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Questions and Answers
What was the percentage decrease in the population of Bristol over the last thirty years?
What was the percentage decrease in the population of Bristol over the last thirty years?
What equation can represent the relationship between the original price ($p$) and discounted price ($d$) with a 60% discount?
What equation can represent the relationship between the original price ($p$) and discounted price ($d$) with a 60% discount?
What will the expected cost of the new Des-car be next year if it costs $17,000 this year and the expected increase is 2.9%?
What will the expected cost of the new Des-car be next year if it costs $17,000 this year and the expected increase is 2.9%?
If each can of paint covers 15% of Dalia's room, how many cans will she need to paint her entire room?
If each can of paint covers 15% of Dalia's room, how many cans will she need to paint her entire room?
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If Dalia has already painted 20% of her room using 75% of a can of paint, how much more paint does she need to finish?
If Dalia has already painted 20% of her room using 75% of a can of paint, how much more paint does she need to finish?
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What is the closest approximation of the circumference of a circle with a radius of 40 centimeters?
What is the closest approximation of the circumference of a circle with a radius of 40 centimeters?
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Which order from least accurate to most accurate is correct for the area of a circle with a radius of 6 units calculated by three students?
Which order from least accurate to most accurate is correct for the area of a circle with a radius of 6 units calculated by three students?
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Which statement about the diameter of the wheel is true if the diameter is approximately 31.5 inches?
Which statement about the diameter of the wheel is true if the diameter is approximately 31.5 inches?
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What does the area of a circular window correspond to among the following?
What does the area of a circular window correspond to among the following?
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In which situation would circumference be relevant?
In which situation would circumference be relevant?
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Which measurement is always proportional to the diameter of a circle?
Which measurement is always proportional to the diameter of a circle?
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How is the area of a circle with a diameter of 10 inches calculated?
How is the area of a circle with a diameter of 10 inches calculated?
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Which of the following best describes the relationship between the distance traveled and the number of rotations of a wheel?
Which of the following best describes the relationship between the distance traveled and the number of rotations of a wheel?
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What is the area of Pool A with a 6-foot radius?
What is the area of Pool A with a 6-foot radius?
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How much area does one box of tile cover?
How much area does one box of tile cover?
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How many boxes of tile are needed to cover the bottom of Pool B, which has a 12-foot radius?
How many boxes of tile are needed to cover the bottom of Pool B, which has a 12-foot radius?
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If Charlie's pond has a diameter of 6.3 meters, what is the circumference around the pond?
If Charlie's pond has a diameter of 6.3 meters, what is the circumference around the pond?
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What is the width of the sidewalk that Charlie wants to build around his pond?
What is the width of the sidewalk that Charlie wants to build around his pond?
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If a pencil is 120 millimeters long and a marker is 9% longer, how long is the marker?
If a pencil is 120 millimeters long and a marker is 9% longer, how long is the marker?
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What is an accurate estimate for the total amount of gas needed to mow the entire field, if 1/8 of the field requires 1/2 gallon?
What is an accurate estimate for the total amount of gas needed to mow the entire field, if 1/8 of the field requires 1/2 gallon?
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What is the total cost Na'ilah will pay for the rug after applying the sales tax and discount?
What is the total cost Na'ilah will pay for the rug after applying the sales tax and discount?
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If segment GH is three times longer than segment AB, what can be concluded about the relationship between polygons EFGH and ABCD?
If segment GH is three times longer than segment AB, what can be concluded about the relationship between polygons EFGH and ABCD?
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What is the area of the rectangular park if it is 330 yards long and the drawing is 11 inches long?
What is the area of the rectangular park if it is 330 yards long and the drawing is 11 inches long?
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Which statement is true when comparing the old map (scale 1 cm to 400 m) and the new map (scale 1 cm to 100 m)?
Which statement is true when comparing the old map (scale 1 cm to 400 m) and the new map (scale 1 cm to 100 m)?
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If the scale factor from polygon EFGH to ABCD is 3, what is the relationship of their areas?
