This is an end of chapter assessment. Give students one class period to complete this assessment.

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1 Teacher Notes Pre- and Post-Tests This pre-assessment is designed to be completed by students before they start work on Chapter. Students should be given about 0 30 minutes to complete this pre-assessment. The teacher can use this assessment formatively, to understand what material students have mastered going into the start of Chapter. This post-assessment is designed to be completed at the culmination of Chapter. This test is a parallel form to the pre-assessment. In accordance, students should be allowed 0 30 minutes to complete this post-assessment. Student performance on the post- and pre-assessment can be compared in order to measure gains in student learning from Chapter. Mid-Chapter Test This mid-chapter assessment is designed to be completed by students when they have completed the first four lessons in Chapter. Students should be given about 0 30 minutes to complete this mid-chapter assessment. End of Chapter Test This is an end of chapter assessment. Give students one class period to complete this assessment. Students will need a protractor to complete this assessment. Many of the figures are not drawn to scale, so students should not depend on visual cues. They should instead use the information given to reason through the questions. Standardized Test Practice This test will provide practice for standardized tests that students may take during the school year. Content from all previous chapters will be included on the practice exams. To prepare students for standardized testing, allow students 5 to 0 minutes of time to complete the exam. Emphasize that students should work quickly but carefully to perform well. Chapter Assessments 85A

2 85B Chapter Assessments

3 Pre-Test Name Date. A rectangle has a length of 4. meters and a width of 5.6 meters. a. Sketch and label a diagram of the rectangle. 4. m 5.6 m b. Find the perimeter of the rectangle. The perimeter of the rectangle is equal to the sum of twice the length and twice the width. (4.) (5.6) 9.6 The perimeter is 9.6 meters. c. Find the area of the rectangle. The area of the rectangle is equal to the product of the length and width of the rectangle The area of the rectangle is 3.5 square meters. d. What is the difference between the units of perimeter and the units of area? Units of perimeter are linear while the units of area are squared. Chapter Assessments 85

4 Pre-Test PAGE. A circle has a diameter of 5 centimeters. a. Sketch and label a diagram of the circle. 5 cm b. Find the circumference of the circle. Use 3.4 for. The circumference of the circle is equal to the product of and the diameter of the circle. (5) (3.4)(5) 5.7 The circumference of the circle is 5.7 centimeters. c. Find the area of the circle. Use 3.4 for. The area of the circle is equal to the product of and the square of the radius. (.5 ) (3.4)(.5 ) (3.4)(6.5) 9.65 The area of the circle is 9.65 square centimeters. d. What is the difference between the units of circumference and the units of area? The units of area are measured in square units while the units of circumference are measured in linear units. 86 Chapter Assessments

5 Pre-Test PAGE 3 Name Date 3. A triangle has a height of centimeters and base length of 8 centimeters. a. Sketch and label three different triangles with these dimensions. cm cm cm 8 cm 8 cm 8 cm b. Find the area of a triangle with these dimensions. The area of the triangle is equal to one half of the product of the base length and height. (8)() 48 The area of the triangle is 48 square centimeters. 4. A parallelogram has a height of centimeters and a base length of 4 centimeters. a. Sketch and label three different parallelograms with these dimensions. cm cm cm 4 cm 4 cm 4 cm b. Find the area of a parallelogram with these dimensions. The area of the parallelogram is equal to the product of the base length and the height The area of the parallelogram is 88 square centimeters. Chapter Assessments 87

6 Pre-Test PAGE 4 5. Find the area of the trapezoid below. ft ft 7 ft The area of the trapezoid is equal to one half of the sum of the bases multiplied by the height. ( 7)() (7)() The area of the trapezoid is square feet. 6. Find the area and perimeter of the figure below. 5 in. w 3 in. v y x 7 in. 5 in. z in. To find the area of the figure, add the areas of the rectangles that make up the figure. The area of the bottom rectangle is 5 55 square inches. The area of the top rectangle is 4 square inches. So, the area of the figure is square inches. To find the perimeter, add the lengths of all the sides of the polygon. Starting clockwise from the bottom of the figure, the lengths of the sides are inches, 5 inches, 3 inches, v 7 5 inches, w 5 3 inches, x v inches, y 5 4 inches, and z 5 inches. The perimeter of the figure is inches. 88 Chapter Assessments

