431 Questions
What is the main purpose of a national road map?
To show major routes, roads, and distances between major cities and towns
What is the primary use of a strip chart?
To determine more accurate traveling distances on specific sections of a route
What is the formula to convert a map measurement to an actual distance?
Actual distance = Map measurement × Scale factor
What is the purpose of a housing complex map?
To work with a map that shows a small area with limited detail
What is the main skill required when using a street map?
Identifying locations using symbols
What is the purpose of a distance table?
To determine distances between major cities and towns
What type of calculation is required when a distance table or distance markers are not provided on a map?
Calculation Type 1: Map Measurement to Actual Distance
What is the primary use of a scale on a map?
To convert map measurements to actual distances
What is the formula to convert an actual distance to a map measurement?
Map measurement = Actual distance ÷ Scale factor
What type of scale is expressed in the format 1:50,000?
Number scale
What is the purpose of a floor plan?
To show a 2-dimensional perspective of a building from above, without the roof
If a map has a scale of 1:50,000, how many times smaller is the map compared to the actual size?
50,000 times
What is the advantage of using a bar scale over a number scale?
Bar scales remain accurate even when the map is resized
What is the formula to convert a map measurement to an actual distance?
Actual distance = Map measurement × Scale factor
What type of scale shows the relationship between a measured length and an actual distance?
Bar scale
Why can't you determine distances accurately on a map using a scale?
Because many factors can affect the accuracy of a distance calculation
What happens to a number scale if the size of the map is changed?
The number scale becomes inaccurate
What is the purpose of a scale on a map?
To allow users to estimate traveling distances accurately
What is the primary purpose of an elevation plan?
To show the design and dimensions of the outside of a building or structure.
What is the purpose of a design drawing?
To see what a completed item will look like and the dimensions of its parts.
What is the formula to calculate the plan measure from an actual dimension?
Plan Measure = Actual Dimension ÷ Scale Factor
What is the purpose of a floor plan?
To show the design and dimensions of the inside of a building or structure.
What is a key concept for working with plans?
Describing features of a building or structure
What is a key concept for design drawings?
Describing the item or object shown on the design plan
What is the purpose of building 3D models from 2D plans/nets?
To facilitate the movement between 2D and 3D representations of objects
What is the primary purpose of the models section?
To facilitate the movement between 2D and 3D representations of objects
What is a key skill for Grade 11 learners in the models section?
Building 3D models from 2D plans/nets
What is the process of moving from a 2D drawing to constructing a 3D object?
Building 3D models
Which of the following formats is the original form resulting from the calculation of a probability value?
Fraction Format
What is the purpose of a two-way table in compound events?
To compare two different variables and determine probability values
What is the key concept in understanding probability values?
The probability value is a prediction, not a guarantee
Which of the following is an example of a simple event?
Weather forecasts
What is the purpose of a tree diagram in compound events?
To map out all possible outcomes of events
Which of the following is a characteristic of a compound event?
Involves more than one occurrence or trial
What is the result of multiplying a fraction by 100 in probability calculations?
Percentage format
Which of the following is an example of a compound event?
Car insurance rates for different genders and age groups
What is the purpose of observing historical trends in probability calculations?
To predict future events
What is the formula to calculate the probability of a simple event?
P(event) = number of ways in which an event can happen / total number of possible outcomes
What is a characteristic of a step-function relationship?
The graph has distinct steps indicating different fees for different time intervals.
What type of relationship is represented by a graph that becomes steeper at an increasing rate?
Constant ratio relationship
What is the purpose of drawing graphs in unfamiliar situations?
To make sense of the situation and reveal patterns and trends
What is an example of a combination of relationships?
A cell phone contract with a fixed monthly subscription fee and additional charges for call minutes beyond a certain threshold
What is the main difference between a step-function relationship and a constant ratio relationship?
The shape of the graph
What is represented by the flat portion of a graph?
A fixed fee that does not change with usage
What is an example of a constant ratio relationship?
A household's food purchases that increase at a rate of 7.4% per year
What is the importance of recognizing and understanding the implications of different relationships?
To make sense of real-world situations and reveal patterns and trends
What is the purpose of drawing a graph for a situation with an unknown formula or pattern?
To make sense of the situation and reveal patterns and trends
What is the characteristic of a graph that represents a combination of relationships?
The graph has a flat portion representing a fixed fee and an increasing portion representing additional charges
What is the primary purpose of identifying the point of intersection between two graphs?
To identify the point where the cost of electricity is the same
What is the benefit of using the trial and improvement method to find the point of intersection?
It allows for estimation of the point of intersection
What is the significance of understanding the intersection points and the regions around them?
It provides insights into where different systems or scenarios yield the same results
What is the conversion factor used to convert weight from kilograms to pounds?
2.206
What is the formula used to convert temperature from Celsius to Fahrenheit?
°F = (1.8 × °C) + 32
What is the purpose of using conversion factors in measurements?
To ensure accurate conversions between units
What is the benefit of drawing and interpreting graphs for unfamiliar situations?
It reveals patterns and trends that were not visible without the graph
What is the term used to describe the point where two graphs intersect?
Point of intersection
What is the purpose of using the method of trial and improvement to find the point of intersection?
To estimate the point of intersection
What is the significance of the point of intersection in the context of comparing the cost of electricity on different systems?
