the second step in converting from cubic units to liters?

    <p>Identify the volume in cubic units</p> Signup and view all the answers

    Why is it important to double-check your calculations when performing conversions?

    <p>To ensure accuracy</p> Signup and view all the answers

    What is the purpose of breaking down the time values into hours, minutes, and seconds when calculating time differences?

    <p>To perform the subtraction correctly</p> Signup and view all the answers

    What is the formula to convert hours to seconds?

    <p>Seconds = Hours × 3600</p> Signup and view all the answers

    What is the primary skill required when using a street map?

    <p>Identifying locations using symbols.</p> Signup and view all the answers

    What is the purpose of using a scale on a map?

    <p>To estimate the actual distance when a distance table or distance markers are not provided.</p> Signup and view all the answers

    What is the main difference between a national road map and a strip chart?

    <p>The level of detail shown on the map.</p> Signup and view all the answers

    What is the primary skill required when using a housing complex map?

    <p>Working with a map that shows a small area with limited detail.</p> Signup and view all the answers

    What is the formula to calculate the actual distance from a map measurement?

    <p>Actual distance = Map measurement × Scale factor</p> Signup and view all the answers

    What is the primary purpose of using a strip chart?

    <p>To determine more accurate traveling distances on specific sections of a route.</p> Signup and view all the answers

    What is the primary purpose of measuring materials accurately during assembly?

    <p>To ensure the components fit together properly</p> Signup and view all the answers

    What is the primary purpose of using a national road map?

    <p>To determine the distance between major cities and towns.</p> Signup and view all the answers

    What is the main benefit of following the assembly steps in the correct sequence?

    <p>It minimizes the risk of errors and misalignments</p> Signup and view all the answers

    What is the purpose of estimating the quantities of materials needed for assembly?

    <p>To determine the total cost of the project</p> Signup and view all the answers

    What is the primary skill required when using a national road map?

    <p>Deciding on the most appropriate route between destinations.</p> Signup and view all the answers

    What is the term used to describe the value that describes the likelihood that an event may occur?

    <p>Probability value</p> Signup and view all the answers

    What is the purpose of regularly checking the assembled parts against the instructions or plans?

    <p>To identify mistakes or misalignments and make adjustments</p> Signup and view all the answers

    What is the formula used to calculate the probability of a simple event?

    <p>P(event) = number of ways in which an event can happen / total number of possible outcomes</p> Signup and view all the answers

    What is the purpose of using mathematical tools and techniques in assembly?

    <p>To measure materials accurately and calculate quantities and costs</p> Signup and view all the answers

    What is the main purpose of interpreting instructions or plans during assembly?

    <p>To understand the assembly process and identify all components and tools needed</p> Signup and view all the answers

    What is the purpose of estimating the time required for each step of the assembly process?

    <p>To plan and schedule the assembly process effectively</p> Signup and view all the answers

    What is the primary purpose of drawing 2D plans or nets?

    <p>To understand the faces and edges of the 3D model and unfold it into a flat layout</p> Signup and view all the answers

    What is the purpose of using a scale on a map?

    <p>To show the relationship between the size of the area on the map and the actual size of that area</p> Signup and view all the answers

    What is the advantage of a bar scale over a number scale?

    <p>It shows the relationship between measured length and actual distance</p> Signup and view all the answers

    If a map has a scale of 1:50,000, how can you convert an actual distance to a map measurement?

    <p>Divide the actual distance by 50,000</p> Signup and view all the answers

    What is the main difference between Calculation Type 1 and Calculation Type 2?

    <p>The purpose of the calculation is different</p> Signup and view all the answers

    What happens to a number scale if the size of the map is changed?

    <p>The number scale becomes invalid</p> Signup and view all the answers

    What is the purpose of using a scale to determine dimensions?

    <p>To show the relationship between the size of the area on the map and the actual size of that area</p> Signup and view all the answers

    Why is it only possible to estimate distances on a map using a scale and not to determine distances accurately?

    <p>Because of the many factors affecting distance calculations</p> Signup and view all the answers

    What is the formula to convert a map measurement to an actual distance?

    <p>Actual distance = Map measurement × Scale factor</p> Signup and view all the answers

    What type of scale is expressed in the format 1:50,000?

    <p>Number scale</p> Signup and view all the answers

    What is the primary purpose of using a scale when using a map?

    <p>To estimate distances accurately</p> Signup and view all the answers

    What is the primary function of a floor plan?

    <p>To show the design and dimensions of the inside of a building or structure</p> Signup and view all the answers

    What is the key concept for matching features between plans?

    <p>Match features between plans</p> Signup and view all the answers

    What is the purpose of a design drawing?

    <p>To show the design, layout, and components of an item to be constructed or manufactured</p> Signup and view all the answers

    What is the formula to calculate plan measure from actual dimension?

    <p>Plan Measure = Actual Dimension ÷ Scale Factor</p> Signup and view all the answers

    What is the primary purpose of building 3D models from 2D plans?

    <p>To facilitate the movement between 2D and 3D representations of objects</p> Signup and view all the answers

    What is the process of creating a 2D net from a 3D object?

    <p>Unfolding the 3D object to form the 2D net</p> Signup and view all the answers

    What is the key concept for describing the item or object shown on a design plan?

    <p>Describe the item or object shown on the design plan</p> Signup and view all the answers

    What is the purpose of using a scale to determine dimensions?

    <p>To accurately measure and determine the actual dimensions of features shown on the plan</p> Signup and view all the answers

    What is the primary purpose of drawing 2D plans or nets?

    <p>To facilitate the movement between 2D and 3D representations of objects</p> Signup and view all the answers

    What is the process of building a 3D model from a 2D net?

    <p>Folding the 2D net to form the 3D object</p> Signup and view all the answers

    What is the primary purpose of using tree diagrams in probability calculations?

    <p>To visualize all possible outcomes of events and determine their probabilities</p> Signup and view all the answers

    What is the main difference between simple and compound events?

    <p>Simple events involve a single occurrence or trial, while compound events involve multiple occurrences or trials</p> Signup and view all the answers

    What is the purpose of determining probability values?

    <p>To describe the likelihood that an event may occur</p> Signup and view all the answers

    What is the main application of probability values in advertisements?

    <p>To predict the outcome of a campaign based on historical data</p> Signup and view all the answers

    What is the main limitation of probability values?

    <p>They do not guarantee the outcome of an event</p> Signup and view all the answers

    What is the original form of probability value resulting from the calculation?

    <p>Fraction format</p> Signup and view all the answers

    What is the purpose of two-way tables in probability calculations?

    <p>To compare two different variables and make predictions</p> Signup and view all the answers

    What is the percentage format of probability values obtained by?

    <p>Multiplying the fraction by 100</p> Signup and view all the answers

    What is the main characteristic of compound events?

    <p>They involve multiple occurrences or trials</p> Signup and view all the answers

    What is the importance of understanding probability values?

    <p>It helps to describe the likelihood that an event may occur</p> Signup and view all the answers

    What is the main difference between a simple event and a compound event?

    <p>A simple event involves a single trial, while a compound event involves multiple trials.</p> Signup and view all the answers

    What is the purpose of a tree diagram in probability calculations?

    <p>To list all possible outcomes of an event and determine their probabilities.</p> Signup and view all the answers

    What is the main application of probability values in advertisements?

    <p>To predict the likelihood of an event based on historical data.</p> Signup and view all the answers

    What is the main limitation of probability values?

    <p>They predict the likelihood of an event, but do not guarantee the outcome.</p> Signup and view all the answers

    What is the formula for calculating the probability of a simple event?

    <p>P(event) = number of ways in which an event can happen / total number of possible outcomes</p> Signup and view all the answers

    What is the purpose of two-way tables in probability calculations?

    <p>To compare two different variables and determine their probabilities.</p> Signup and view all the answers

    What is the percentage format of probability values obtained by?

    <p>Multiplying the fraction by 100.</p> Signup and view all the answers

    What is the main characteristic of compound events?

    <p>They involve multiple occurrences or trials.</p> Signup and view all the answers

    What is the original form of probability value resulting from the calculation?

    <p>Fraction format.</p> Signup and view all the answers

    What is the importance of understanding uncertainty in prediction?

    <p>It helps to predict the likelihood of an event, but does not guarantee the outcome.</p> Signup and view all the answers

    What is the purpose of drawing graphs in situations where no specific formula or pattern is immediately obvious?

    <p>To reveal patterns and trends that were not visible without the graph</p> Signup and view all the answers

    What does the point of intersection of two graphs represent?

    <p>The quantity or unit where both graphs have the same value</p> Signup and view all the answers

    What is the first step in estimating the point of intersection from a graph?

    <p>Identify the two graphs</p> Signup and view all the answers

    What is the purpose of using the trial and improvement method to determine the point of intersection?

    <p>To find the values at which two relationships are equal</p> Signup and view all the answers

    Why is understanding the intersection points and the regions around them crucial?

    <p>To analyze and interpret data</p> Signup and view all the answers

    What is the conversion factor to convert weight from kilograms to pounds?

    <p>2.206</p> Signup and view all the answers

    What is the formula to convert temperature from Celsius to Fahrenheit?

    <p>°F = (1.8 × °C) + 32</p> Signup and view all the answers

    What is the purpose of converting between solid and liquid quantities?

    <p>To ensure accurate conversions in various contexts such as baking and construction</p> Signup and view all the answers

    What is the importance of understanding intersection points?

    <p>To provide insights into where different systems or scenarios yield the same results</p> Signup and view all the answers

    What is the process of finding the values at which two relationships are equal using their equations?

    <p>Trial and improvement method</p> Signup and view all the answers

    What is the formula to convert weight in grams to volume in milliliters?