7 Pre-Test PAGE 5 Name Date 7. The area of a square is 96 square centimeters. a. Sketch and label a diagram of the square. 96 cm 96 cm A 96 cm b. Find the length of a side of the square. The area of a square is equal to the square root of one of the side lengths. If we know the area of the square, we can find the length of one side by taking the square root of the area. The square root of 96 is between 9 and ( 9 8 and 0). The length of a side is centimeters. 8. Place the following numbers on a number line. 0,,,, 0 0 Chapter Assessments 89

8 Pre-Test PAGE 6 9. Use the Pythagorean theorem to determine which of the triangles below are right triangles. 8 m 3 ft A 5 ft 4 ft 6 m B m 6 yd 7 yd C 3 yd Triangle A: Triangle B: Triangle C: Triangles A and B are right triangles. Triangle C is not.. Find the area of the shaded region below. in. in. in. in. To find the area of the shaded region, subtract the areas of the three unshaded right triangles from the total area of the rectangle. The area of the rectangle is 4 3 square inches. The area of the first right triangle is (4)() 4 square inches. The area of the second right triangle is ()() square inch. The area of the third right triangle is ()(3) 3 square inches square inches. So the area of the shaded region is 90 Chapter Assessments

9 Pre-Test PAGE 7 Name Date. The figure below is made up of a square and parts of a circle. 5 cm 5 cm 5 cm 5 cm a. Find the area of the shaded region. Use 3.4 for. To find the area of the shaded region, subtract the area of a circle with a radius of 5 centimeters from the area of the square with a side length of centimeters. The area of the circle is (5 ) (3.4)(5 ) (3.4)(5) 78.5 square centimeters. The area of the square is 0 square centimeters. So, the area of the shaded region is square centimeters. b. Find the perimeter of the shaded region. Use 3.4 for. The perimeter of the shaded region is equal to the circumference of a circle with a radius of 5 centimeters. So, the perimeter of the shaded region is ()(5) (3.4)()(5) 3.4 centimeters. Chapter Assessments 9

10 9 Chapter Assessments

11 Post-Test Name Date. A rectangle has a length of 3.6 meters and a width of 7.8 meters. a. Sketch and label a diagram of the rectangle. 3.6 m 7.8 m b. Find the perimeter of the rectangle. The perimeter of the rectangle is equal to the sum of twice the length and twice the width. (3.6) (7.8).8 The perimeter is.8 meters. c. Find the area of the rectangle. The area of the rectangle is equal to the product of the length and width of the rectangle The area of the rectangle is 8.08 square meters. d. What is the difference between the units of perimeter and the units of area? The units of perimeter are linear while the units of area are squared. Chapter Assessments 93

12 Post-Test PAGE. A circle has a diameter of centimeters. a. Sketch and label a diagram of the circle. cm b. Find the circumference of the circle. Use 3.4 for. The circumference of the circle is equal to the product of and the diameter of the circle. () (3.4)() The circumference of the circle is centimeters. c. Find the area of the circle. Use 3.4 for. The area of the circle is equal to the product of and the square of the radius. (6 ) (3.4)(6 ) (3.4)(36) 3.04 The area of the circle is 3.04 square centimeters. d. What is the difference between the units of circumference and the units of area? The units of area are measured in square units while the units of circumference are measured in linear units. 94 Chapter Assessments

13 Post-Test PAGE 3 Name Date 3. A triangle has a height of 4 inches and base length of 8 inches. a. Sketch and label three different triangles with these dimensions. 4 cm 4 cm 4 cm 8 cm 8 cm 8 cm b. Find the area of a triangle with these dimensions. The area of the triangle is equal to one half of the product of the base length and height. (8)(4) 6 The area of the triangle is 6 square centimeters. 4. A parallelogram has a height of 5 centimeters and a base length of 30 centimeters. a. Sketch and label three different parallelograms with these dimensions. 5 cm 5 cm 5 cm 30 cm 30 cm 30 cm b. Find the area of a parallelogram with these dimensions. The area of any parallelogram is equal to the product of the base length and height The area of the parallelogram is 450 square centimeters. Chapter Assessments 95