It indicates where the cost of electricity on the two systems is the same
What is the primary step in assembling a 3D model?
Understanding instructions and identifying all parts
Which of the following is NOT a key concept in assembling components?
Calculating the probability of an event
What is the primary limitation of probability values in prediction?
They do not guarantee outcomes.
What is the purpose of measuring materials accurately?
To ensure that materials fit together correctly
What is the formula to calculate the probability of a simple event?
P(event) = number of ways in which an event can happen / total number of possible outcomes
What is the primary difference between simple and compound events?
The complexity of the probability calculation.
What is the purpose of a tree diagram in probability calculations?
To visualize the possible outcomes of a compound event.
What is the primary purpose of estimating quantities and costs of materials?
To plan and budget for the assembly process
What is the result of not following the assembly steps in sequence?
The components may not fit together properly
What is the characteristic of a constant ratio relationship?
A graph that becomes steeper at an increasing rate.
What is the purpose of regularly checking the assembled parts against the instructions or plans?
To ensure accuracy and make adjustments as needed
What is the advantage of using a two-way table in probability calculations?
It enables the conversion of actual values to percentage probability values.
What is the final step in assembling a 3D model?
Completing the assembly and double-checking all parts
What is the formula for calculating the probability of a simple event?
P(event) = number of ways in which an event can happen / total number of possible outcomes.
What is the primary application of probability values in advertisements?
To predict the likelihood of an event based on historical data.
What is the formula to convert weight from grams to milliliters?
Volume (ml) = (Weight (g) ÷ Conversion Factor) × Conversion Factor for Volume
What is the purpose of using mathematical tools and techniques in assembling components?
To measure and cut materials accurately
What is the relationship between the probability value and the number of possible outcomes?
The probability value decreases as the number of possible outcomes increases.
What is the result of not measuring materials accurately?
The components may not fit together properly
What is the first step in calculating the amount of paint needed?
Identify the surface area to be painted
What is the purpose of breaking down the conversion process into smaller steps?
To ensure accuracy in the conversion
What is the primary difference between a flat portion and an increasing portion in a graph?
The flat portion represents a fixed fee, while the increasing portion represents a variable rate.
What is the formula to convert hours to seconds?
Seconds = Hours × 3600
What is the first step in calculating the difference between two time values?
Convert both times into a single unit
What is the purpose of identifying the week and dates of the events on a timetable?
To identify the exact date and time of the event
What is the formula to convert minutes to seconds?
Seconds = Minutes × 60
What is the purpose of double-checking your calculations when performing conversions?
To ensure accuracy in the conversion
What is the formula to convert liters to milliliters?
Milliliters = Liters × 1000
What is the purpose of using the correct conversion factor when performing conversions?
To ensure accuracy in the conversion
What is the primary purpose of understanding time conversions?
To plan and organize activities effectively
What is the formula to convert minutes to hours?
Hours = Minutes / 60
What is the primary purpose of calculating time differences?
To find the time elapsed between events accurately
What is the formula to convert hours to seconds?
Seconds = Hours * 3600
What is the primary purpose of using timetables?
To extract key information to plan and organize activities effectively
What is the formula to convert seconds to hours?
Hours = Seconds / 3600
What is the primary purpose of understanding units of measurement?
To recognize and use standard units of measurement
What is the primary purpose of measuring techniques?
To use appropriate tools to measure length, area, and volume
What is the primary purpose of estimation techniques?
To make reasonable estimates of quantities when exact measurement is not possible
What is the primary purpose of accuracy and precision?
To use significant figures correctly in measurement and calculation
What is the surface area of a rectangular box with a length of 5 cm, width of 3 cm, and height of 2 cm?
62 cm^2
What is the volume of a cylindrical container with a radius of 4 cm and a height of 10 cm?
160π cm^3
If a paint can covers 5 m^2 of surface area, how many litres of paint are needed to cover a wall with a surface area of 20 m^2?
80 litres
What is the conversion factor to convert cubic centimetres to millilitres?
1 cm^3 = 1 ml
If a rectangular box has a length of 10 cm, width of 5 cm, and height of 2 cm, what is the volume of the box in cubic millimetres?
100000 mm^3
What is the surface area of a cylinder with a radius of 3 cm and a height of 6 cm?
90π cm^2
If a cylindrical container has a volume of 200 cm^3, what is the height of the container if the radius of the base is 2 cm?
5 cm
What is the conversion factor to convert cubic metres to litres?
1 m^3 = 1000 litres
If a rectangular box has a surface area of 120 cm^2, what is the length of the box if the width is 4 cm and the height is 2 cm?
6 cm
What is the volume of a rectangular box with a length of 6 cm, width of 4 cm, and height of 3 cm in cubic millimetres?
72000 mm^3
What is the primary advantage of using a national road map over a strip chart?
It allows for the estimation of traveling costs and times over long distances.
When using a street map, what is the most effective way to identify a specific location?
Using a grid reference system with the street index.
What is the purpose of using a scale on a map?
To estimate traveling distances when a distance table or distance markers are not provided.
What is the primary skill required when using a housing complex map?
Working with a map that shows a small area with limited detail.
What is the correct formula for converting a map measurement to an actual distance?