    <p>Volume (ml) = (Weight (g) / Conversion Factor) × Conversion Factor for Volume</p> Signup and view all the answers

    What is the step to calculate the total liters of paint needed?

    <p>Identify the surface area and spread rate, then use the formula Paint Needed (liters) = Surface Area (m²) / Spread Rate (m²/liter)</p> Signup and view all the answers

    How do you convert time recording values from hours, minutes, and seconds to a single unit?

    <p>Multiply the hours by 3600, then add the minutes multiplied by 60 and the seconds</p> Signup and view all the answers

    What is the formula to calculate the total seconds from hours, minutes, and seconds?

    <p>Total Seconds = Hours × 3600 + Minutes × 60 + Seconds</p> Signup and view all the answers

    What is the step to find the difference between two time values?

    <p>Break down the time values into hours, minutes, and seconds, then subtract the smaller time value from the larger one</p> Signup and view all the answers

    What is the purpose of using conversion factors in calculations?

    <p>To ensure accuracy in the calculations</p> Signup and view all the answers

    What is the importance of understanding the context in which the conversion is being performed?

    <p>It helps to identify the correct conversion factor</p> Signup and view all the answers

    What is the formula to convert cubic meters to liters?

    <p>Volume (liters) = Volume (m³) × 1,000</p> Signup and view all the answers

    What is the importance of double-checking calculations when performing conversions?

    <p>It helps to identify errors in the calculations</p> Signup and view all the answers

    What is the purpose of using timetables?

    <p>To identify the week and dates of the events</p> Signup and view all the answers

    What is the characteristic of a constant ratio relationship?

    <p>The graph becomes steeper at an increasing rate.</p> Signup and view all the answers

    What is the name of the relationship that is characterized by a graph that looks like a series of steps?

    <p>Step-function relationship</p> Signup and view all the answers

    What is the purpose of drawing graphs in unfamiliar situations?

    <p>To make sense of the situation and reveal patterns and trends.</p> Signup and view all the answers

    What is the term used to describe the portion of a graph that represents a fixed fee that does not change with usage?

    <p>Flat portion</p> Signup and view all the answers

    What is the characteristic of a step-function relationship?

    <p>The graph looks like a series of steps.</p> Signup and view all the answers

    What is the purpose of analyzing and interpreting graphs in real-world situations?

    <p>To make sense of the situation and reveal patterns and trends.</p> Signup and view all the answers

    What is the name of the relationship that is characterized by a graph that is made up of a combination of different types of relationships?

    <p>Combination relationship</p> Signup and view all the answers

    What is the term used to describe the portion of a graph that represents additional charges that increase linearly with usage?

    <p>Increasing portion</p> Signup and view all the answers

    What is the importance of recognizing and understanding the implications of different types of relationships?

    <p>To make sense of the situation and reveal patterns and trends.</p> Signup and view all the answers

    What is the main skill that learners need to develop in order to analyze and interpret graphs?

    <p>Drawing graphs to represent various non-linear relationships.</p> Signup and view all the answers

    What is the formula to convert minutes to seconds?

    <p>Seconds = Minutes × 60</p> Signup and view all the answers

    What is the purpose of converting hours and minutes to seconds when calculating time differences?

    <p>To convert to a single unit</p> Signup and view all the answers

    What is the primary application of measuring time in real-life contexts?

    <p>Interpreting stopwatch values and calculating time differences</p> Signup and view all the answers

    What is the key concept when measuring mass and weight?

    <p>Using scales and balances</p> Signup and view all the answers

    What is the purpose of estimation techniques in measurement?

    <p>To make an estimate when exact measurement is not possible</p> Signup and view all the answers

    What is the correct order of steps when measuring and estimating?

    <p>Identify the quantity, choose the tool, perform the measurement</p> Signup and view all the answers

    What is the purpose of using significant figures in measurement?

    <p>To reflect the precision of the data</p> Signup and view all the answers

    What is the primary purpose of scaling in real-life contexts?

    <p>To represent real-life objects or distances accurately</p> Signup and view all the answers

    What is the formula to convert minutes to hours?

    <p>Hours = Minutes / 60</p> Signup and view all the answers

    What is the main concept in calculating time differences?

    <p>Converting to a single unit</p> Signup and view all the answers

    What is the unit of measurement for the surface area of a 3-dimensional object?

    <p>Square units (e.g., mm^2, cm^2, m^2)</p> Signup and view all the answers

    What is the formula to calculate the volume of a rectangular box?

    <p>V = l × w × h</p> Signup and view all the answers

    Why is it necessary to convert between units when calculating surface area and volume?

    <p>To convert between different types of units (e.g., square to cubic units)</p> Signup and view all the answers

    What is the conversion ratio between cubic meters (m^3) and liters (L)?

    <p>1 m^3 = 1000 L</p> Signup and view all the answers

    What is the purpose of calculating surface area and volume?

    <p>To solve problems in real-world contexts</p> Signup and view all the answers

    What is the formula to calculate the surface area of a cylinder with a lid and base?

    <p>SA = πr^2 + 2πrh</p> Signup and view all the answers

    What is the importance of considering the units when calculating surface area and volume?

    <p>To ensure accuracy in the calculations</p> Signup and view all the answers

    What is the conversion ratio between cubic centimeters (cm^3) and milliliters (mL)?

    <p>1 cm^3 = 1 mL</p> Signup and view all the answers

    What is the purpose of calculating the volume of a rectangular box?

    <p>To determine the amount of space inside the box</p> Signup and view all the answers

    Why is it important to consider the level of precision when recording measurements or estimations?

    <p>To ensure accuracy in the calculations</p> Signup and view all the answers

    What is the purpose of a bar scale on a map?

    <p>To show how many measured units are equal to actual distance</p> Signup and view all the answers

    What is the main difference between a number scale and a bar scale?

    <p>A number scale shows a specific relationship between the size of the area on the map and the actual size of that area</p> Signup and view all the answers

    What is the formula to calculate the actual distance from a map measurement?

    <p>Actual distance = Map measurement × Scale factor</p> Signup and view all the answers

    What happens to a number scale if the size of the map is changed?

    <p>The number scale becomes invalid and a new number scale must be determined</p> Signup and view all the answers

    Why is it only possible to estimate distances on a map using a scale and not to determine distances accurately?

    <p>Because many factors can affect the accuracy of a distance calculation on a map</p> Signup and view all the answers

    What is the purpose of using a scale on a map?

    <p>To estimate traveling distances when a distance table or distance markers are not provided</p> Signup and view all the answers

    What is the advantage of a bar scale over a number scale?

    <p>A bar scale remains accurate even if the size of the map is changed</p> Signup and view all the answers

    What is the formula to calculate the map measurement from an actual distance?

    <p>Map measurement = Actual distance / Scale factor</p> Signup and view all the answers

    What type of scale is expressed in the format 1:50,000?

    <p>Number scale</p> Signup and view all the answers

    What is the primary purpose of using a map measurement and a scale?

    <p>To estimate traveling distances when a distance table or distance markers are not provided</p> Signup and view all the answers

    What is the characteristic of a constant ratio relationship graph?

    <p>A curve that becomes steeper at an increasing rate</p> Signup and view all the answers

    Which type of relationship is characterized by a graph with a flat portion and an increasing portion?

    <p>Combination relationship</p> Signup and view all the answers

    What is the purpose of drawing graphs in unfamiliar situations?

    <p>To make sense of the situation and reveal patterns and trends</p> Signup and view all the answers

    What is the characteristic of a step-function relationship graph?

    <p>A series of steps</p> Signup and view all the answers

    What is the purpose of recognizing and understanding the implications of constant ratio relationships, combination relationships, and step-function relationships?

    <p>To develop skills and competencies in graph drawing and interpretation</p> Signup and view all the answers

    What is the characteristic of a combination relationship graph?

    <p>A combination of different portions</p> Signup and view all the answers

    What is the purpose of interpreting and analyzing the meaning of different portions of a graph?

    <p>To understand the context and implications of the graph</p> Signup and view all the answers

    What is the characteristic of an increasing portion in a graph?

    <p>Additional charges that increase linearly with usage</p> Signup and view all the answers

    What is the purpose of drawing graphs to represent various non-linear relationships?

    <p>To understand and analyze non-linear relationships</p> Signup and view all the answers

    What is the implication of a step-function relationship in a real-world situation?

    <p>Different fees or values are charged for different time intervals</p> Signup and view all the answers

    What is the primary purpose of using a floor plan?

    <p>To show the design and dimensions of the inside of a building or structure</p> Signup and view all the answers

    What is the function of an elevation plan?

    <p>To show the design and dimensions of the outside of a building or structure</p> Signup and view all the answers

    What is the purpose of a design drawing?

    <p>To show the design and layout of an item to be constructed or manufactured</p> Signup and view all the answers

    What is the key concept for describing features of a building or structure?

    <p>Describe features of a building or structure</p> Signup and view all the answers

    What is the purpose of using a scale to determine dimensions?

    <p>To accurately measure and determine the actual dimensions of features shown on the plan</p> Signup and view all the answers

    What is the formula for calculating plan measure from actual dimension?

    <p>Plan Measure = Actual Dimension ÷ Scale Factor</p> Signup and view all the answers

    What is the primary purpose of building 3D models from 2D plans?

    <p>To facilitate the movement between 2D and 3D representations of objects</p> Signup and view all the answers

    What is the process of creating a 2D net from a 3D object?

    <p>Drawing 2D plans or nets of 3D models</p> Signup and view all the answers

    What is the primary skill required when using a national road map?

    <p>Estimating traveling costs and times.</p> Signup and view all the answers

    What is the main difference between a national road map and a street map?

    <p>A street map shows more detailed information.</p> Signup and view all the answers

    What is the purpose of creating a 2D net?