14 Post-Test PAGE 4 5. Find the area of the trapezoid below. 4 ft ft 6 ft The area of a trapezoid is equal to one half of the sum of the bases multiplied by the height. (4 6)() (0)() 0 The area of the trapezoid is 0 square feet. 6. Find the area and perimeter of the figure below. 5 in. x in. w 4 in. 7 in. 5 in. y z 3 in. To find the area of the figure, add the areas of the rectangles that make up the figure. The area of the rectangle on the left is square inches. The area of the rectangle on the right is 4 48 square inches. So, the area of the figure is square inches. To find the perimeter, add the lengths of all the sides of the polygon. Starting clockwise from the bottom of the figure, the lengths of the sides are 3 inches, 5 inches, w 3 inches, inches, x 5 3 inches, 4 inches, y x inches, and z inches. The perimeter of the figure is inches. 96 Chapter Assessments

15 Post-Test PAGE 5 Name Date 7. The area of a square is 7 square centimeters. a. Sketch and label a diagram of the square. 7 cm 7 cm A 7 cm b. Find the length of a side of the square. The area of a square is equal to the square root of one of the side lengths. If we know the area of the square, we can find the length of one side by taking the square root of the area. The square root of 7 is between 8 and 9 ( 8 64 and 9 8). The length of a side is centimeters. 8. Place the following numbers on a number line. 0, 3, 3, 3, Chapter Assessments 97

16 Post-Test PAGE 6 9. Use the Pythagorean theorem to determine which of the triangles below are right triangles. km 6 m 7 m A 4 m 3 in. B 5 in. 4 in. 9 km C 5 km Triangle A: Triangle B: Triangle C: Triangles B and C are right triangles. Triangle A is not a right triangle. 98 Chapter Assessments

17 Post-Test PAGE 7 Name Date. Find the area of the shaded region below. 5 in. in. 4 in. 4 in. To find the area of the shaded region, subtract the areas of the three unshaded right triangles from the total area of the rectangle. The area of the rectangle is square inches. The area of the first right triangle is (8)(5) 0 square inches. The area of the second right triangle is (4)() 4 square inches. The area of the third right triangle is (4)(7) 4 square inches. So, the area of the shaded region is square inches. Chapter Assessments 99

18 Post-Test PAGE 8. The figure below is made up of a square and parts of a circle. 7 cm 7 cm 7 cm 7 cm a. Find the area of the shaded region. Use 3.4 for. To find the area of the shaded region, subtract the area of a circle with a radius of 7 centimeters from the area of the square with a side length of 4 centimeters. The area of the circle is (7 ) (3.4)(7 ) (3.4)(49) square centimeters. The area of the square is 4 96 square centimeters. So, the area of the shaded region is square centimeters. b. Find the perimeter of the shaded region. Use 3.4 for. The perimeter of the shaded region is equal to the circumference of a circle with a radius of 7 centimeters. So, the perimeter of the shaded region is ()(7) (3.4)()(7) centimeters. 00 Chapter Assessments

19 Mid-Chapter Test Name Date. The figure below is made up of parts of circles. 6 cm 3 cm a. Find the area of the shaded region. Use 3.4 for. The figure is made of half circles. The top half of the figure is a half circle that has a diameter of 9 centimeters with a half circle that has a diameter of 3 centimeters cut out. The bottom half of the figure is a half circle that has a diameter of 6 centimeters. The area of the shaded region of the figure is (3.4)(4.5 ) (3.4)(.5 ) (3.4)(3 ) square centimeters. b. Find the perimeter of the shaded region. Use 3.4 for. The perimeter of the shaded region is equal to the sum of half of the circumference of each of the three circles. The circumference of the first half circle is (3.4)(9) 4.3 centimeters. The circumference of the second half circle is (3.4)(6) 9.4 centimeters. The circumference of the third half circle is (3.4)(3) 4.7 centimeters. So the perimeter of the shaded region is centimeters. Chapter Assessments 0

20 Mid-Chapter Test PAGE. This figure below is a rectangle with a parallelogram-shaped section cut out. x y a. What is the perpendicular height of the parallelogram? The height of the parallelogram is y units. z b. Write an expression for the area of the shaded portion of the rectangle. The area of the shaded regions is equal to the area of the rectangle minus the area of the parallelogram. So, the area is yz xy square units. 0 Chapter Assessments