Actual distance = Map measurement × Scale factor
When using a strip chart, what is the primary benefit of using distance markers and indicators?
It provides more accurate traveling distances on specific sections of a route.
What is the primary advantage of using a scale on a map over a distance table?
It can be used when a distance table or distance markers are not provided.
What is the primary purpose of using a street map over a national road map?
It provides more detailed information about a specific city or town.
What is the main purpose of a floor plan?
To show the interior layout and dimensions of a building
What is the function of an elevation plan?
To show the exterior design of a building
What is the purpose of a design drawing?
To show the design and dimensions of an item to be constructed or manufactured
What is the key concept for working with plans?
All of the above
What is the formula to calculate the plan measure from an actual dimension?
Plan Measure = Actual Dimension / Scale Factor
What is the primary purpose of the models section?
To facilitate the movement between 2D and 3D representations of objects
What is a key skill for Grade 11 learners in the models section?
All of the above
What is the process of moving from a 2D drawing to constructing a 3D object?
Cutting out the 2D net and folding along the indicated lines
What is a 2D net?
A flat layout that, when folded along specific lines, forms a 3D object
What is the main purpose of building 3D models from 2D plans/nets?
To construct a 3D object from a 2D net
What is the primary purpose of using probability values in predictions?
To understand historical trends and make informed decisions
Which of the following representations is used to list all possible outcomes of events and determine their probabilities?
Tree diagrams
What is the result of multiplying a decimal format probability value by 100?
Percentage format
What is the key concept in understanding probability values?
That they predict the likelihood of an event occurring
Which of the following is an example of a compound event?
Rolling a die twice
What is the purpose of using two-way tables in compound events?
To determine the probability values and make predictions
What is the primary purpose of drawing a 2D plan/net of a 3D model?
To visualize the model's faces and edges
What is the formula to calculate the probability of a simple event?
P(event) = number of ways in which an event can happen / total number of possible outcomes
Which of the following skills is essential when interpreting instructions for assembly?
Understanding the instructions and identifying all components and tools required
What is the purpose of observing historical trends in probability calculations?
To understand the past patterns and make informed decisions
What is the primary purpose of regularly checking the assembled parts against the instructions or plans?
To ensure accuracy and make adjustments as necessary
Which of the following is a characteristic of a compound event?
Involves more than one occurrence or trial
What is the formula used to calculate the probability of a simple event?
P(event) = number of ways in which an event can happen / total number of possible outcomes
What is the primary use of tree diagrams in compound events?
To list all possible outcomes of events and determine their probabilities
What is the primary purpose of using mathematical tools and techniques in the assembly process?
To measure and cut materials accurately
What is the primary purpose of estimating the quantities of materials needed for the assembly?
To ensure that all necessary materials are available before starting the assembly
What is the primary purpose of following the assembly steps in the correct sequence?
To ensure that the components fit together properly
What is the primary purpose of calculating the total time needed for the entire assembly?
To plan and schedule the assembly process effectively
What is the primary purpose of using probability values in real-life situations?
To predict the likelihood of an event occurring
What is the primary purpose of assembling the components in the correct sequence?
To ensure that the components fit together properly
What is the primary reason why distances calculated on a map using a scale are only estimates and not exact?
Many factors affect the accuracy of the distance calculation
What is the advantage of a bar scale over a number scale?
A bar scale remains valid even if the map is resized
What is the formula to convert a map measurement to an actual distance if the scale is 1:50,000?
Actual distance = Map measurement × 50,000
What is the purpose of a floor plan?
To show a 2-dimensional perspective of a building or structure as seen from above, without the roof
What is the relationship between the size of the area on the map and the actual size of that area according to a number scale of 1:50,000?
The map is 50,000 times smaller than the actual size
What is the primary purpose of using a scale on a map?
To estimate the distance between two points when a distance table or distance markers are not provided
What is the formula to convert an actual distance to a map measurement if the scale is 1:50,000?
Map measurement = Actual distance ÷ 50,000
What is the primary difference between a number scale and a bar scale?
A bar scale shows the relationship between measured length and actual distance
What happens to a number scale if the size of the map is changed?
The number scale becomes invalid
What is the purpose of using a scale to estimate distances on a map?
To estimate the distance between two points when a distance table or distance markers are not provided
What is a common way to express probability values in simple events?
In fraction, decimal, or percentage formats
What is the main purpose of using tree diagrams in compound events?
To list all possible outcomes and determine their probabilities
What is a characteristic of a compound event?
It involves more than one occurrence or trial
What is the result of multiplying a probability value in fraction format by 100?
A percentage value
What is the purpose of observing historical trends in probability calculations?
To predict the likelihood of future events
What is a characteristic of a graph that represents a constant ratio relationship?
It becomes steeper at an increasing rate
What is the purpose of drawing graphs in unfamiliar situations?
To identify the type of relationship
What is an example of a combination of relationships?
A graph that represents a constant ratio relationship and a flat portion
What is the main difference between a step-function relationship and a constant ratio relationship?
A step-function relationship has a flat portion, while a constant ratio relationship does not
What is the importance of recognizing and understanding the implications of different relationships?
It helps in making predictions and informed decisions
What is the purpose of converting hours to seconds in a time conversion?
To determine the time elapsed between events
Which of the following formulas is used to convert minutes to seconds?