    <p>To create a 3D object from a 2D net</p> Signup and view all the answers

    What is the process of creating a 3D object from a 2D net?

    <p>Cutting out the 2D net from the provided plans and folding along the indicated lines to form the edges and faces of the 3D object</p> Signup and view all the answers

    What is the purpose of using a scale on a map?

    <p>To estimate traveling distances when a distance table or distance markers are not provided.</p> Signup and view all the answers

    What is the formula to calculate the actual distance from a map measurement?

    <p>Actual distance = Map measurement × Scale factor</p> Signup and view all the answers

    What is the primary skill required when using a strip chart?

    <p>Determining more accurate traveling distances on specific sections of a route.</p> Signup and view all the answers

    What is the main difference between a national road map and a housing complex map?

    <p>A housing complex map shows more detailed information.</p> Signup and view all the answers

    What is the purpose of using distance tables or distance markers on a map?

    <p>To estimate traveling distances when a scale is not provided.</p> Signup and view all the answers

    What is the primary skill required when using a street map?

    <p>Following and providing directions using street names and directional indicators.</p> Signup and view all the answers

    What is the first step in converting a weight from grams to milliliters?

    <p>Identify the weight in grams</p> Signup and view all the answers

    What is the formula to calculate the total liters of paint needed?

    <p>Paint Needed (liters) = Surface Area (m²) / Spread Rate (m²/liter)</p> Signup and view all the answers

    What is the step to convert minutes to seconds?

    <p>Multiply the number of minutes by 60</p> Signup and view all the answers

    What is the step to convert hours to seconds?

    <p>Multiply the number of hours by 3600</p> Signup and view all the answers

    What is the purpose of breaking down time values into hours, minutes, and seconds?

    <p>To find the difference between two time values</p> Signup and view all the answers

    What is the first step in using a timetable?

    <p>Identify the week of the event</p> Signup and view all the answers

    What is the purpose of converting time values to a single unit?

    <p>To perform calculations involving time values</p> Signup and view all the answers

    What is the formula to calculate the total seconds from hours, minutes, and seconds?

    <p>Total Seconds = (Hours × 3600) + (Minutes × 60) + Seconds</p> Signup and view all the answers

    What is the purpose of double-checking calculations when performing conversions?

    <p>To ensure accuracy</p> Signup and view all the answers

    What is the purpose of understanding the context in which conversions are being performed?

    <p>To use the correct conversion factor</p> Signup and view all the answers

    What is the significance of the point of intersection on a graph?

    <p>It indicates where the cost of electricity on two different systems is the same.</p> Signup and view all the answers

    What is the first step in estimating the point of intersection from a graph?

    <p>Identify the two graphs.</p> Signup and view all the answers

    What is the purpose of the trial and improvement method?

    <p>To estimate the point of intersection.</p> Signup and view all the answers

    What is the primary purpose of estimating the quantities of materials needed for the assembly?

    <p>To calculate the total cost of the assembly</p> Signup and view all the answers

    What is the conversion factor to convert weight from kilograms to pounds?

    <p>2.206</p> Signup and view all the answers

    What is the main characteristic of a constant ratio relationship?

    <p>A graph that becomes steeper at an increasing rate</p> Signup and view all the answers

    What is the formula to convert temperature from Celsius to Fahrenheit?

    <p>°F = (1.8 × °C) + 32</p> Signup and view all the answers

    What is the key concept in understanding instructions in assembly?

    <p>Identifying all parts and components needed</p> Signup and view all the answers

    What is the purpose of two-way tables in probability calculations?

    <p>To compare two different variables</p> Signup and view all the answers

    What is the purpose of regularly checking the assembled parts against the instructions or plans?

    <p>To make adjustments as needed to correct any mistakes or misalignments</p> Signup and view all the answers

    What is the importance of understanding intersection points in graph analysis?

    <p>It helps in identifying the regions where different systems yield the same results.</p> Signup and view all the answers

    What is the purpose of drawing graphs in unfamiliar situations?

    <p>To make sense of the situation and reveal patterns and trends.</p> Signup and view all the answers

    What is the main limitation of probability values?

    <p>They do not guarantee outcomes</p> Signup and view all the answers

    What is the formula used to calculate the probability of a simple event?

    <p>P(event) = number of ways in which an event can happen / total number of possible outcomes</p> Signup and view all the answers

    What is the formula for calculating the probability of a simple event?

    <p>P(event) = number of ways in which an event can happen / total number of possible outcomes</p> Signup and view all the answers

    What is the purpose of using mathematical tools and techniques in assembly?

    <p>To measure and cut materials accurately</p> Signup and view all the answers

    What is the result of using the trial and improvement method to determine the point of intersection?

    <p>A pair of values that produce the same result in both equations.</p> Signup and view all the answers

    What is the main difference between simple and compound events?

    <p>Simple events involve a single trial, while compound events involve multiple trials</p> Signup and view all the answers

    What is the primary purpose of drawing 2D plans or nets?

    <p>To visualize how the model can be unfolded into a flat layout</p> Signup and view all the answers

    What is the purpose of conversions in measurements?

    <p>To switch between different units of measurement.</p> Signup and view all the answers

    What is the importance of following the assembly steps in the correct sequence?

    <p>To ensure that the components fit together properly</p> Signup and view all the answers

    What is the characteristic of non-joined segments in graph analysis?

    <p>They have a completely different fee structure.</p> Signup and view all the answers

    What is the purpose of tree diagrams in probability calculations?

    <p>To list all possible outcomes of events</p> Signup and view all the answers

    What is the original form of probability value resulting from the calculation?

    <p>Fraction format</p> Signup and view all the answers

    What is the purpose of calculating the time required for each step of the assembly process?

    <p>To schedule the assembly process efficiently</p> Signup and view all the answers

    What is the main application of probability values in advertisements?

    <p>To make predictions about future events</p> Signup and view all the answers

    What is the primary purpose of interpreting instructions in assembly?

    <p>To identify all components and tools required</p> Signup and view all the answers

    What is the percentage format of probability values obtained by?

    <p>Multiplying the fraction by 100</p> Signup and view all the answers

    What is the importance of measuring materials accurately in assembly?

    <p>To ensure that the components fit together properly</p> Signup and view all the answers

    What is the main difference between a flat portion and an increasing portion in a graph?

    <p>A flat portion represents a fixed fee, while an increasing portion represents a variable fee</p> Signup and view all the answers

    What is the unit of measurement for the surface area of a 3-dimensional object?

    <p>square units</p> Signup and view all the answers

    What is the formula to calculate the surface area of a rectangular box?

    <p>SA = 2lw + 2lh + 2wh</p> Signup and view all the answers

    What is the purpose of converting between units in surface area and volume calculations?

    <p>To convert between different units of measurement</p> Signup and view all the answers

    What is the conversion ratio between cubic meters and liters?

    <p>1 cubic meter = 1000 liters</p> Signup and view all the answers

    What is the formula to calculate the volume of a cylindrical container?

    <p>V = πr^2h</p> Signup and view all the answers

    Why is it important to understand that 1m^2 is not equal to 100cm^2?

    <p>Because the conversion ratio is different for square units</p> Signup and view all the answers

    What is the purpose of calculating the surface area of an object?

    <p>To solve problems or make decisions in real-world contexts</p> Signup and view all the answers

    What is the formula to calculate the volume of a rectangular box?

    <p>V = lwh</p> Signup and view all the answers

    What is the conversion ratio between cubic centimeters and milliliters?

    <p>1 cubic centimeter = 1 milliliter</p> Signup and view all the answers

    What is the purpose of calculating the volume of an object?

    <p>To solve problems or make decisions in real-world contexts</p> Signup and view all the answers

    What is the formula to convert minutes to seconds?

    <p>Seconds = Minutes × 60</p> Signup and view all the answers

    What is the purpose of using formulas for time conversions?

    <p>To convert between different units of time</p> Signup and view all the answers

    What is the formula to convert hours to seconds?

    <p>Seconds = Hours × 3600</p> Signup and view all the answers

    What is the purpose of measuring time in different units?

    <p>To understand the concept of time in different contexts</p> Signup and view all the answers

    What is the formula to convert seconds to hours?

    <p>Hours = Seconds ÷ 3600</p> Signup and view all the answers

    What is the purpose of calculating time differences?

    <p>To determine the time elapsed between two events</p> Signup and view all the answers

    What is the formula to convert minutes to hours?

    <p>Hours = Minutes ÷ 60</p> Signup and view all the answers

    What is the purpose of understanding units of measurement?

    <p>To understand the concept of measurement in different contexts</p> Signup and view all the answers

    What is the purpose of measuring techniques?

    <p>To understand the concept of measurement in different contexts</p> Signup and view all the answers

    What is the purpose of estimation techniques?

    <p>To make reasonable estimates of quantities when exact measurement is not possible</p> Signup and view all the answers

    What is the primary purpose of using tree diagrams in probability calculations?

    <p>To list all possible outcomes and determine their probabilities</p> Signup and view all the answers

    What is the main difference between simple and compound events?

    <p>Simple events involve a single occurrence, while compound events involve multiple occurrences</p> Signup and view all the answers

    What is the purpose of converting probability values to percentage format?

    <p>To make it easier to interpret probabilities</p> Signup and view all the answers

    What is the main limitation of probability values?

    <p>They do not guarantee the outcome of an event</p> Signup and view all the answers

    What is the purpose of using two-way tables in probability calculations?

    <p>To compare two different variables</p> Signup and view all the answers

    What is the original form of probability value resulting from the calculation?

    <p>Fraction format</p> Signup and view all the answers

    What is the purpose of observing past trends to predict future events?

    <p>To determine the likelihood of an event occurring</p> Signup and view all the answers

    What is the main application of probability values in advertisements?