21 Mid-Chapter Test PAGE 3 Name Date 3. A garden roller has a radius of 5 centimeters. a. What is the circumference of the roller? Use 3.4 for. The circumference of the roller is equal to the product of and the diameter of the roller. The radius is 5 centimeters, so the diameter is 50 centimeters. (50) (3.4)(50) 57 The circumference of the roller is 57 centimeters. b. How many revolutions are required to roll the edge of a lawn that is 78.5 meters long? There are 0 centimeters in meter. So, in 78.5 meters, there are 7850 centimeters. To find the number of revolutions that will be needed to roll 7850 centimeters, divide this value by the circumference of the roller, So, 50 revolutions are required to roll the edge of the lawn. Chapter Assessments 03

22 Mid-Chapter Test PAGE 4 4. The figure below shows the dimensions of a plot of land and a house on the plot. 30 m 44 m 0 m House m 6 m Figure not drawn to scale 8 m a. Find the perimeter of the house. The perimeter of the house is equal to the sum of twice the length and twice the width. () (6) 3 The perimeter of the house is 3 meters. b. Find the perimeter of the plot. The perimeter of the plot is equal to the sum of the lengths of the sides The perimeter of the plot is meters. c. Find the area of the plot including the area covered by the house. The plot is in the shape of a trapezoid. The area is equal to one half of the sum of the bases multiplied by the height. (44 0)(8) (64)(8) 576 The area of the plot of land is 576 square meters. 04 Chapter Assessments

23 Mid-Chapter Test PAGE 5 Name Date 5. A triangle is shown on the grid below. 9 y A B C x a. Write the coordinates of the vertices A, B, and C. The coordinates of A are (6, 9). The coordinates of B are (, ). The coordinates of C are (6, ). b. Find the area of the triangle. The area of a triangle is equivalent to one half the area of a rectangle with the same dimensions. The triangle above is inscribed in a rectangle that is 8 units by 4 units. So, the area of the triangle is (8 4) 6 square units. Chapter Assessments 05

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25 End of Chapter Test Name Date. Plot the numbers on the given number line and explain your reasoning. a. 5 and The square root of 30 is between 5 and 6 because 5 5 and So, 30 is to the right of 5. b. 0 and is equal to 5. 0 (or 5) is between 4 and 5 because 4 6 and 5 5. c. 3 and The square root of 3 is between.5 and because.5.5 and 4. So, 3 is the the left of. Chapter Assessments 07

26 End of Chapter Test PAGE. The diagram below is a scale drawing of a building site. The scale of the diagram is inch : 4 meters. This means that a distance of one inch on the scale drawing is equal to a distance of four meters on the site. Scale Key inch B C inch : 4 meters A D a. Measure angle ABC. The measure of angle ABC is 0º. b. A water main runs from corner A through the building site and makes an angle of 45º with side AD. Draw a dotted line to represent the water main. The dotted line from A to C forms an angle of 45º with side AD. c. Classify triangle ABC based on its angle measures. This triangle is an obtuse triangle because angle ABC is greater than 90º. d. Explain why ABC is not an isosceles triangle. Triangle ABC is not an isosceles triangle because it does not have two angle measures (or two side measures) that are congruent. 08 Chapter Assessments

27 End of Chapter Test PAGE 3 Name Date e. Use the measurements from the scale diagram to find the approximate perimeter of the building site. Student answers may vary slightly, as they are dependent on students accuracy using the scale measure. Using a piece of string or a piece of paper, students will find that AD.5 inches, DC.75 inches, CB.8 inches, and BA.5 inches. So, one approximation for the perimeter of the scale drawing is.3 inches. So, the perimeter of the building site is approximately meters. f. Find the area of the building site using the scale drawing with the given dimensions below. (The scale of the diagram is inch : 4 meters.) C 0.5 in. B.75 in. A D 0.5 in..75 in. To find the area of the building site, use what you know about the areas of composite figures. First, find the area of the square. The side length of the square in the scale drawing is.75 inches, so the side length in real life is.75 4 meters. The area of the square is () square meters. Next, find the area of the shaded region. The first triangle has a base length of meters and a height of.75 4 meters. The second triangle has a base length of meter and a height of.75 4 meters. So, the area of the shaded region is ()() ()() square meters. The area of the building site is equal to the area of the square minus the area of the shaded region, or square meters. Chapter Assessments 09