If the scale factor from polygon EFGH to ABCD is 3, what is the relationship of their areas?
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What is the actual distance between the school and the playground if they are 8 centimeters apart on the map, assuming a scale of 1 cm to 5 kilometers?
What is the actual distance between the school and the playground if they are 8 centimeters apart on the map, assuming a scale of 1 cm to 5 kilometers?
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In which scenario would the mapped distance between two locations be represented accurately?
In which scenario would the mapped distance between two locations be represented accurately?
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If a trail is 20 cm long on the old map, how long is this trail on the new map that has a scale of 1 cm to 100 m?
If a trail is 20 cm long on the old map, how long is this trail on the new map that has a scale of 1 cm to 100 m?
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What conclusion can be drawn from a graph representing a proportional relationship?
What conclusion can be drawn from a graph representing a proportional relationship?
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Which statement correctly identifies a true proportional relationship about strawberries?
Which statement correctly identifies a true proportional relationship about strawberries?
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What is the correct equation for the time it takes Abdullah to walk a distance of $d$ miles?
What is the correct equation for the time it takes Abdullah to walk a distance of $d$ miles?
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Which runner, based on the distance they ran, can be identified as running more slowly?
Which runner, based on the distance they ran, can be identified as running more slowly?
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Which scenario represents a proportional relationship between the number of blueberries and their weight?
Which scenario represents a proportional relationship between the number of blueberries and their weight?
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What is the meaning of the point (1, 1.25) in the context of the recipe for tortillas?
What is the meaning of the point (1, 1.25) in the context of the recipe for tortillas?
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Is there a proportional relationship between the mass in pounds and mass in kilograms in the equation $p = 2.2x$?
Is there a proportional relationship between the mass in pounds and mass in kilograms in the equation $p = 2.2x$?
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What would be the correct proportion for each column in the height and running speed table?
What would be the correct proportion for each column in the height and running speed table?
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If 5 cups of flour are used for every 4 cups of water, which ratio best describes the relationship?
If 5 cups of flour are used for every 4 cups of water, which ratio best describes the relationship?
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Study Notes
Unit 1 Review Problems
- Rectangle Scaling: Identify scaled copies of rectangle A. Multiple rectangles are shown.
Polygon Scaling
- Scaled Copies: Polygon EFGH is a scaled copy of polygon ABCD. True statements about the scale factor and relationships between corresponding segments are selected.
- Scale Factor: The scale factor from EFGH to ABCD is given as 3/5.
- Segment Lengths: The length of segment BC is not explicitly given but implied by corresponding segment relationships.
- Area Scaling: The area of EFGH is three times the area of ABCD.
Scale Drawings and Area
- Scale Drawing Dimensions: A rectangular park is represented in a scale drawing. Dimensions are 8 inches wide and 11 inches long on the map. The actual length of the park is 330 yards.
- Actual Area: Calculate the actual area of the park in square yards. The correct answer is 79 200 square yards.
Scaling Polygons
- Scale Factor: Draw a scaled copy of a polygon using a scale factor of 1/4.
Distance and Scale
- Map Distance to Real Distance (Hospital/School): Calculate the map distance between a school and a hospital that are 15 kilometers apart. A scale of 2 cm equals 5 km is used. The distance between them on the map is asked for.
- Map Distance to Real Distance (School/Playground): Calculate the actual distance between a school and a playground when they are 8 centimeters apart on a map with a scale of 2 cm to 5 km.
Map Scale and Size
- Map Size Relationship: A trail runner has two maps of a mountain. Her old map scale is 1cm to 400 m, and her new map scale is 1 cm to 100 m. If the maps represent the same area, how will the new map compare in size to the old map?
- Trail Length (Old to New Maps): A trail on the old map was 20 cm long. What is the length of the trail on the new map?
Campus Map and Distances
- Campus Map Scale: A campus map has a scale of 5 cm to 200 m. Distances (in cm) are provided for segments on the map between buildings.
- Distance Calculations: Calculate the distances between various buildings (Clarkson Hall to Barge Commons, Barge Commons to Pressly Hall, and Clarkson Hall to Pressly Hall) in meters, using the scale.
