1-4. a: 40 b: 6 c: 7 d: a: 3 b: 5 c: 6 d: 2

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1 Lesson Shapes (a), (c), (d), and (e) are rectangles a: 40 b: 6 c: 7 d: a: 3 b: 5 c: 6 d: a: 22a + 28 b: 23x 17 c: x 2 + 5x d: x 2 + 8x 1-7. Possibilities: Goes to bank, gets money from parent, gets paid; buys lunch, goes shopping, pays a bill, Lesson Answers vary. Possible responses include How many sides does it have?, Does it have a right angle?, Are any sides parallel? Answers vary. Possible responses include They have 3 sides of equal length and They have 3 angles of equal measure a: 3 b: 2 c: a: x = 7 b: c = 4.5 c: x = 16 d: k = a: 12 b: 35 c: 24 d: 7 Lesson c is correct; x = No if the points are collinear then they will not form a triangle See answers in bold below. y = x 3 x y a: 55.5 sq. units b: 42 sq. units a: 5 b: 12 c: 7 Selected Answers 2014 CPM Educational Program. All rights reserved. 1

2 Lesson a: x = = b: No solution c: x 6.44 d: x = Yes, his plants will be dead. If his plants are indoors, they will be dead because he will be gone for 2 weeks and so he did not water them at least once a week. If he left them outdoors, they will still be dead because it has not rained for 2 weeks, so he needed to water them once a week as well a: y = 2 3 x 4 b: y = a: 6x + 6 b: 6x + 6 = 78, so x = 12 and the rectangle is 15 cm by 24 cm. ( )( 2 + 3) = 360 c: a: 5 3 b: 6 3 = 2 1 = 2 c: 6 3 = 1 2 d: 0 7 = 0 Lesson a: 100 b: 170 c: a: Yes, it is correct because the two angles make up a 90 angle. b: x = 33 so one angle is = 23 while the other is 2(33) + 1 = Perimeter: 74 centimeters, Area: 231 cm a: y = 5 b: r = 12 c: a = 6 d: m = While there are an infinite number of rectangles, possible dimensions with integral measurements are: 1 by 24 (perimeter = 50 units), 2 by 12 (perimeter = 28 units), 3 by 8 (perimeter = 22 units), and 4 by 6 (perimeter = 20 units). Selected Answers 2014 CPM Educational Program. All rights reserved. 2

3 Lesson See graph at right. y y = 3x a: % b: = 13 1 c: 0 d: % 4 4 y = 2 3 x x x 2 + 2x + 6 = 67, x = 9, so 5(9) 2 = 43 miles 4 y = 4x a: x = 3.75 b: x = 3 c: x = 0 d: x = 3 e: x f: x = The flag would need to be a rectangle. The height of the cylinder would match the height of the rectangle along the pole, and the cylinder s radius would match the width of the rectangle. Lesson Yes; yes; no a: Reflection b: Translation (or two reflections over parallel lines) c: Rotation or rotation and translation d: Rotation or rotation and translation depending on point of rotation e: Reflection f: Reflection and then translation or rotation or both x +10x + 3 = 52, so x = 2. Side lengths are 19, 10, and a: Area 16 square units b: Area 15 square units a: y = 4 b: y = 25 c: y = 2 Selected Answers 2014 CPM Educational Program. All rights reserved. 3

4 Lesson a: Yes b: 2 5 c: 3 5 d: 1 5 e: a: y = 5 2 x 3 b: y = 3 2 x C a: p = 5 b: w = 20 c: x = 14 d: y = See answers in bold below. y = 3x + 2 x y Lesson a: Yes. It has four sides. mab = mcd = 1 2 and mbc = mad = 2, so each pair of consecutive sides is perpendicular and forms 90 angles. b: A (4, 3), B (6, 1), C ( 2, 5), D ( 4, 1) a: x = 4.75 b: x = 94 c: x 1.14 d: a = a: There are 10 combinations: a & b, a & c, a & d, a & e, b & c, b & d, b & e, c & d, c & e, d & e b: Yes. If the outcomes are equally likely, we can use the theoretical probability computation in the Math Notes box in Lesson c: 3 10 d: 9 10 e: The outcomes that satisfy part (d) include the outcomes that satisfy part (c), but there are others on the part (d) list as well a: y = 4 3 x b: The resulting line coincides with the original line; y = 4 3 x 2 c: The image is parallel; y = 4 3 x 7 d: They are parallel, because they all have a slope of 4 3. e: y = 3 4 x +16 Selected Answers 2014 CPM Educational Program. All rights reserved. 4

5 Lesson ; No, this probability is very small a: (9, 3) b: (3, 3) c: ( 2, 7) d: ( 52, 1483) a: 10 square units b: 20 square units c: 208,680 square units a: b: A B P l c: d: C D Q m a: The orientation of the hexagon does not change. b: The orientation of the hexagon does not change. c: There are 6 lines of symmetry, through opposite vertices and through the midpoints of opposite sides. Selected Answers 2014 CPM Educational Program. All rights reserved. 5

6 Lesson (a) and (b) are perpendicular, while (b) and (c) are parallel a: One possibility: 4(5x + 2) = 48 b: x = 2 c: = 144 square units a: 4 52 = 1 13 b: = 1 4 c: 1 52 d: = a: It looks the same as the original. b: Solution should be any value of 45k where k is an integer. c: circle a: b: A l B P c: d: Q C D m Selected Answers 2014 CPM Educational Program. All rights reserved. 6

7 Lesson Carol: only inside circle #2, Bob: outside both circles, Pedro: only inside circle #1. In order to belong to the intersection of both circles, a person would need to have long hair and study a lot for class a: Sandy s probability = 2 4, while Robert s is 5 3. Therefore, Robert has a greater chance. b: Sandy (Sandy s probability = 1 while Robert s is 0) c: Sandy s probability = 4 3, while Robert s is 5 3. Therefore, Sandy is more likely to select a shape with two sides that are parallel a: x = 33 9 = 11 3 b: x = 5 and x = 2 3 c: x = 1 d: x = a: heart b: square c: hexagon d: Answer vary a: ( 6, 3) b: The vertices are: (6, 2), (2, 3), (5, 6) c: (8, 3) Lesson Isosceles: (a) and (c); Scalene: (b) a: 7 16 c: % b: % 6% d: 6 16 = % a: isosceles triangle b: pentagon c: parallelogram d: obtuse scalene triangle e: isosceles right triangle f: trapezoid Reflection only: A, B, C, D, E, M, T, U, V, W, Y Rotation only: N, S, Z Intersection only: H, I, O, X Outside both regions: F, G, J, K, L, P, Q, R a: x = 2 b: x = 2 3 = c: x = 3 d: No solution Selected Answers 2014 CPM Educational Program. All rights reserved. 7

Chapter Possibilities: goes to bank, gets money from parent, gets paid; buys lunch, goes shopping, pays a bill,

Chapter Possibilities: goes to bank, gets money from parent, gets paid; buys lunch, goes shopping, pays a bill, 1.1.1: Chapter 1 1-3. Shapes (a), (c), (d), and (e) are rectangles. 1-4. a: 40 b: 6 c: 7 d: 59 1-5. a: y = x + 3 b: y =!x 2 c: y = x 2 + 3 d: y = 3x! 1 1-6. a: 22a + 28 b:!23x! 17 c: x 2 + 5x d: x 2 +