28 End of Chapter Test PAGE 4 3. A boy rolls a hoop along the ground, as shown below. The hoop has a diameter of 90 centimeters. 90 cm a. What is the circumference of the hoop? Use 3.4 for. The circumference of the hoop is equal to the product of and the diameter of the hoop. (90) (3.4)(90) 8.6 The circumference of the hoop is 8.6 centimeters. b. What is the minimum number of complete revolutions that the hoop must make to cover a distance of 5 meters? There are 0 centimeters in meter. So, in 5 meters, there are 500 centimeters. To find the number of revolutions that will be needed to roll 500 centimeters, divide this value by the circumference of the hoop, The hoop will need to make complete revolutions to cover 5 meters. Chapter Assessments

29 End of Chapter Test PAGE 5 Name Date 4. A restaurant s new industrial-size refrigerator is 7 feet tall and 5 feet wide. The refrigerator is lying on its side. The owners want to tilt the refrigerator upright, but they are worried that the refrigerator might hit the 8-foot ceiling, as shown below. Will the refrigerator hit the ceiling when it is tilted upright? 7 ft 5 ft Ceiling Floor Use the Pythagorean theorem to find the length of the diagonal of the refrigerator, 7 5 d. This gives 49 5 d, or 74 d, or d 74, or about 8.6 feet. Because the length of the diagonal of the refrigerator is greater than the height of the ceiling, the refrigerator will hit the ceiling when it is tilted upright. 5. Determine whether angle ABC in the triangle below is a right angle. Explain your reasoning. 7 m B A 8 m 4 m C Use the Pythagorean theorem to determine whether this is a right triangle. If the square of the longest side is equal to the sum of the squares of the two legs, then this is a right triangle So, this triangle is not a right triangle, and ABC is not a right angle. Chapter Assessments

30 End of Chapter Test PAGE 6 6. A metal water tank is shown below. Side ABCD is a trapezoid. The length of AD is 0.9 meter. 0.7 m D 0.9 m A.55 m C B 0.4 m a. Find the area of side ABCD. Side ABCD is a trapezoid with base lengths of 0.9 meter and 0.4 meter, and a height of 0.7 meter. The area of a trapezoid is equal to one half of the sum of the bases multiplied by the height. ( )(0.7) (.3)(0.7) The area of side ABCD is square meter. b. When the tank is full of water, what is the depth of the water? The depth of the water will be 0.7 meter. c. The tank is made of five pieces of metal welded together. Sketch each of the five pieces and label their dimensions. There are two congruent trapezoids (the ends), two congruent wide rectangles (the sides), and one thin rectangle (the bottom). 0.9 m 0.4 m.55 m 0.9 m 0.4 m 0.7 m.55 m 0.4 m.55 m 0.74 m 0.74 m The width of the larger rectangles are 0.74 rather than 0.7 because the 0.7 represents depth of the tank, and not the length of the seam between the two sides. The figure to the left illustrates this point. 0.7 Use the Pythagorean theorem to find the length of the side of the trapezoid. (0.7) (0.5) (0.74) Chapter Assessments

31 End of Chapter Test PAGE 7 Name Date d. Find the area of each of the five pieces of metal. How many total square meters of metal will be needed to make this tank? Round your answer to the nearest thousandth. To find the number of square meters of metal needed, find the area of each of the five pieces from part (c) and then add the areas. The area of the rectangular bottom piece is square meters. The area of one of the rectangular sides is square meters. From part (a), you know that the area of one of the trapezoidal sides is square meter. So, the total number of square meters of metal needed is.0 (.887) (0.455) square meters. 7. In the figure of the exercise bicycle shown below, AE and BC are parallel and DE and are parallel. AB A E D B C a. Triangles ABC and DEA are similar. Explain how you know that triangles ABC and DEA are similar. If AE BC, then EAD ACB. If AB ED, then CAB ADE. Because the sum of the measures of the interior angles of a triangle is 80 degrees, then EAD ADE AED 80º and CAB ABC ACB 80º. Our congruency statements from above allow us to say that ABC AED. So, all of the corresponding angles of the triangles are congruent, and the triangles are similar. b. The length of the cross-bar AE is 35 centimeters and the length of the bar AD is 35 centimeters. The length of the support beam AC is 70 centimeters. Find the length of BC. Triangles ABC and DEA are similar, so use corresponding sides to write a proportion to find the length of BC. AE BC AD 35 35, so AC BC 70 So, the length of BC is 70 centimeters. Chapter Assessments 3