Proportional Relationships
- Graph Types: Identify the graph that represents a proportional relationship. Multiple graphs are provided.
- Cost of Strawberries (Graph): A graph shows the cost of strawberries in pounds. True statements related to the price/quantity are listed. A specific point is mentioned.
- Constant Speed: An equation representing constant speed (1 mile in 15 minutes) that relates distance to time is needed.
- Runner Comparison: Determine which of two runners ran more slowly given a graph showing distance vs. time.
Proportional Relationship (Weight)
- Blueberry Weight Table: A table showing the relationship between the number of blueberries and their weight needs to be completed so that the relationship is proportional.
Tortillas (Recipe)
- Proportional Relationship (Recipe): A recipe for tortillas calls for 5 cups of flour for every 4 cups of water. Graph the relationship. A point is given (1, 1.25). Label the axes. The equation representing this relationship needs to be determined, and the meaning of (1, 1.25) is explained.
Height vs. Running Speed
- Proportionality: Determine if there is a proportional relationship between height and running speed based on the information in a table. Explain your answer.
Circle Circumference
- Circle Circumference Calculation: Calculate the circumference of a circle with a given radius. Multiple choices of circumference values are given.
Circle Area
- Circle Area Calculation: A circle with a radius of 6 units has its area calculations compared (in terms of most & least accurate).
- Wheel Rotations: Calculate wheel circumference/diameter and state true statements (relationships in a table).
Circle Perimeter/Area
- Combined Shape: Calculate the perimeter and area of a shape that is made of part of a circle and a rectangle.
Pool Tiling
- Pool Area (Pool A): Calculate the area (in square feet) of a circular pool with a given radius. This area represents the amount of tile that is needed.
- Pool B Comparison: A second pool (Pool B) has a larger radius. Determine whether the amount of tile needed for Pool B is four times as much as Pool A's tile.
Concrete Sidewalk
- Concrete Sidewalk Distance: Calculate the distance around a circular fish pond (including a sidewalk). The radius of the fish pond and the sidewalk width are given.
- Concrete Area: Calculate the area of the concrete needed for the sidewalk.
Pencil/Marker Length
- Percent Increase: A pencil is 120 mm long. A marker is 9% longer. Determine the length of the marker.
Gas Consumption
- Gas for Mowing a Field: Kayleen is mowing a field. 1/8 of the field is mowed, and 1/2 gallon of gas is used. Find the total number of gallons required to mow the entire field.
Temperature Error
- Temperature Error: The temperature in a room is 20.0°C. A thermometer measures it as 20.8°C. Find the percent error of this measurement.
Rug Purchase
- Sales Tax and Coupon: Na'ilah buys a rug that costs $50. A 10% sales tax and a subsequent 10% off coupon are applied. Find the final cost.
Population Change
- Population Decrease: The population of Bristol, PA is currently 53,110. Thirty years ago the population was 56,500. Calculate the percentage decrease between the two values.
Discount Price
- Discount Relationship: Determine if a 60% discount on items is proportional to the original price of the item. Explain your answer.
- Discount Price Equation: Write an equation for the relationship between an item's discount price "d" and its original price "p".
Car Value Increase
- Car Price Increase: The price of a Des-car is expected to increase by 2.9% next year. The current cost is $17,000. Find the expected price next year.
- Car Price Increase Equation: Write an equation representing the increase in car cost and specify variables used (current year cost and next year's cost)
- Future Car Value: Find the expected cost of a Des-truck (currently $22,000) in two years if its percent increase stays constant. Explain your reasoning.
Paint Usage
- Percentage of Paint (Room): Helen is painting her room. She used 75% of a can of paint after painting 20% of her room. Identify the true statements related to the total paint needed/the percentage of the room.
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Description
This quiz covers scaling concepts in geometry, including the identification of scaled copies of rectangles and polygons, understanding scale factors, and calculating actual areas through scale drawings. Participants will engage with problems that challenge their knowledge on the relationships between dimensions and area in various geometric figures.