    <p>To determine the likelihood of an event occurring based on historical data</p> Signup and view all the answers

    What is the formula for calculating the probability of a simple event?

    <p>P(event) = number of ways in which an event can happen / total number of possible outcomes</p> Signup and view all the answers

    What is the purpose of understanding the distinction between simple and compound events?

    <p>To accurately determine and interpret probability values</p> Signup and view all the answers

    What is the primary purpose of using a national road map?

    <p>To plan stopping points for accommodation, breaks, or refuelling</p> Signup and view all the answers

    What is the formula to calculate the actual distance from a map measurement when given a scale of 1:50,000?

    <p>Actual distance = Map measurement × Scale factor</p> Signup and view all the answers

    What skill is most important when working with a housing complex map?

    <p>Working with a map that shows a small area with limited detail</p> Signup and view all the answers

    What is the purpose of using a strip chart?

    <p>To determine more accurate traveling distances on specific routes</p> Signup and view all the answers

    What is the advantage of using a scale on a map?

    <p>It allows for the calculation of actual distances from map measurements</p> Signup and view all the answers

    What type of scale is used on a national road map?

    <p>Bar scale</p> Signup and view all the answers

    What is the primary purpose of using a street map?

    <p>To follow and provide directions using street names and directional indicators</p> Signup and view all the answers

    What is the formula to convert an actual distance to a map measurement when given a scale of 1:50,000?

    <p>Map measurement = Actual distance / Scale factor</p> Signup and view all the answers

    What is the primary reason why a number scale becomes invalid when the map is resized?

    <p>The relationship between the map size and actual size changes</p> Signup and view all the answers

    If a map has a scale of 1:50,000, what is the actual distance represented by 5 cm on the map?

    <p>2,500 meters</p> Signup and view all the answers

    What is the main difference between a number scale and a bar scale?

    <p>A number scale shows the relationship between the map size and actual size, while a bar scale shows the relationship between measured length and actual distance</p> Signup and view all the answers

    If a map measurement is 3 cm and the scale is 1:25,000, what is the actual distance represented?

    <p>7,500 meters</p> Signup and view all the answers

    What is the purpose of using a scale on a map?

    <p>To estimate the distance between two points</p> Signup and view all the answers

    What is the advantage of a bar scale over a number scale?

    <p>A bar scale remains valid even if the map is resized</p> Signup and view all the answers

    If an actual distance is 10 km, what is the map measurement on a map with a scale of 1:50,000?

    <p>10 cm</p> Signup and view all the answers

    What is the main limitation of using a scale to determine distances on a map?

    <p>It can only estimate distances, not determine them accurately</p> Signup and view all the answers

    What is the primary purpose of using tree diagrams in compound events?

    <p>To list all possible outcomes and determine their probability values</p> Signup and view all the answers

    What is the formula to convert an actual distance to a map measurement?

    <p>Map measurement = Actual distance / Scale factor</p> Signup and view all the answers

    What is the main limitation of probability values in making predictions?

    <p>They do not guarantee the outcome of an event</p> Signup and view all the answers

    In what format are percentage probability values obtained?

    <p>By multiplying the fraction by 100</p> Signup and view all the answers

    What is the primary purpose of measuring materials accurately in the assembly process?

    <p>To ensure that the components fit together properly</p> Signup and view all the answers

    Why is it important to understand the concept of scales when using maps?

    <p>To plan routes and travels efficiently</p> Signup and view all the answers

    What is the main application of probability values in advertisements?

    <p>To determine insurance rates based on historical data</p> Signup and view all the answers

    What is the key concept in understanding probability values?

    <p>The probability value is a prediction, not a guarantee</p> Signup and view all the answers

    What is the primary purpose of two-way tables in compound events?

    <p>To compare two different variables and make predictions</p> Signup and view all the answers

    What is the purpose of regularly checking the assembled parts against the instructions or plans?

    <p>To make adjustments as necessary to correct any mistakes or misalignments</p> Signup and view all the answers

    What is the main difference between simple and compound events?

    <p>Simple events involve a single occurrence, while compound events involve more than one occurrence</p> Signup and view all the answers

    What is the purpose of estimating the time required for each step of the assembly process?

    <p>To allocate sufficient time for each step of the assembly process</p> Signup and view all the answers

    What is the primary purpose of using mathematical tools and techniques in assembly?

    <p>To ensure accuracy and precision in measuring and cutting materials</p> Signup and view all the answers

    What is the formula for calculating the probability of a simple event?

    <p>P(event) = number of ways in which an event can happen / total number of possible outcomes</p> Signup and view all the answers

    What is the primary purpose of using a 2D plan to construct a 3D object?

    <p>To facilitate the movement between 2D and 3D representations of the object</p> Signup and view all the answers

    What is the term used to describe the process of converting a 3D object into a 2D representation?

    <p>Netting</p> Signup and view all the answers

    What is the purpose of historical trends in probability calculations?

    <p>To predict future events based on past trends</p> Signup and view all the answers

    What is the purpose of interpreting instructions or plans in the assembly process?

    <p>To identify all components and tools required for the assembly</p> Signup and view all the answers

    What is the primary purpose of following the assembly steps in the correct sequence?

    <p>To ensure that the components fit together properly</p> Signup and view all the answers

    What is the purpose of using a scale to determine dimensions on a 2D plan?

    <p>To calculate the actual dimensions of the object's features</p> Signup and view all the answers

    What is the original form of probability value resulting from the calculation?

    <p>Fraction format</p> Signup and view all the answers

    What is the main characteristic of compound events?

    <p>They involve more than one occurrence or trial</p> Signup and view all the answers

    What is the key concept for describing features of a building or structure?

    <p>Identifying the different rooms and windows on the plan</p> Signup and view all the answers

    What is the purpose of calculating the probability of a simple event?

    <p>To determine the likelihood of an event occurring</p> Signup and view all the answers

    What is the purpose of creating a 2D net from a 3D object?

    <p>To facilitate the movement between 2D and 3D representations of the object</p> Signup and view all the answers

    What is the primary purpose of assembling the folds to create the final 3D model?

    <p>To ensure that the components fit together properly</p> Signup and view all the answers

    What is the purpose of drawing 2D plans or nets in the assembly process?

    <p>To visualize how the model can be unfolded into a flat layout</p> Signup and view all the answers

    What is the formula for calculating the plan measure from an actual dimension?

    <p>Plan Measure = Actual Dimension / Scale Factor</p> Signup and view all the answers

    What is the primary purpose of building 3D models from 2D plans?

    <p>To facilitate the movement between 2D and 3D representations of the object</p> Signup and view all the answers

    What is the purpose of using a scale on a 2D plan?

    <p>To calculate the actual dimensions of the object's features</p> Signup and view all the answers

    What is the key concept for describing the design of an item or object?

    <p>Describing the design plan of the item</p> Signup and view all the answers

    What is the purpose of using 2D plans to investigate various problems?

    <p>To involve calculations related to packaging, perimeter, area, and volume</p> Signup and view all the answers

    What is the primary reason why probability values are used in predicting outcomes?

    <p>To determine the likelihood of events</p> Signup and view all the answers

    Which of the following is a characteristic of compound events?

    <p>Involves multiple possible outcomes</p> Signup and view all the answers

    What is the purpose of using tree diagrams in probability calculations?

    <p>To list all possible outcomes and determine their probabilities</p> Signup and view all the answers

    What is the main difference between simple and compound events?

    <p>Simple events involve a single occurrence or trial, while compound events involve multiple possible outcomes</p> Signup and view all the answers

    What is the purpose of using two-way tables in probability calculations?

    <p>To compare two different variables and determine their probability values</p> Signup and view all the answers

    What is the main limitation of probability values?

    <p>They do not guarantee outcomes</p> Signup and view all the answers

    What is the surface area of a rectangular box with a length of 5cm, a width of 3cm, and a height of 2cm?

    <p>40cm²</p> Signup and view all the answers

    What is the purpose of converting probability values to percentage format?

    <p>To make it easier to compare with other probability values</p> Signup and view all the answers

    What is the volume of a cylinder with a radius of 4cm and a height of 10cm?

    <p>240π cm³</p> Signup and view all the answers

    If a cylindrical container has a volume of 1000 cm³, what is the equivalent volume in litres?

    <p>1 L</p> Signup and view all the answers

    What is the primary purpose of identifying the point of intersection when comparing the cost of electricity on different systems?

    <p>To identify the point where the cost of electricity on the two systems is the same</p> Signup and view all the answers

    What is the main application of probability values in advertisements?

    <p>To predict the likelihood of a consumer responding to an advertisement</p> Signup and view all the answers

    What is the main characteristic of a constant ratio relationship?

    <p>It is a graph that becomes steeper at an increasing rate</p> Signup and view all the answers

    What is the term used to describe the method of substituting different values into equations to find a pair of values that produce the same result in both equations?

    <p>Trial and Improvement Method</p> Signup and view all the answers

    What is the surface area of a cylinder with a radius of 2cm and a height of 6cm?

    <p>56π cm²</p> Signup and view all the answers

    What is the purpose of using graphs to represent relationships?

    <p>To visualize and understand patterns and relationships</p> Signup and view all the answers

    If a rectangular box has a surface area of 240 cm², and a length of 4cm, what is the width of the box?

    <p>3cm</p> Signup and view all the answers

    What is the conversion factor for converting weight from kilograms to pounds?

    <p>2.206</p> Signup and view all the answers

    What is the volume of a rectangular box with a length of 6cm, a width of 4cm, and a height of 3cm?

    <p>72 cm³</p> Signup and view all the answers

    What is the formula to convert temperature from Celsius to Fahrenheit?

    <p>°F = (1.8 × °C) + 32</p> Signup and view all the answers

    What is the purpose of understanding the intersection points and the regions around them?