Seconds = Minutes × 60
What is the purpose of measuring time in seconds?
To determine the time elapsed between events
Which of the following is a key concept in measuring time?
Understanding units of measurement
What is the purpose of using a stopwatch?
To measure time in seconds
Which of the following is a practical application of measuring time?
Extracting key information from timetables
What is the purpose of calculating the difference in time between two events?
To determine the time elapsed between events
Which of the following is a key concept in understanding time conversions?
Understanding standard units of measurement
What is the purpose of converting seconds to hours?
To understand time conversions
Which of the following is a practical application of time conversions?
Interpreting stopwatch values and other time recordings
What is the main purpose of drawing graphs for unfamiliar situations?
To make sense of the situation and reveal patterns and trends
What is the characteristic of a graph that represents a combination of relationships?
It has multiple points of intersection
What is the purpose of estimating the point of intersection from a graph?
To determine the values at which two relationships are equal
What is the importance of understanding intersection points?
It provides insights into where different systems or scenarios yield the same results
What is the trial and improvement method used for?
To determine the values at which two relationships are equal
What is the purpose of converting between solid and liquid quantities?
To make conversions in various contexts such as baking and construction
What is the formula to convert weight from kilograms to pounds?
Weight (pounds) = Weight (kg) × 2.206
What is the formula to convert temperature from Celsius to Fahrenheit?
°F = (1.8 × °C) + 32
What is the benefit of using the trial and improvement method?
It helps to determine the values at which two relationships are equal
What is represented by the values read from the horizontal and vertical axes at the point of intersection?
The quantity or unit and the corresponding amount
What is the characteristic of a graph that represents a constant ratio relationship?
The graph becomes steeper at an increasing rate
What is the purpose of drawing graphs in unfamiliar situations?
To make sense of the situation and reveal patterns and trends
What is an example of a combination of relationships?
The cost of making calls on a particular cell phone contract
What is the main difference between a step-function relationship and a constant ratio relationship?
The type of relationship represented
What is represented by the increasing portion of a graph?
Additional charges that increase linearly with usage
What is the purpose of recognizing and understanding the implications of different relationships?
To apply the skills and competencies to real-world situations
What is the characteristic of a step-function relationship?
The graph looks like a series of steps
What is the importance of drawing graphs for situations with unknown formulas or patterns?
To make sense of the situation and reveal patterns and trends
What is an example of a constant ratio relationship?
The monthly cost of food purchases in a household increasing at a rate of 7.4% per year
What is the benefit of being able to draw and interpret graphs for any situation?
To make sense of unfamiliar situations and reveal patterns and trends
What is the formula to calculate the surface area of a rectangular box?
SA = 2lw + 2lh + 2wh
What is the formula to calculate the volume of a cylindrical container?
V = πr^2h
What is the conversion ratio between cubic meters and liters?
1 m^3 = 1000 L
What is the unit of measurement for surface area?
Square units
What is the process of converting from square units to liters called?
Conversion of units
What is the formula to calculate the volume of a rectangular box?
V = lwh
What is the formula to convert the weight in grams to volume in milliliters?
Volume (ml) = (Weight (g) / Conversion Factor) × Conversion Factor for Volume
What is the unit of measurement for volume?
Cubic units
What is the conversion ratio between cubic centimeters and milliliters?
1 cm^3 = 1 mL
What is the formula to calculate the total liters of paint needed?
Paint Needed (liters) = Surface Area (m²) / Spread Rate (m²/liter)
What happens when you convert from cubic meters to cubic centimeters?
The value increases by a factor of 1000
What is the step to convert time recording values to a single unit?
Multiply the number of minutes by 60 to get seconds
What is the purpose of breaking down the time values into hours, minutes, and seconds?
To find the difference between two time values
Why is it important to understand the conversion ratios between different units of measurement?
To ensure accuracy in calculations
What is the formula to convert minutes to seconds?
Seconds = Minutes × 60
What is the step to calculate the total hours from hours, minutes, and seconds?
Multiply the hours by 3600 and add the minutes and seconds
What is the purpose of identifying the week and dates of the events when using a timetable?
To locate the specific week in which the event is scheduled
What is the formula to convert hours to seconds?
Seconds = Hours × 3600
What is the step to calculate the difference between two time values?
Subtract the smaller time value from the larger one
What is the purpose of using a conversion factor when performing conversions?
To ensure accuracy
What is the primary purpose of understanding instructions in the assembly process?
To identify all parts and components needed for assembly
What is the main benefit of using mathematical tools and techniques in the assembly process?
To ensure accurate measurement and cutting of materials
What is the primary purpose of estimating quantities and costs in the assembly process?
To calculate the total cost of materials
What is the main benefit of following the sequence of assembly steps?
To ensure that the components fit together properly
What is the primary skill required when using a national road map to plan a trip?
Deciding on the most appropriate route
What is the primary purpose of checking and adjusting during the assembly process?
To correct any mistakes or misalignments
A strip chart is used to determine the distance between two towns on a specific route. If the distance measured on the chart is 5 cm, and the scale is 1:500,000, what is the actual distance?
25 km
When using a street map, what is the primary purpose of a grid reference system?
To find specific streets using the street index
What is the formula to calculate the probability of a simple event?
P(event) = number of ways in which an event can happen / total number of possible outcomes
What is the characteristic of a simple event in probability?