32 End of Chapter Test PAGE 8 c. The height of triangle ABC is 60 centimeters. Find the area of triangle ABC. Triangle ABC has a height of 60 centimeters and a base length of 70 centimeters. The area is equal to one half of the product of the base length and height. (70)(60) 0 The area of the triangle is 0 square centimeters. d. Find the area of triangle DEA. If the height of triangle ABC is 60 centimeters, then the height of DEA is 30 centimeters (from similarity). The base length of triangle DEA is 35 centimeters. The area is equal to one half of the product of the base length and height. (35)(30) 55 The area of the triangle is 55 square centimeters. 8. The figure shows the part of a kitchen counter that is to be tiled and the size of tile to be used. 40 cm cm 30 cm cm cm 0 cm a. How many -centimeter by -centimeter tiles are needed to tile the kitchen counter? b. Find the area of the surface to be covered. Not drawn to scale This part of the kitchen counter can be thought of as a 0-centimeter by 0-centimeter square and a -centimeter by 40-centimeter rectangle. To cover the 0-centimeter by 0-centimeter square, we will need 4 of the -centimeter by -centimeter tiles. To cover the -centimeter by 40-centimeter square, we will also need 4 of the -centimeter by -centimeter tiles. In all, we will need 8 tiles. Each tile is centimeters by centimeters or 0 square centimeters. Because we need 8 tiles, the surface area is square centimeters. 4 Chapter Assessments

33 Standardized Test Practice Name Date. Find the area of the rectangle. 8 in. 4 in. 4 in. 8 in. a. 4 square inches b. 6 square inches c. 3 square inches d. 56 square inches. Simplify 5. a. 5 b. 5 c. 35 d The circumference of a circle is equal to 8 units. Find the area of the circle. a. 6 square units b. 64 square units c. 4 square units d. 8 square units 4. M {, 3, 5, 7,, 3, 3, 9}. Which of the following is a true statement concerning M? a. All numbers in M are odd. b. All numbers in M are prime. c. All numbers in M are even. d. All numbers in M are composite. Chapter Assessments 5

34 Standardized Test Practice PAGE 5. Chase cut four congruent triangles off of the corners of a rectangle to make a hexagon, as shown below. What is the area of the shaded hexagon? 3 cm 6 cm 3 cm cm a. 30 square centimeters b. 8 square centimeters c. 66 square centimeters d. 48 square centimeters 6. Which of the following best represents 39? A number between... a. 3 and 4 b. 6 and 7 c. 7 and 8 d. 8 and 9 7. Find the area of QPR. Q 8 cm R 4 cm a. 8 square centimeters P b. square centimeters c. 54 square centimeters d. 56 square centimeters 6 Chapter Assessments

35 Standardized Test Practice PAGE 3 Name Date 8. Find the coordinates of point A on the graph below. y A x a. (4, ) b. (4, ) c. (, 4) d. (4, 0) 9. Find the perimeter of the figure shown below. 4 m 6 m 8 m a. 3 meters b. 40 meters c. 44 meters d. 88 meters 4 m Not drawn to scale Chapter Assessments 7

36 Standardized Test Practice PAGE 4. Simplify a. 3 4 b. 4 c. 5 4 d Simplify (.56) (.34). a.. b c d Triangles DEF and LMN are congruent. E x 8 inches M D x F L N Not drawn to scale The perimeter of DEF is 6 inches. What is the length of side LN in LMN? a. 8 inches b. 6 inches c. 9 inches d. inches 8 Chapter Assessments

37 Standardized Test Practice PAGE 5 Name Date 3. What type of triangle is shown below? a. isosceles b. scalene c. obtuse d. equilateral 4. The sum of 4 times a number n and 4 equals 48. Write an equation to show this relationship. a. 4n 4 48 b. c. d. 4 4n 48 4n 48 n What is the length of EF? D yd E a. 4 yards b. 3 yards 6 yd x F Not drawn to scale c. 4 yards 6 d. 4 yards Chapter Assessments 9

38 0 Chapter Assessments