    <p>To analyze and interpret data, providing insights into different systems or scenarios</p> Signup and view all the answers

    If 1 m³ can hold 1000 L, how many litres can 2000 cm³ hold?

    <p>20 L</p> Signup and view all the answers

    What is the importance of using conversion factors correctly in measurement conversions?

    <p>To ensure accurate conversions</p> Signup and view all the answers

    What is the surface area of a rectangular box with a length of 8cm, a width of 5cm, and a height of 3cm?

    <p>122 cm²</p> Signup and view all the answers

    What is the purpose of drawing graphs in unfamiliar situations?

    <p>To make sense of the situation and reveal patterns and trends</p> Signup and view all the answers

    What is the volume of a cylinder with a radius of 3cm and a height of 8cm?

    <p>192π cm³</p> Signup and view all the answers

    What is the term used to describe the process of finding the point where two graphs intersect by estimating the values from the graphs?

    <p>Estimation Method</p> Signup and view all the answers

    If a cylindrical container has a volume of 5000 cm³, what is the equivalent volume in litres?

    <p>5 L</p> Signup and view all the answers

    What is the purpose of converting between solid and liquid quantities in various contexts?

    <p>To facilitate conversions in contexts such as baking and construction</p> Signup and view all the answers

    What is the importance of understanding the relationships between different variables in a system?

    <p>To analyze and interpret data, providing insights into different systems or scenarios</p> Signup and view all the answers

    What is the purpose of converting minutes to seconds in a time conversion?

    <p>To convert to a single unit of measurement</p> Signup and view all the answers

    What is the formula to convert hours to seconds?

    <p>Seconds = Hours × 3600</p> Signup and view all the answers

    What type of relationship is characterized by a graph that is not a straight line but becomes steeper at an increasing rate?

    <p>Constant ratio relationship</p> Signup and view all the answers

    What is the purpose of measuring time using clocks and stopwatches?

    <p>To understand stopwatch values and other time recordings</p> Signup and view all the answers

    What is the term used to describe the different fees charged for different time intervals in a step-function relationship?

    <p>Steps</p> Signup and view all the answers

    What is the purpose of using significant figures in measurement and calculation?

    <p>To reflect the precision of the data</p> Signup and view all the answers

    What is the purpose of error analysis in measurement?

    <p>To understand and account for potential errors</p> Signup and view all the answers

    What is the purpose of drawing graphs in unfamiliar situations?

    <p>To make sense of the situation and reveal patterns and trends</p> Signup and view all the answers

    What is the purpose of scaling in maps, diagrams, and models?

    <p>To represent real-life objects or distances</p> Signup and view all the answers

    What type of relationship occurs when a value is increased by a factor and then this new increased value is again increased by the factor or percentage?

    <p>Constant ratio relationship</p> Signup and view all the answers

    What is the term used to describe a graph that is made up of a combination of different types of relationships?

    <p>Combination graph</p> Signup and view all the answers

    What is the purpose of perimeter, area, and volume calculations?

    <p>To apply formulas to calculate the perimeter, area, and volume of various shapes and objects</p> Signup and view all the answers

    What is the purpose of rate and proportion in measurement?

    <p>To solve problems involving speed, density, and other rate-based measures</p> Signup and view all the answers

    What type of relationship is characterized by a graph that looks like a series of steps?

    <p>Step-function relationship</p> Signup and view all the answers

    What is the purpose of recognizing and understanding the implications of different types of relationships?

    <p>To make sense of the situation and reveal patterns and trends</p> Signup and view all the answers

    What is the purpose of choosing the appropriate tool or method in measurement?

    <p>To select the right tool or method based on the quantity to be measured</p> Signup and view all the answers

    What is the purpose of identifying the quantity to be measured or estimated?

    <p>To determine what needs to be measured or estimated</p> Signup and view all the answers

    What is the term used to describe a fixed fee that does not change with usage?

    <p>Flat portion</p> Signup and view all the answers

    What type of relationship occurs when different fees or values are charged for different time intervals, but within each interval, the same fee applies regardless of the exact value within that interval?

    <p>Step-function relationship</p> Signup and view all the answers

    What is the purpose of drawing graphs to represent various non-linear relationships?

    <p>To make sense of the situation and reveal patterns and trends</p> Signup and view all the answers

    What is the conversion factor to convert cm³ to milliliters?

    <p>1</p> Signup and view all the answers

    What is the formula to calculate the total liters of paint needed?

    <p>Paint Needed (liters) = Surface Area (m²) / Spread Rate (m²/liter)</p> Signup and view all the answers

    What is the step to convert minutes to seconds?

    <p>Multiply the number of minutes by 60</p> Signup and view all the answers

    What is the formula to calculate the total hours from hours, minutes, and seconds?

    <p>Total Hours = Hours + (Minutes / 60) + (Seconds / 3600)</p> Signup and view all the answers

    What is the purpose of identifying the week and dates of the events in a timetable?

    <p>To locate the specific week in which the event is scheduled</p> Signup and view all the answers

    What is the conversion factor to convert m³ to liters?

    <p>1000</p> Signup and view all the answers

    What is the step to calculate the difference between two time values?

    <p>Subtract the smaller time value from the larger one</p> Signup and view all the answers

    What is the purpose of using the provided conversion factors?

    <p>To ensure accuracy in calculations</p> Signup and view all the answers

    What is the formula to convert hours to seconds?

    <p>Seconds = Hours × 3600</p> Signup and view all the answers

    What is the purpose of double-checking calculations when performing conversions?

    <p>To ensure accuracy</p> Signup and view all the answers

    Study Notes

    Maps, Plans, and Other Representations

    National Road Maps

    • Show major routes, roads, and distances between major cities and towns in South Africa
    • Skills required:
      • Deciding on the most appropriate route between destinations
      • Estimating traveling costs and times
      • Planning stopping points for accommodation, breaks, or refuelling
      • Using distance tables to determine distances

    Strip Charts

    • Show locations of towns, other roads, and points of interest on a specific route
    • Skills required:
      • Determining more accurate traveling distances on specific sections of a route
      • Deciding on appropriate stopping points for refuelling or breaks
      • Estimating traveling costs and times
      • Using distance markers and indicators on the chart

    Street Maps

    • Show positions and names of streets and other locations within a city
    • Skills required:
      • Identifying locations using symbols
      • Following and providing directions using street names and directional indicators (e.g., left, right)
      • Using a grid reference system with the street index to find specific streets

    Housing Complex Maps

    • Show positions of houses within a small housing complex
    • Skills required:
      • Working with a map that shows a small area with limited detail
      • Following and describing directions to a specific location within the complex

    Using Scales

    • Essential to use the given scale to estimate traveling distances when a distance table or distance markers are not provided
    • Two types of scale calculations:
      • Calculation Type 1: Map Measurement to Actual Distance
        • Measure a distance on a map
        • Use the given scale to convert this measurement to the actual distance
        • Formula: Actual distance = Map measurement × Scale factor
      • Calculation Type 2: Actual Distance to Map Measurement
        • Start with a known actual distance
        • Use the given scale to convert this actual distance to the map measurement
        • Formula: Map measurement = Actual distance ÷ Scale factor

    Types of Scales

    Number Scale

    • Expressed in the format 1:50,000
    • Shows the relationship between the size of the area on the map and the actual size of that area
    • Conversion is straightforward: enlarge or reduce by the scale factor

    Bar Scale

    • Shows the relationship between measured length and actual distance
    • Measuring with a ruler on the bar scale shows how many measured units are equal to actual distance
    • Different from a number scale in that it does not state how many times smaller the map is from the actual size

    Building Plans

    Key Concepts

    • Floor Plan: shows a 2-dimensional perspective of a building or structure as seen from above, without the roof
    • Elevation Plan: shows a 2-dimensional perspective of a building or structure as seen from the side
    • Design Drawing: shows the design, layout, and components of an item to be constructed or manufactured

    Key Concepts for Working with Plans

    • Describe features of a building/structure
    • Match features between plans
    • Understand compass directions
    • Use scale to determine dimensions

    Section 2: Design Drawings

    • Describe the item/object shown on the design plan
    • Identify the dimensions of the item/object
    • Describe the different component parts required to make the item/object
    • If necessary, identify a cutting list of parts needed to make the item/object

    Section 3: Drawing Scaled Plans

    • Calculate plan measure from actual dimension
    • Scale calculation: when converting from an actual dimension to a plan measure, use the given scale to reduce the actual measurement proportionately
    • Formula: Plan Measure = Actual Dimension ÷ Scale Factor

    Section 4: Models

    • Build 3D models from 2D plans/nets
    • Draw 2D plans/nets of 3D models
    • Use models to investigate various problems
    • Purpose: to facilitate the movement between 2D and 3D representations of objects
    • Process:
      • Understanding 2D plans/nets
      • Building 3D models
      • Drawing 2D plans/nets

    Section 5: Assembling

    • Understand instructions
    • Gather materials and tools
    • Measure and cut materials
    • Estimate quantities and costs
    • Calculate time
    • Follow steps in sequence
    • Check and adjust
    • Use mathematical tools and techniques
    • Steps to assemble components:
      • Interpret instructions
      • Prepare materials and tools
      • Measure accurately
      • Cut materials as needed
      • Estimate quantities and costs
      • Estimate time
      • Follow the sequence
      • Check and adjust
      • Complete the assembly### Probability in Predictions
    • Historical trends: probability values are determined by observing past trends to predict future events
    • Advertisements: examples of probability in practice, such as car insurance rates based on historical accident data
    • Uncertainty in prediction: probability values do not guarantee outcomes

