FPA Fall Exam Review Packet PDF

Foundations of PreAlgebra Fall Exam Review Packet Name: ____________________________ Unit 1 Review Problems: 1. Circle all the scaled copies of rectangle 𝐴. 2. Polygon 𝐸𝐹𝐺𝐻 is a scaled copy of polygon 𝐴𝐵𝐶𝐷. Select all of the true state...

Foundations of PreAlgebra Fall Exam Review Packet Name: ____________________________ Unit 1 Review Problems: 1. Circle all the scaled copies of rectangle 𝐴. 2. Polygon 𝐸𝐹𝐺𝐻 is a scaled copy of polygon 𝐴𝐵𝐶𝐷. Select all of the true statements. ▢ Segment 𝐺𝐻 is three times as long as segment 𝐴𝐵. ▢ Segment 𝐻𝐸 is three times as long as segment 𝐴𝐷. 1 ▢ The scale factor from 𝐸𝐹𝐺𝐻 to 𝐴𝐵𝐶𝐷 is. 3 ▢ The length of segment 𝐵𝐶 is 2 units. ▢ The area of 𝐸𝐹𝐺𝐻 is three times the area of 𝐴𝐵𝐶𝐷. 3. A scale drawing of a rectangular park is 8 inches wide and 11 inches long. The actual park is 330 yards long. What is its area? A. 88 square yards B. 240 square yards C. 2 640 square yards D. 79 200 square yards 1  1 4. Draw a scaled copy of the polygon using a scale factor of. 4 Roberto is drawing a map of his town. 5.1 He wants to include a school and a hospital, which are 15 kilometers apart. What should the distance between the school and the hospital be on the map? 5.2 On the map, the school and the playground are 8 centimeters apart. What is the actual distance between the school and the playground? 2 A trail runner gets a new map of her favorite mountain. Her old map has a scale of 1 cm to 400 m. Her new map has a scale of 1 cm to 100 m. 6.1 If the maps represent the same area, will the new map be larger, smaller, or the same size as the old map? A. Larger B. Smaller C. The same size Explain your thinking. 6.2 She ran a trail that was 20 cm long on her old map. How long is this trail on her new map? Explain your thinking. 3 INTERMEDIATE: Look at this campus map to answer the following questions: The dashed line from Clarkson Hall to Barge Commons is 4.2 cm. The dashed line from Barge Commons to Pressly Hall is 6.1 cm. The solid line from Clarkson Hall to Pressly Hall is 3.3 cm. How many meters is the walk to lunch this year, following the dashed line? How many meters will the walk to lunch be next year, following the solid line? 4 Unit 2 Review Problems: 1. Which graph represents a proportional relationship? A. B. C. D. 5 2. This graph shows the cost in dollars, 𝐶, of 𝑤 pounds of strawberries. The relationship is proportional. Select all of the true statements. ▢ 3. 25 pounds of strawberries cost $1. ▢ 1 pound of strawberries costs $3. 25. ▢ 4 pounds of strawberries cost $13. ▢ 10 pounds of strawberries cost $32. ▢ The point (3, 10) is on the graphed line. 3. Abdullah walked to school at a constant speed. He walked 1 mile in 15 minutes. Which equation represents the amount of time in minutes, 𝑡, that it took for him to walk a distance of 𝑑 miles? A. 𝑡 = 𝑑 + 14 B. 𝑡 = 𝑑 − 14 C. 𝑡 = 15𝑑 1 D. 𝑡 = 𝑑 15 4. These two lines represent the distance two runners ran in a race. Which runner ran more slowly? Circle one runner. Runner E Runner F Explain or show your thinking. 6 5. The table shows the weight of 100 blueberries at a market. Complete the table so that there is a proportional relationship between the number of blueberries and their weight. Number of Weight (kg) Blueberries 60 100 0. 60 400 6. The equation 𝑝 = 2. 22𝑥 relates mass in pounds, 𝑝, to mass in kilograms, 𝑥. Is there a proportional relationship between 𝑝 and 𝑥? Explain or show your thinking. 7 A recipe for tortillas uses 5 cups of flour for every 4 cups of water. The line represents the relationship between the amount of flour and the amount of water needed for this recipe. The point (1, 1. 25) is on the line. 7.1 Label the axes appropriately. 7.2 Write an equation that represents the graphed line. Use 𝑓 for the number of cups of flour and 𝑤 for the number of cups of water. 7.3 Explain what the point (1, 1. 25) means in terms of this situation. 8 INTERMEDIATE: 8. Determine whether the relationship between height and running speed in this table is proportional. Height Running Speed Jake 58 in. 4 2 mph 3 Christina 63 in. 5 1 mph 8 Winston 60 in. 4 9 mph 10 Circle: YES or NO Justify your answer: Unit 3 Review Problems: 1. A circle has a radius of 40 centimeters. Which of these is closest to its circumference? A. 126 centimeters B. 251 centimeters C. 1 600 centimeters D. 5 027 centimeters 9  2. This circle has a radius of 6 units. Three students tried to calculate the area. Order their answers from least accurate to most accurate. 