It involves a single occurrence or trial
A housing complex map shows the positions of houses within a small area. What is the primary skill required when working with this type of map?
Working with a map that shows a small area with limited detail
What is the primary purpose of using mathematical tools and techniques in design drawings?
To ensure accuracy and precision in design drawings
What is the purpose of using a scale on a map?
To convert map measurements to actual distances
A map has a scale of 1:100,000. If the distance between two towns on the map is 8 cm, what is the actual distance?
80 km
What is the primary purpose of creating 3D models from 2D plans/nets?
To visualize and understand the structure of the design
What is the primary purpose of using probability values in everyday life?
To make predictions about the likelihood of an event occurring
What is the primary purpose of a distance table on a map?
To provide accurate distances between locations
What is the primary difference between Calculation Type 1 and Calculation Type 2 when using a scale on a map?
The direction of the calculation
What is the primary purpose of an elevation plan?
To show the design and dimensions of the outside of a building or structure
What is the key concept in working with plans that involves understanding terms like North, South, East, and West Elevation?
Understand compass directions
What is the main difference between a number scale and a bar scale on a map?
A number scale is a ratio of the map distance to the actual distance, while a bar scale is a visual representation of the ratio.
What is the formula to calculate the plan measure from an actual dimension?
Plan Measure = Actual Dimension ÷ Scale Factor
If a map has a scale of 1:50,000, what is the relationship between the map measurement and the actual distance?
The map measurement is 50,000 times smaller than the actual distance.
What is the primary purpose of building 3D models from 2D plans/nets?
To facilitate the movement between 2D and 3D representations of objects
What is the purpose of using a scale on a map?
To estimate the distance between two points on the map when a distance table or distance markers are not provided.
What is the primary reason for using tree diagrams in compound events?
To visualize and determine all possible outcomes of events
What is the result of multiplying a probability fraction by 100?
The percentage format of the probability value
What is the formula to convert a map measurement to an actual distance?
Actual distance = Map measurement x Scale factor
What is the key concept for design drawings that involves identifying the dimensions of the different components shown on the design plan?
Identify the dimensions of the different components shown on the design plan
What is the process of moving from a 3D model to creating 2D drawings/nets/plans of the model?
Drawing 2D plans/nets of 3D models
What is a characteristic of a compound event?
It involves more than one occurrence or trial
Why is it not possible to determine distances accurately on a map using a scale?
Because there are many factors that affect the accuracy of the distance calculation.
What is the purpose of observing historical trends in probability calculations?
To determine the probability value of a future event
What happens to a number scale if the size of the map is changed?
The number scale becomes invalid and a new number scale must be determined.
What is the key skill for Grade 11 learners in the models section?
All of the above
What is the primary purpose of using two-way tables in compound events?
To determine the probability value of an event and make predictions
What is the advantage of using a bar scale over a number scale?
A bar scale remains valid even if the size of the map is changed.
What is the primary purpose of the models section?
To facilitate the movement between 2D and 3D representations of objects
What is the key concept in understanding probability values?
That they are predictions, not guarantees
What is the purpose of a floor plan?
To show a 2-dimensional perspective of a building or structure as seen from above, without the roof.
What is the key concept for working with plans that involves identifying various elements like rooms, windows, and doors on the plan?
Describe features of a building or structure
What type of calculation is required when a distance table or distance markers are not provided on a map?
An estimation using a scale.
What is the key concept for design drawings that involves describing the different component parts required to make the item or object?
Describe the different component parts required to make the item or object
Which of the following is an example of a compound event?
A car insurance rate prediction
What is the formula to convert an actual distance to a map measurement?
Map measurement = Actual distance / Scale factor
What is the formula to calculate the probability of a simple event?
P(event) = number of ways in which an event can happen / total number of possible outcomes
What is the purpose of using decimals in probability calculations?
To derive a probability value from a fraction
Which of the following formats is the original form resulting from the calculation of a probability value?
Fraction format
What is the primary purpose of using probability values in predictions?
To understand the uncertainty involved in predicting the likelihood of events
Which of the following is a characteristic of a compound event?
Involves multiple possible outcomes
What is the result of converting a fraction to a percentage in probability calculations?
The probability value is multiplied by 100
What is the purpose of using historical trends in probability calculations?
To predict the likelihood of future events based on past trends
What is the characteristic of a graph that represents a constant ratio relationship?
The graph becomes steeper at an increasing rate
What is the purpose of using tree diagrams in compound events?
To visualize the possible outcomes of an event
What is the key concept in understanding probability values?
Probability values predict the likelihood of an event, but do not guarantee the outcome
What is the purpose of using two-way tables in compound events?
To determine the probability values of multiple variables
What is the characteristic of a graph that represents a combination of relationships?
The graph has multiple sections with different trends
What is the importance of recognizing and understanding the implications of different relationships?
It helps to make accurate predictions and informed decisions
What is the correct formula to convert weight in grams to volume in milliliters?
Volume (ml) = (Weight (g) / Conversion Factor) × Conversion Factor for Volume
What is the correct step to calculate the total liters of paint needed?
Divide the surface area by the spread rate of the paint
What is the purpose of breaking down the conversion process into smaller steps?
To ensure accuracy and avoid mistakes
What is the correct formula to convert time recording values from hours to seconds?