    Patterns and Relationships

    • Constant ratio relationship: a value increases by a factor, and then this new value is increased by the same factor, and so on
      • Characterized by a graph that is not a straight line, but becomes steeper at an increasing rate
      • Example: monthly cost of food purchases increasing at a rate of 7.4% per year
    • Combination of relationships: graphs can be made up of different types of relationships
      • Example: cost of making calls on a cell phone contract with a flat portion and an increasing portion
    • Step-function relationships: different fees or values are charged for different time intervals
      • Example: parking fees at a supermarket
      • Characterized by a graph that looks like a series of steps

    Working with 2 Relationships

    • Point of intersection: where two graphs intersect, and the values represented by the graphs are exactly equal
    • Estimating points of intersection: a method to determine the values at which two relationships are equal
      • Identify the two graphs, locate the intersection point, read the horizontal and vertical values
    • Trial and improvement method: another method to determine the values at which two relationships are equal
      • Write the equations, substitute values, and refine estimates

    Measurements

    • Conversions: conversion factors are used to switch between different units of measurement
    • Converting weight: from kilograms to pounds, and from pounds to kilograms
    • Converting temperature: from Celsius to Fahrenheit, and from Fahrenheit to Celsius
    • Converting between solid and liquid quantities: using conversion factors specific to ingredients or materials
    • Converting from m² to liters to determine paint quantities: calculating the amount of paint needed based on the surface area and the spread rate of the paint

    Practical Tips for Performing Conversions

    • Always use the provided conversion factors
    • Convert units step-by-step
    • Double-check calculations
    • Understand the context

    Time

    • Interpreting time recording values: converting time values into a single unit, such as seconds
    • Performing calculations involving time recording values: calculating the difference between two time values
    • Designing and making sense of timetables: identifying the week, date, and time of an event, and the venue

    Formulas Summary

    • Time conversions: converting minutes to seconds, hours to seconds, minutes to hours, and seconds to hours
    • Calculating time differences: converting to a single unit, subtracting the values, and converting back to the desired time format

    Practical Application

    • Interpreting time: converting and understanding stopwatch values and other time recordings
    • Calculating differences in time: determining the time elapsed between events accurately
    • Using timetables: extracting key information to plan and organize activities effectively

    Measuring and Estimating

    • Understanding units of measurement: standard units, conversion of units, and measurement techniques
    • Measuring techniques: measuring length, area, and volume, and measuring mass and weight
    • Estimation techniques: rounding and approximating, estimating quantities, and using benchmarks
    • Application of measurement in real-life contexts: scaling, perimeter, area, and volume calculations, and rate and proportion
    • Accuracy and precision: using significant figures, and error analysis

    Steps to Measure and Estimate

    • Identify the quantity to be measured or estimated
    • Choose the appropriate tool or method
    • Perform the measurement or estimation
    • Convert units if necessary
    • Record the measurement or estimation
    • Analyze and apply the results

    Calculate

    • Surface area: the total area of all the surfaces of a 3-dimensional object

      • Formulae: surface area of a rectangular box, and surface area of a cylinder
      • Appropriate units: square units such as mm², cm², or m²

    • Volume: the amount of space inside a hollow 3-dimensional object, or the amount of space that a solid 3-dimensional object takes up

      • Formulae: general formula for volume of a rectangular-based container, volume of a rectangular box, and volume of a cylindrical container
      • Appropriate units: cubic units such as mm³, cm³, or m³

    • Conversion between units: often necessary when performing surface area and volume calculations### Converting between Units for Surface Area and Volume

    • When painting a wall, paint is sold in liters, not in square units, so a conversion method is needed to convert from square units to liters.

    Volume Conversion Ratios

    • 1 cubic meter (m³) can hold 1000 liters (L) of water.
    • 1 cubic centimeter (cm³) equals 1 milliliter (mL) of water.

    Important Conversion Considerations

    • Even though 1 meter (m) equals 100 centimeters (cm), this does not mean that 1 square meter (m²) equals 100 square centimeters (cm²) or that 1 cubic meter (m³) equals 100 cubic centimeters (cm³).
    • Converting between units involves multiplying or dividing by the correct conversion factor: for example, 1 m³ = 1,000,000 cm³.
    • Similarly, converting between units involves multiplying or dividing by the correct conversion factor: for example, 1 cm² = 100 mm².

    Maps, Plans, and Other Representations

    National Road Maps

    • Show major routes, roads, and distances between major cities and towns in South Africa
    • Skills required:
      • Deciding on the most appropriate route between destinations
      • Estimating traveling costs and times
      • Planning stopping points for accommodation, breaks, or refuelling
      • Using distance tables to determine distances

    Strip Charts

    • Show locations of towns, other roads, and points of interest on a specific route
    • Skills required:
      • Determining more accurate traveling distances on specific sections of a route
      • Deciding on appropriate stopping points for refuelling or breaks
      • Estimating traveling costs and times
      • Using distance markers and indicators on the chart

    Street Maps

    • Show positions and names of streets and other locations within a city
    • Skills required:
      • Identifying locations using symbols
      • Following and providing directions using street names and directional indicators (e.g., left, right)
      • Using a grid reference system with the street index to find specific streets

    Housing Complex Maps

    • Show positions of houses within a small housing complex
    • Skills required:
      • Working with a map that shows a small area with limited detail
      • Following and describing directions to a specific location within the complex

    Using Scales

    • Essential to use the given scale to estimate traveling distances when a distance table or distance markers are not provided
    • Two types of scale calculations:
      • Calculation Type 1: Map Measurement to Actual Distance
        • Measure a distance on a map
        • Use the given scale to convert this measurement to the actual distance
        • Formula: Actual distance = Map measurement × Scale factor
      • Calculation Type 2: Actual Distance to Map Measurement
        • Start with a known actual distance
        • Use the given scale to convert this actual distance to the map measurement
        • Formula: Map measurement = Actual distance ÷ Scale factor

    Types of Scales

    Number Scale

    • Expressed in the format 1:50,000
    • Shows the relationship between the size of the area on the map and the actual size of that area
    • Conversion is straightforward: enlarge or reduce by the scale factor

    Bar Scale

    • Shows the relationship between measured length and actual distance
    • Measuring with a ruler on the bar scale shows how many measured units are equal to actual distance
    • Different from a number scale in that it does not state how many times smaller the map is from the actual size

    Building Plans

    Key Concepts

    • Floor Plan: shows a 2-dimensional perspective of a building or structure as seen from above, without the roof
    • Elevation Plan: shows a 2-dimensional perspective of a building or structure as seen from the side
    • Design Drawing: shows the design, layout, and components of an item to be constructed or manufactured

    Key Concepts for Working with Plans

    • Describe features of a building/structure
    • Match features between plans
    • Understand compass directions
    • Use scale to determine dimensions

    Section 2: Design Drawings

    • Describe the item/object shown on the design plan
    • Identify the dimensions of the item/object
    • Describe the different component parts required to make the item/object
    • If necessary, identify a cutting list of parts needed to make the item/object

    Section 3: Drawing Scaled Plans

    • Calculate plan measure from actual dimension
    • Scale calculation: when converting from an actual dimension to a plan measure, use the given scale to reduce the actual measurement proportionately
    • Formula: Plan Measure = Actual Dimension ÷ Scale Factor

    Section 4: Models

    • Build 3D models from 2D plans/nets
    • Draw 2D plans/nets of 3D models
    • Use models to investigate various problems
    • Purpose: to facilitate the movement between 2D and 3D representations of objects
    • Process:
      • Understanding 2D plans/nets
      • Building 3D models
      • Drawing 2D plans/nets

    Section 5: Assembling

    • Understand instructions
    • Gather materials and tools
    • Measure and cut materials
    • Estimate quantities and costs
    • Calculate time
    • Follow steps in sequence
    • Check and adjust
    • Use mathematical tools and techniques
    • Steps to assemble components:
      • Interpret instructions
      • Prepare materials and tools
      • Measure accurately
      • Cut materials as needed
      • Estimate quantities and costs
      • Estimate time
      • Follow the sequence
      • Check and adjust
      • Complete the assembly### Probability in Predictions
    • Historical trends: probability values are determined by observing past trends to predict future events
    • Advertisements: examples of probability in practice, such as car insurance rates based on historical accident data
    • Uncertainty in prediction: probability values do not guarantee outcomes

    Patterns and Relationships

    • Constant ratio relationship: a value increases by a factor, and then this new value is increased by the same factor, and so on
      • Characterized by a graph that is not a straight line, but becomes steeper at an increasing rate
      • Example: monthly cost of food purchases increasing at a rate of 7.4% per year
    • Combination of relationships: graphs can be made up of different types of relationships
      • Example: cost of making calls on a cell phone contract with a flat portion and an increasing portion
    • Step-function relationships: different fees or values are charged for different time intervals
      • Example: parking fees at a supermarket
      • Characterized by a graph that looks like a series of steps

    Working with 2 Relationships

    • Point of intersection: where two graphs intersect, and the values represented by the graphs are exactly equal
    • Estimating points of intersection: a method to determine the values at which two relationships are equal
      • Identify the two graphs, locate the intersection point, read the horizontal and vertical values
    • Trial and improvement method: another method to determine the values at which two relationships are equal
      • Write the equations, substitute values, and refine estimates

    Measurements

    • Conversions: conversion factors are used to switch between different units of measurement
    • Converting weight: from kilograms to pounds, and from pounds to kilograms
    • Converting temperature: from Celsius to Fahrenheit, and from Fahrenheit to Celsius
    • Converting between solid and liquid quantities: using conversion factors specific to ingredients or materials
    • Converting from m² to liters to determine paint quantities: calculating the amount of paint needed based on the surface area and the spread rate of the paint

    Practical Tips for Performing Conversions

    • Always use the provided conversion factors
    • Convert units step-by-step
    • Double-check calculations
    • Understand the context