113. 1 sq. units 36π sq. units 113. 1π sq. units Least accurate ________ ________ ________ Most accurate 3. Arjun measured the distance that a wheel traveled in different numbers of rotations. Select all of the true statements. Number of Distance ▢ The diameter of the wheel is about 31. 5 inches. Rotations Traveled (in.) ▢ The circumference of the wheel is 31. 5 inches. 1 31. 5 ▢ The diameter of the wheel is about 10 inches. 2 63 ▢ The radius of the wheel is about 10 inches. 3 94. 5 ▢ The relationship in the table appears to be proportional. 5 157. 5 Decide whether each quantity describes a circle's circumference or area. 4.1 The amount of glass in a circular window. Circumference Area 4.2 The number of tiles needed to go around a circular pool. Circumference Area 4.3 The amount of paint needed to paint a circular table top. Circumference Area 4.4 The distance a toy car travels around a circular track. Circumference Area 10 5. Which measurement is always proportional to the diameter of a circle? A. Circumference B. Area C. Both D. Neither Explain your thinking. 6. This figure is made of part of a circle and a rectangle. What is the perimeter of the figure? What is the area of the figure? 11 Brielle needs to tile the bottom of Pool A. One box of tile covers 25 square feet. 7.1 Pool A is a circular Pool with a 6-foot radius. What is the fewest number of boxes Brielle must buy to cover the bottom of Pool A? 7.2 Pool B is a circular Pool with a 12-foot radius. Brielle says she will need four times as much tile for Pool B compared to Pool A. Is this correct? A. Yes B. No C. Not Enough Information Explain your thinking. 12 INTERMEDIATE: The diameter of Charlie’s circular fish pond is 6.3 meters. He wants to build a 0.8 meter wide concrete sidewalk that circles the pond. 8.1 What will be the distance around the outside edge of the concrete sidewalk? Use π ≈ 3.14 and round to the nearest hundredth if needed. 8.2 How many square meters of concrete will Philip need to build his sidewalk? Use π ≈ 3.14 and round to the nearest hundredth if needed. 13 Unit 4 Review Problems: 1. A pencil is 120 millimeters long. A marker is 9% longer than the pencil. How long is the marker? A. 130. 8 mm B. 10. 8 mm C. 228 mm D. 129 mm 1 1 2. Kayleen is mowing a field. After mowing of the field, she used of a gallon of gas. 8 2 Select all of the true statements. ▢ Mowing the entire field requires 4 gallons of gas. ▢ Mowing the entire field requires 16 gallons of gas. 1 ▢ Each gallon of gas will mow of the field. 4 1 ▢ Mowing of the field requires 2 gallons of gas. 2 ▢ 3 gallons of gas will mow 50% of the field. 3. The temperature in a room is 20. 0ºC. 4. Na’ilah purchases a rug that costs $50. A A thermometer measures it as 20. 8ºC. 10% sales tax is applied. After the tax, Na’ilah uses a 10% off coupon. She will What is the percent error in this situation? pay: A. 40% A. Exactly $50. B. 4% B. More than $50. C. 1. 04% C. Less than $50. D. 0. 8% Explain your thinking. 5. The population of Bristol, PA, is about 53 110 people. Thirty years ago, the population was about 56 500 people. By what percent did the population decrease between thirty years ago and now? 14 Nicolas has a coupon for a 60% discount at his favorite store. 6.1 Is there a proportional relationship between the original price of an item and its price after the discount? Explain your thinking. 6.2 Write an equation for the relationship 6.3 The price of a coat after the discount is between the discount price of an item, 𝑑, $21. What was the original price? and its original price, 𝑝. The cost of new cars and trucks are expected to increase 2. 9% next year. 7.1 The Des-car currently costs $17 000. 7.2 Write an equation that will help calculate the cost of other cars next year. What is the expected cost of the new Des-car next year? Use 𝑡 to represent this year's cost and 𝑛 to represent next year's cost. 7.3 The cost of the new Des-truck is currently $22 000. If the percent increase stays constant, what will the cost be in two years? Explain your thinking. 15 INTERMEDIATE: Helen is painting her room. After painting 20% of her room, Dalia has used 75% of a can of paint. Select all of the true statements. A. Each can of paint will cover 15% of Dalia's room. B. 3 cans of paint will cover 80% of Dalia's room. C. Dalia's entire room requires 4 cans of paint. D. Painting 50% of Dalia's room requires 3 cans of paint. 16