Seconds = Hours × 3600
What is the purpose of identifying the week and dates of the events in a timetable?
To locate the specific week in which the event is scheduled
What is the correct formula to calculate the total hours from time recording values?
Total Hours = Hours + (Minutes ÷ 60) + (Seconds ÷ 3600)
What is the purpose of double-checking your calculations when performing conversions?
To ensure accuracy and avoid mistakes
What is the primary purpose of checking the venue for an event?
To plan the activities of the event
What is the correct formula to convert from milliliters to liters?
Liters = Milliliters ÷ 1000
Which formula is used to convert hours to seconds?
Seconds = Hours × 3600
What is the purpose of converting to a single unit when calculating time differences?
To ensure accuracy in the calculation
What is the purpose of understanding the context of the conversion?
To use the right units and conversion factors
What is the correct formula to calculate the difference between two time values?
Time Difference = Larger Time Value - Smaller Time Value
What is the primary purpose of using a stopwatch in practical applications?
To measure time accurately
Which of the following is an example of a measurement technique?
Using a thermometer to measure temperature
What is the purpose of using significant figures in measurement and calculation?
To reflect the precision of the data
What is the primary purpose of identifying the quantity to be measured or estimated?
To determine the type of measurement or estimation required
Which of the following is an example of estimation technique?
Rounding numbers to a specified degree of accuracy
What is the primary purpose of using benchmarks in estimation techniques?
To make the estimation more accurate
What is the purpose of calculating the perimeter, area, and volume of various shapes and objects?
To apply formulas in real-life contexts
What is the main difference between a step-function relationship and a constant ratio relationship in terms of the calculation of the new value?
In a step-function relationship, the new value is calculated based on the previous value, whereas in a constant ratio relationship, the new value is calculated based on the initial value.
What is the unit of measurement for the surface area of a rectangular box?
square units
What is the primary purpose of drawing graphs for unfamiliar situations?
To make sense of the situation and reveal patterns and trends that were not visible without the graph.
What is the characteristic of a graph that represents a combination of relationships?
It has different portions representing different relationships.
What is the formula for calculating the volume of a cylindrical container?
V = πr²h
If 1m³ = 1000L, how many litres are in 2m³?
2000L
What is an example of a constant ratio relationship?
The monthly cost of food purchases in a household increasing at a rate of 7.4% per year.
What is the importance of recognizing and understanding the implications of different relationships?
It helps in making predictions and forecasts in real-world applications.
What is the conversion ratio between cubic centimetres and millilitres?
1cm³ = 1ml
What is represented by the flat portion of a graph?
A fixed fee that does not change with usage.
If a surface area is calculated to be 100cm², what is the equivalent area in square millimetres?
10000mm²
What is the primary purpose of identifying the different portions of a graph?
To analyze the meaning of different portions of a graph in the context of real-world situations.
What is the formula for calculating the surface area of a rectangular box?
SA = 2lw + 2lh + 2wh
What is the characteristic of a graph that represents a step-function relationship?
It has a series of steps.
If a volume is calculated to be 1000cm³, what is the equivalent volume in litres?
1L
What is the purpose of drawing graphs for situations with unknown formulas or patterns?
To make sense of the situation and reveal patterns and trends that were not visible without the graph.
What is the importance of converting between units when working with surface area and volume?
To make calculations more practical and applicable to real-world situations
What is the difference between the formula for calculating the surface area of a rectangular box and the formula for calculating the volume of a rectangular box?
The surface area formula has more terms
What is an example of a combination of relationships?
The cost of making calls on a cell phone contract with a fixed subscription fee and additional charges for call minutes.
What is the purpose of understanding the difference between surface area and volume?
To solve problems in real-world contexts
What is the main difference between a non-joined segment and a joined segment in a graph?
A non-joined segment is discontinuous, whereas a joined segment is continuous.
What is the primary purpose of drawing a graph for a situation with an unknown formula or pattern?
To make sense of the situation and reveal patterns and trends that were not visible without the graph.
What is represented by the point of intersection between two graphs?
The point where the two graphs intersect, and the values are exactly equal.
What is the purpose of using the trial and improvement method to determine the point of intersection?
To use their equations and the process of trial and improvement to find the values at which two relationships are equal.
What is the importance of understanding the point of intersection and the regions around it?
It provides insights into where different systems or scenarios yield the same results.
What is the purpose of converting between different units of measurement?
To ensure accurate conversions.
What is the formula to convert a weight from kilograms to pounds?
Weight (pounds) = Weight (kg) × 2.206
What is the purpose of converting between solid and liquid quantities?
To simplify complex calculations in various contexts such as baking and construction.
What is the benefit of using the trial and improvement method to find the point of intersection?
It allows for estimation of the point of intersection by using equations and the process of trial and improvement.
What is the importance of recognizing and understanding the implications of different relationships?
It is essential for analyzing and interpreting data, making decisions, and understanding the implications of different relationships.
What is the primary purpose of using a street map?
To identify locations using symbols and follow directions.
What is the primary advantage of using a strip chart?
It provides more accurate traveling distances on specific sections of a route.
What is the formula to convert a map measurement to an actual distance when using a scale?
Actual distance = Map measurement × Scale factor
What is the primary skill required when using a national road map?