    Time

    • Interpreting time recording values: converting time values into a single unit, such as seconds
    • Performing calculations involving time recording values: calculating the difference between two time values
    • Designing and making sense of timetables: identifying the week, date, and time of an event, and the venue

    Formulas Summary

    • Time conversions: converting minutes to seconds, hours to seconds, minutes to hours, and seconds to hours
    • Calculating time differences: converting to a single unit, subtracting the values, and converting back to the desired time format

    Practical Application

    • Interpreting time: converting and understanding stopwatch values and other time recordings
    • Calculating differences in time: determining the time elapsed between events accurately
    • Using timetables: extracting key information to plan and organize activities effectively

    Measuring and Estimating

    • Understanding units of measurement: standard units, conversion of units, and measurement techniques
    • Measuring techniques: measuring length, area, and volume, and measuring mass and weight
    • Estimation techniques: rounding and approximating, estimating quantities, and using benchmarks
    • Application of measurement in real-life contexts: scaling, perimeter, area, and volume calculations, and rate and proportion
    • Accuracy and precision: using significant figures, and error analysis

    Steps to Measure and Estimate

    • Identify the quantity to be measured or estimated
    • Choose the appropriate tool or method
    • Perform the measurement or estimation
    • Convert units if necessary
    • Record the measurement or estimation
    • Analyze and apply the results

    Calculate

    • Surface area: the total area of all the surfaces of a 3-dimensional object

      • Formulae: surface area of a rectangular box, and surface area of a cylinder
      • Appropriate units: square units such as mm², cm², or m²

    • Volume: the amount of space inside a hollow 3-dimensional object, or the amount of space that a solid 3-dimensional object takes up

      • Formulae: general formula for volume of a rectangular-based container, volume of a rectangular box, and volume of a cylindrical container
      • Appropriate units: cubic units such as mm³, cm³, or m³

    • Conversion between units: often necessary when performing surface area and volume calculations### Converting between Units for Surface Area and Volume

    • When painting a wall, paint is sold in liters, not in square units, so a conversion method is needed to convert from square units to liters.

    Volume Conversion Ratios

    • 1 cubic meter (m³) can hold 1000 liters (L) of water.
    • 1 cubic centimeter (cm³) equals 1 milliliter (mL) of water.

    Important Conversion Considerations

    • Even though 1 meter (m) equals 100 centimeters (cm), this does not mean that 1 square meter (m²) equals 100 square centimeters (cm²) or that 1 cubic meter (m³) equals 100 cubic centimeters (cm³).
    • Converting between units involves multiplying or dividing by the correct conversion factor: for example, 1 m³ = 1,000,000 cm³.
    • Similarly, converting between units involves multiplying or dividing by the correct conversion factor: for example, 1 cm² = 100 mm².

    Maps, Plans, and Other Representations

    National Road Maps

    • Show major routes, roads, and distances between major cities and towns in South Africa
    • Skills required:
      • Deciding on the most appropriate route between destinations
      • Estimating traveling costs and times
      • Planning stopping points for accommodation, breaks, or refuelling
      • Using distance tables to determine distances

    Strip Charts

    • Show locations of towns, other roads, and points of interest on a specific route
    • Skills required:
      • Determining more accurate traveling distances on specific sections of a route
      • Deciding on appropriate stopping points for refuelling or breaks
      • Estimating traveling costs and times
      • Using distance markers and indicators on the chart

    Street Maps

    • Show positions and names of streets and other locations within a city
    • Skills required:
      • Identifying locations using symbols
      • Following and providing directions using street names and directional indicators (e.g., left, right)
      • Using a grid reference system with the street index to find specific streets

    Housing Complex Maps

    • Show positions of houses within a small housing complex
    • Skills required:
      • Working with a map that shows a small area with limited detail
      • Following and describing directions to a specific location within the complex

    Using Scales

    • Essential to use the given scale to estimate traveling distances when a distance table or distance markers are not provided
    • Two types of scale calculations:
      • Calculation Type 1: Map Measurement to Actual Distance
        • Measure a distance on a map
        • Use the given scale to convert this measurement to the actual distance
        • Formula: Actual distance = Map measurement × Scale factor
      • Calculation Type 2: Actual Distance to Map Measurement
        • Start with a known actual distance
        • Use the given scale to convert this actual distance to the map measurement
        • Formula: Map measurement = Actual distance ÷ Scale factor

    Types of Scales

    Number Scale

    • Expressed in the format 1:50,000
    • Shows the relationship between the size of the area on the map and the actual size of that area
    • Conversion is straightforward: enlarge or reduce by the scale factor

    Bar Scale

    • Shows the relationship between measured length and actual distance
    • Measuring with a ruler on the bar scale shows how many measured units are equal to actual distance
    • Different from a number scale in that it does not state how many times smaller the map is from the actual size

    Building Plans

    Key Concepts

    • Floor Plan: shows a 2-dimensional perspective of a building or structure as seen from above, without the roof
    • Elevation Plan: shows a 2-dimensional perspective of a building or structure as seen from the side
    • Design Drawing: shows the design, layout, and components of an item to be constructed or manufactured

    Key Concepts for Working with Plans

    • Describe features of a building/structure
    • Match features between plans
    • Understand compass directions
    • Use scale to determine dimensions

    Section 2: Design Drawings

    • Describe the item/object shown on the design plan
    • Identify the dimensions of the item/object
    • Describe the different component parts required to make the item/object
    • If necessary, identify a cutting list of parts needed to make the item/object

    Section 3: Drawing Scaled Plans

    • Calculate plan measure from actual dimension
    • Scale calculation: when converting from an actual dimension to a plan measure, use the given scale to reduce the actual measurement proportionately
    • Formula: Plan Measure = Actual Dimension ÷ Scale Factor

    Section 4: Models

    • Build 3D models from 2D plans/nets
    • Draw 2D plans/nets of 3D models
    • Use models to investigate various problems
    • Purpose: to facilitate the movement between 2D and 3D representations of objects
    • Process:
      • Understanding 2D plans/nets
      • Building 3D models
      • Drawing 2D plans/nets

    Section 5: Assembling

    • Understand instructions
    • Gather materials and tools
    • Measure and cut materials
    • Estimate quantities and costs
    • Calculate time
    • Follow steps in sequence
    • Check and adjust
    • Use mathematical tools and techniques
    • Steps to assemble components:
      • Interpret instructions
      • Prepare materials and tools
      • Measure accurately
      • Cut materials as needed
      • Estimate quantities and costs
      • Estimate time
      • Follow the sequence
      • Check and adjust
      • Complete the assembly### Probability in Predictions
    • Historical trends: probability values are determined by observing past trends to predict future events
    • Advertisements: examples of probability in practice, such as car insurance rates based on historical accident data
    • Uncertainty in prediction: probability values do not guarantee outcomes

    Patterns and Relationships

    • Constant ratio relationship: a value increases by a factor, and then this new value is increased by the same factor, and so on
      • Characterized by a graph that is not a straight line, but becomes steeper at an increasing rate
      • Example: monthly cost of food purchases increasing at a rate of 7.4% per year
    • Combination of relationships: graphs can be made up of different types of relationships
      • Example: cost of making calls on a cell phone contract with a flat portion and an increasing portion
    • Step-function relationships: different fees or values are charged for different time intervals
      • Example: parking fees at a supermarket
      • Characterized by a graph that looks like a series of steps

    Working with 2 Relationships

    • Point of intersection: where two graphs intersect, and the values represented by the graphs are exactly equal
    • Estimating points of intersection: a method to determine the values at which two relationships are equal
      • Identify the two graphs, locate the intersection point, read the horizontal and vertical values
    • Trial and improvement method: another method to determine the values at which two relationships are equal
      • Write the equations, substitute values, and refine estimates

    Measurements

    • Conversions: conversion factors are used to switch between different units of measurement
    • Converting weight: from kilograms to pounds, and from pounds to kilograms
    • Converting temperature: from Celsius to Fahrenheit, and from Fahrenheit to Celsius
    • Converting between solid and liquid quantities: using conversion factors specific to ingredients or materials
    • Converting from m² to liters to determine paint quantities: calculating the amount of paint needed based on the surface area and the spread rate of the paint

    Practical Tips for Performing Conversions

    • Always use the provided conversion factors
    • Convert units step-by-step
    • Double-check calculations
    • Understand the context

    Time

    • Interpreting time recording values: converting time values into a single unit, such as seconds
    • Performing calculations involving time recording values: calculating the difference between two time values
    • Designing and making sense of timetables: identifying the week, date, and time of an event, and the venue

    Formulas Summary

    • Time conversions: converting minutes to seconds, hours to seconds, minutes to hours, and seconds to hours
    • Calculating time differences: converting to a single unit, subtracting the values, and converting back to the desired time format

    Practical Application

    • Interpreting time: converting and understanding stopwatch values and other time recordings
    • Calculating differences in time: determining the time elapsed between events accurately
    • Using timetables: extracting key information to plan and organize activities effectively

    Measuring and Estimating

    • Understanding units of measurement: standard units, conversion of units, and measurement techniques
    • Measuring techniques: measuring length, area, and volume, and measuring mass and weight
    • Estimation techniques: rounding and approximating, estimating quantities, and using benchmarks
    • Application of measurement in real-life contexts: scaling, perimeter, area, and volume calculations, and rate and proportion
    • Accuracy and precision: using significant figures, and error analysis

    Steps to Measure and Estimate

    • Identify the quantity to be measured or estimated
    • Choose the appropriate tool or method
    • Perform the measurement or estimation
    • Convert units if necessary
    • Record the measurement or estimation
    • Analyze and apply the results

    Calculate

    • Surface area: the total area of all the surfaces of a 3-dimensional object

      • Formulae: surface area of a rectangular box, and surface area of a cylinder
      • Appropriate units: square units such as mm², cm², or m²

    • Volume: the amount of space inside a hollow 3-dimensional object, or the amount of space that a solid 3-dimensional object takes up

      • Formulae: general formula for volume of a rectangular-based container, volume of a rectangular box, and volume of a cylindrical container
      • Appropriate units: cubic units such as mm³, cm³, or m³

    • Conversion between units: often necessary when performing surface area and volume calculations### Converting between Units for Surface Area and Volume

    • When painting a wall, paint is sold in liters, not in square units, so a conversion method is needed to convert from square units to liters.

    Volume Conversion Ratios

    • 1 cubic meter (m³) can hold 1000 liters (L) of water.
    • 1 cubic centimeter (cm³) equals 1 milliliter (mL) of water.

    Important Conversion Considerations

    • Even though 1 meter (m) equals 100 centimeters (cm), this does not mean that 1 square meter (m²) equals 100 square centimeters (cm²) or that 1 cubic meter (m³) equals 100 cubic centimeters (cm³).
    • Converting between units involves multiplying or dividing by the correct conversion factor: for example, 1 m³ = 1,000,000 cm³.
    • Similarly, converting between units involves multiplying or dividing by the correct conversion factor: for example, 1 cm² = 100 mm².

    Maps, Plans, and Other Representations

    National Road Maps

    • Show major routes, roads, and distances between major cities and towns in South Africa
    • Skills required:
      • Deciding on the most appropriate route between destinations
      • Estimating traveling costs and times
      • Planning stopping points for accommodation, breaks, or refuelling
      • Using distance tables to determine distances

    Strip Charts

    • Show locations of towns, other roads, and points of interest on a specific route
    • Skills required:
      • Determining more accurate traveling distances on specific sections of a route
      • Deciding on appropriate stopping points for refuelling or breaks
      • Estimating traveling costs and times
      • Using distance markers and indicators on the chart

    Street Maps

    • Show positions and names of streets and other locations within a city
    • Skills required:
      • Identifying locations using symbols
      • Following and providing directions using street names and directional indicators (e.g., left, right)
      • Using a grid reference system with the street index to find specific streets

    Housing Complex Maps

    • Show positions of houses within a small housing complex
    • Skills required:
      • Working with a map that shows a small area with limited detail
      • Following and describing directions to a specific location within the complex

    Using Scales

    • Essential to use the given scale to estimate traveling distances when a distance table or distance markers are not provided
    • Two types of scale calculations:
      • Calculation Type 1: Map Measurement to Actual Distance
        • Measure a distance on a map
        • Use the given scale to convert this measurement to the actual distance
        • Formula: Actual distance = Map measurement × Scale factor
      • Calculation Type 2: Actual Distance to Map Measurement
        • Start with a known actual distance
        • Use the given scale to convert this actual distance to the map measurement
        • Formula: Map measurement = Actual distance ÷ Scale factor

    Types of Scales

    Number Scale

    • Expressed in the format 1:50,000
    • Shows the relationship between the size of the area on the map and the actual size of that area
    • Conversion is straightforward: enlarge or reduce by the scale factor

    Bar Scale

    • Shows the relationship between measured length and actual distance
    • Measuring with a ruler on the bar scale shows how many measured units are equal to actual distance
    • Different from a number scale in that it does not state how many times smaller the map is from the actual size

    Building Plans

    Key Concepts

    • Floor Plan: shows a 2-dimensional perspective of a building or structure as seen from above, without the roof
    • Elevation Plan: shows a 2-dimensional perspective of a building or structure as seen from the side
    • Design Drawing: shows the design, layout, and components of an item to be constructed or manufactured

    Key Concepts for Working with Plans

    • Describe features of a building/structure
    • Match features between plans
    • Understand compass directions
    • Use scale to determine dimensions

    Section 2: Design Drawings

    • Describe the item/object shown on the design plan
    • Identify the dimensions of the item/object
    • Describe the different component parts required to make the item/object
    • If necessary, identify a cutting list of parts needed to make the item/object

    Section 3: Drawing Scaled Plans

    • Calculate plan measure from actual dimension
    • Scale calculation: when converting from an actual dimension to a plan measure, use the given scale to reduce the actual measurement proportionately
    • Formula: Plan Measure = Actual Dimension ÷ Scale Factor

    Section 4: Models

    • Build 3D models from 2D plans/nets
    • Draw 2D plans/nets of 3D models
    • Use models to investigate various problems
    • Purpose: to facilitate the movement between 2D and 3D representations of objects
    • Process:
      • Understanding 2D plans/nets
      • Building 3D models
      • Drawing 2D plans/nets

    Section 5: Assembling

    • Understand instructions
    • Gather materials and tools
    • Measure and cut materials
    • Estimate quantities and costs
    • Calculate time
    • Follow steps in sequence
    • Check and adjust
    • Use mathematical tools and techniques
    • Steps to assemble components:
      • Interpret instructions
      • Prepare materials and tools
      • Measure accurately
      • Cut materials as needed
      • Estimate quantities and costs
      • Estimate time
      • Follow the sequence
      • Check and adjust
      • Complete the assembly### Probability in Predictions
    • Historical trends: probability values are determined by observing past trends to predict future events
    • Advertisements: examples of probability in practice, such as car insurance rates based on historical accident data
    • Uncertainty in prediction: probability values do not guarantee outcomes

    Patterns and Relationships

    • Constant ratio relationship: a value increases by a factor, and then this new value is increased by the same factor, and so on
      • Characterized by a graph that is not a straight line, but becomes steeper at an increasing rate
      • Example: monthly cost of food purchases increasing at a rate of 7.4% per year
    • Combination of relationships: graphs can be made up of different types of relationships
      • Example: cost of making calls on a cell phone contract with a flat portion and an increasing portion
    • Step-function relationships: different fees or values are charged for different time intervals
      • Example: parking fees at a supermarket
      • Characterized by a graph that looks like a series of steps

    Working with 2 Relationships

    • Point of intersection: where two graphs intersect, and the values represented by the graphs are exactly equal
    • Estimating points of intersection: a method to determine the values at which two relationships are equal
      • Identify the two graphs, locate the intersection point, read the horizontal and vertical values
    • Trial and improvement method: another method to determine the values at which two relationships are equal
      • Write the equations, substitute values, and refine estimates

    Measurements

    • Conversions: conversion factors are used to switch between different units of measurement
    • Converting weight: from kilograms to pounds, and from pounds to kilograms
    • Converting temperature: from Celsius to Fahrenheit, and from Fahrenheit to Celsius
    • Converting between solid and liquid quantities: using conversion factors specific to ingredients or materials
    • Converting from m² to liters to determine paint quantities: calculating the amount of paint needed based on the surface area and the spread rate of the paint

    Practical Tips for Performing Conversions

    • Always use the provided conversion factors
    • Convert units step-by-step
    • Double-check calculations
    • Understand the context

    Time

    • Interpreting time recording values: converting time values into a single unit, such as seconds
    • Performing calculations involving time recording values: calculating the difference between two time values
    • Designing and making sense of timetables: identifying the week, date, and time of an event, and the venue

    Formulas Summary

    • Time conversions: converting minutes to seconds, hours to seconds, minutes to hours, and seconds to hours
    • Calculating time differences: converting to a single unit, subtracting the values, and converting back to the desired time format

    Practical Application

    • Interpreting time: converting and understanding stopwatch values and other time recordings
    • Calculating differences in time: determining the time elapsed between events accurately
    • Using timetables: extracting key information to plan and organize activities effectively

    Measuring and Estimating

    • Understanding units of measurement: standard units, conversion of units, and measurement techniques
    • Measuring techniques: measuring length, area, and volume, and measuring mass and weight
    • Estimation techniques: rounding and approximating, estimating quantities, and using benchmarks
    • Application of measurement in real-life contexts: scaling, perimeter, area, and volume calculations, and rate and proportion
    • Accuracy and precision: using significant figures, and error analysis

    Steps to Measure and Estimate

    • Identify the quantity to be measured or estimated
    • Choose the appropriate tool or method
    • Perform the measurement or estimation
    • Convert units if necessary
    • Record the measurement or estimation
    • Analyze and apply the results

    Calculate

    • Surface area: the total area of all the surfaces of a 3-dimensional object

      • Formulae: surface area of a rectangular box, and surface area of a cylinder
      • Appropriate units: square units such as mm², cm², or m²

    • Volume: the amount of space inside a hollow 3-dimensional object, or the amount of space that a solid 3-dimensional object takes up

      • Formulae: general formula for volume of a rectangular-based container, volume of a rectangular box, and volume of a cylindrical container
      • Appropriate units: cubic units such as mm³, cm³, or m³

    • Conversion between units: often necessary when performing surface area and volume calculations### Converting between Units for Surface Area and Volume

    • When painting a wall, paint is sold in liters, not in square units, so a conversion method is needed to convert from square units to liters.

    Volume Conversion Ratios

    • 1 cubic meter (m³) can hold 1000 liters (L) of water.
    • 1 cubic centimeter (cm³) equals 1 milliliter (mL) of water.

    Important Conversion Considerations

    • Even though 1 meter (m) equals 100 centimeters (cm), this does not mean that 1 square meter (m²) equals 100 square centimeters (cm²) or that 1 cubic meter (m³) equals 100 cubic centimeters (cm³).
    • Converting between units involves multiplying or dividing by the correct conversion factor: for example, 1 m³ = 1,000,000 cm³.
    • Similarly, converting between units involves multiplying or dividing by the correct conversion factor: for example, 1 cm² = 100 mm².

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    Test your skills in reading and understanding national road maps and strip charts in South Africa. Learn to plan routes, estimate travel costs and times, and identify points of interest.

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