Deciding on the most appropriate route between destinations.
What is the purpose of using distance tables on a map?
To determine distances between major cities and towns.
What is the primary purpose of using a housing complex map?
To work with a map that shows a small area with limited detail.
What type of calculation is required when a distance table or distance markers are not provided on a map?
Map measurement to actual distance.
What is the primary purpose of using scales on a map?
To estimate distances when a distance table or distance markers are not provided.
What is the primary purpose of using tree diagrams in compound events?
To determine the probability of multiple outcomes
Which of the following formats is not a result of the calculation of a probability value?
Ratio format
What is the primary purpose of using historical trends in probability calculations?
To predict future events based on past data
What is the result of dividing a fraction by 100 in probability calculations?
Decimal format
What is the characteristic of a compound event that involves more than one occurrence or trial?
The probability calculation takes into account multiple possible outcomes
What is the purpose of using two-way tables in compound events?
To determine the probability of multiple outcomes
What is the key concept in understanding probability values?
Probability is a prediction of an event occurring
What is the primary purpose of expressing probability values in different formats?
To provide different ways of interpreting the probability value
What is the primary purpose of drawing a 2D plan or net of a 3D model?
To understand the faces and edges of the model
What is the primary purpose of understanding the distinction between simple and compound events?
To accurately determine and interpret probability values
What is the result of multiplying a fraction by 100 in probability calculations?
Percentage format
What is the key concept in following instructions for assembly?
Understanding the sequence of steps
What is the purpose of measuring accurately in the assembly process?
To avoid errors in assembly
What is the importance of regularly checking the assembled parts against the instructions or plans?
To make adjustments as necessary to correct any mistakes
What is the formula to calculate the probability of a simple event?
P(event) = number of ways in which an event can happen / total number of possible outcomes
What is the purpose of estimating quantities and costs in the assembly process?
To calculate the total cost of materials required
What is the importance of using mathematical tools and techniques in the assembly process?
To calculate quantities, costs, and time estimates
What is the purpose of following the assembly steps in the correct sequence?
To avoid errors in assembly and ensure that the components fit together properly
What is the importance of understanding the probability value in simple events?
It predicts the likelihood of the event occurring
What is the primary purpose of checking and adjusting the assembled parts during the assembly process?
To make adjustments as necessary to correct any mistakes or misalignments
What is the characteristic of a step-function relationship in a graph?
The graph shows different fees for different time intervals
What is the purpose of drawing graphs for unfamiliar situations?
To make sense of the situation and reveal patterns and trends
What is an example of a combination of relationships?
A cell phone contract with a fixed monthly subscription fee and additional charges for call minutes
What is the importance of recognizing and understanding the implications of different relationships?
To develop skills and competencies in drawing and interpreting graphs
What is represented by the flat portion of a graph?
A fixed fee that does not change with usage
What is the characteristic of a graph that represents a combination of relationships?
The graph has different portions that represent different relationships
What is the primary purpose of identifying the point of intersection between two graphs?
Not applicable to this topic
What is the benefit of using the trial and improvement method to find the point of intersection?
Not applicable to this topic
What is the purpose of drawing a graph for a situation with an unknown formula or pattern?
To make sense of the situation and reveal patterns and trends
What is the main difference between a step-function relationship and a constant ratio relationship?
One is characterized by a graph that becomes steeper at an increasing rate, while the other is not
What is the main advantage of using the trial and improvement method to find the point of intersection between two graphs?
It is a more accurate method than estimating the point of intersection from a graph.
What does the point of intersection between two graphs represent in the context of comparing the cost of electricity on different systems?
The point where the cost of electricity on the two systems is the same.
What is the primary purpose of drawing graphs for unfamiliar situations?
To make sense of the situation and reveal patterns and trends that were not visible without the graph.
What is the importance of understanding intersection points and the regions around them?
It provides insights into where different systems or scenarios yield the same results.
What is the formula to convert a temperature from Celsius to Fahrenheit?
°F = (1.8 × °C) + 32
What is the conversion factor to convert a weight from kilograms to pounds?
2.206
What is the purpose of converting between solid and liquid quantities?
It is essential in various contexts such as baking and construction.
What is the step in the trial and improvement method to determine the point of intersection between two graphs?
Substitute different values into the equations to see if they result in the same output.
What is the purpose of estimating the point of intersection from a graph?
To find an approximate point of intersection when the exact point cannot be determined.
What is the characteristic of a graph that represents a combination of relationships?
It has multiple parts with different slopes.
What is the correct formula to convert a weight from grams to milliliters?
Volume (ml) = (Weight (g) ÷ Conversion Factor) × Conversion Factor for Volume
What is the correct unit to express the volume of a substance when converting from cubic meters (m³) to liters?
Liters (l)
What is the correct formula to calculate the total liters of paint needed based on the surface area and spread rate?
Paint Needed (liters) = Surface Area (m²) ÷ Spread Rate (m²/liter)
What is the correct step to convert a time value from minutes to seconds?
Multiply the minutes by 60
What is the correct step to calculate the total hours from a time value given in hours, minutes, and seconds?
Convert the minutes and seconds to hours and then add
What is the main purpose of identifying the week and dates of the events in a timetable?
To locate the specific event in the timetable
What is the correct formula to convert a time value from hours to seconds?
Seconds = Hours × 3600
What is the correct step to calculate the difference between two time values?
Subtract the smaller time value from the larger one
What is the purpose of breaking down a time value into hours, minutes, and seconds when calculating the difference between two time values?
To make the calculation more accurate
What is the correct unit to express the spread rate of the paint?
Square meters per liter (m²/l)
What is the main limitation of using probability values in predictions?
They do not guarantee outcomes
What is the primary purpose of using tree diagrams in compound events?
To list all possible outcomes and determine their probabilities
What is the characteristic of a graph that represents a constant ratio relationship?
A curved line that becomes steeper at an increasing rate
What is the purpose of observing historical trends in probability calculations?
To predict the likelihood of future events
What is the result of converting a probability value from a fraction to a percentage?
Multiplying the fraction by 100
What is the primary purpose of using two-way tables in compound events?
To determine the probability of a compound event
What is the key concept in understanding probability values?
They are predictions, not guarantees
What is an example of a compound event?
All of the above
What is the characteristic of a graph that represents a combination of relationships?
A combination of flat and increasing portions
What is the importance of recognizing and understanding the implications of different relationships?
It helps to make predictions and understand the uncertainty of outcomes
What is the primary purpose of an elevation plan?
To see the design and dimensions of the outside of a building or structure
What is the key concept for working with plans?
Describe features of a building or structure
What is the purpose of building 3D models from 2D plans/nets?
To facilitate the movement between 2D and 3D representations of objects
What is the formula to calculate the plan measure from an actual dimension?
Plan Measure = Actual Dimension ÷ Scale Factor
What is the primary purpose of the models section?
To facilitate the movement between 2D and 3D representations of objects
What is the key skill for Grade 11 learners in the models section?
Build 3D models from 2D plans/nets
What is the purpose of a design drawing?
To show the design, layout, and components of an item to be constructed or manufactured
What is the process of moving from a 2D drawing to constructing a 3D object?
Understanding 2D plans/nets, building 3D models, and using models to investigate various problems
What is the key concept for design drawings?
Describe the item or object shown on the design plan
What is the primary purpose of a floor plan?
To see the design and dimensions of the inside of a building or structure
What is the main difference between using a number scale and a bar scale on a map?
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.
If a map has a scale of 1:25,000, what is the actual distance represented by 5 cm on the map?
2.5 km
What is the primary reason why distances on a map can only be estimated, not determined accurately?
Many factors, such as accurate measurement and location, affect the accuracy of distance calculations.
What happens to a bar scale if the size of the map is changed?
The bar scale is resized proportionally.
What is the purpose of a floor plan?
To show a 2-dimensional perspective of a building or structure as seen from above, without the roof.
What is the formula to convert an actual distance to a map measurement?
Map measurement = Actual distance / Scale factor
What is the advantage of using a number scale over a bar scale?
A number scale shows the relationship between the size of the area on the map and the actual size.
What is the purpose of using a scale on a map?
To convert map measurements to actual distances or vice versa.
What is the primary purpose of a design drawing?
To design and plan the construction of a building or structure.
What happens to a number scale if the size of the map is changed?
The number scale becomes invalid.
What is the primary purpose of converting minutes to seconds in time conversions?
To make calculations easier
Which of the following is an example of a practical application of time conversions in real-life contexts?
Determining the time elapsed between two events
What is the primary purpose of understanding units of measurement in the context of measurement and estimation?
To recognize and use standard units of measurement
Which of the following measurement techniques involves using known reference points or benchmarks to make estimations more accurate?
Using benchmarks to estimate quantities
What is the primary purpose of calculating the perimeter, area, and volume of various shapes and objects?
To understand the properties of geometric figures
What is the primary importance of using significant figures correctly in measurement and calculation?
To reflect the accuracy of the data
What is the primary purpose of identifying the quantity to be measured or estimated?
To choose the appropriate tool or method
What is the primary purpose of error analysis in measurement and estimation?
To account for potential errors in measurement and calculation
What is the primary purpose of using rates and proportions in measurement and estimation?
To solve problems involving speed, density, and other rate-based measures
What is the primary purpose of understanding scaling in maps, diagrams, and models?
To represent real-life objects or distances accurately
What is the purpose of calculating the surface area of a 3-dimensional object?
To determine the total area of all the surfaces of the object
What is the formula for the surface area of a cylinder with a lid and base?
SA = πr^2 + 2πrh
What is the purpose of converting between units when performing surface area and volume calculations?
To ensure the correct units are used in the calculations
What is the relationship between 1 cm^3 and 1 ml?
1 cm^3 = 1 ml
What is the volume of a rectangular box with a length of 5 cm, a width of 3 cm, and a height of 2 cm?
V = 15 cm^3
What is the surface area of a rectangular box with a length of 5 cm, a width of 3 cm, and a height of 2 cm?
SA = 52 cm^2
What is the purpose of recording the measurement or estimation in the correct units and with the appropriate level of precision?
To ensure the correct units are used in the calculations
What is the formula for the volume of a rectangular-based container?
V = area of base x height
What is the purpose of analysing and applying the results of surface area and volume calculations?
To solve problems or make decisions in real-world contexts
What is the conversion ratio between 1 m^3 and litres?
1 m^3 = 1000 l
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