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SOLUTIONS TO MATH REVIEW Ch. 1 Ch. 2 1. 40 boys and 60 girls 1. a) 40.5 2. 120 gumballs and 130 chocolate bars b) 11 c) 303 d) 332 3. 400 blue and 100 red e) 138 4. $250. f) 30 5. 0.4 hours or 24 minutes. g) 8 6. $57.50 2. 24 (24 x 12 =288) packages of wieners 36 (36 x 8 =288) packages of buns 3. Red: 10: 10, 20, 30, 40, 50, 60, 70, 80, 90 Con.: 25: 25, 50, 75, 100 S.S.: 15: 15, 30, 45, 60, 75, 90 7. a) 36% b) 19% No cars will be a red convertible with a built in stereo system. Ch. 5 1. rectangle Area = 80 cm² Perimeter = 36 cm triangle Area = 25 m² Perimeter = 40 m parallelogram Area = 30 cm² Perimeter = 50 cm trapezoid Area = 210 m² Perimeter = 48 m right triangle Area = 6 m² Perimeter = 12 m parallelogram Area = 7.5 m² Perimeter = 54 m 2. a) Perimeter: 36 cm Area: 56 cm² b) She will have to pay $28. 3. a) Perimeter: 124.7 m Area: 900 m² c) He will have to pay $9000. Ch. 3 a) Students' Grades 120 100 Grade (%) 80 60 40 20 0 0 1 2 3 4 5 Student b) Student 7 c) Student 3, 5 d) 44 e) 75 f) 75 g) 74.5 6 7 8 9 Ch. 6 Ch. 8 1. -9 6. -16 1. $10 2. -1 7. -10 2. $12.50 3. 10 8. -12 3. $9 4. -2 9. -31 4. $210 5. -25 10. 19 5. # of stars = 4 x Figure # –2 OR y = 4x – 2 6. 398 stars Ch. 9 1. a) > b) > c) < d) > e) Pat got the bigger piece because if you cut the cake into 5 slices, the pieces will be bigger than is you cut a cake into 7 slices. 2. a) < b) < c) Noah got the bigger piece. 4. 40 crabby patties have no lettuce. 5. 350 red seats = 117 red seats for children 233 red seats for adults 150 grey seats = 60 grey seats for children 90 grey seats for adults 6. ** Note the fraction for green gumballs should have read 80 blue gumballs = 40 with dots and 40 without dots 60 red gumballs 60 green gumballs 15 12 and not 50 50 7. a) 3 40 b) 31 40 c) 9 40 Ch. 10 1. A net is a 2D pattern that can fold into a 3D object. 2. Congruent means the same. 3. The intercept the point where 2 lines cross each other. 4. The 2 red lines are the diagonals of the rectangle and the black dot is the point of intersection of the diagonals. 5. A quadrilateral is any shape with 4 sides that are straight lines. 6. An isosceles triangle has 2 sided that measure the same. 7. An equilateral triangle has all of its sides measuring the same. 8. Parallel lines go in the same direction and never touch. 9. Complementary angles are 2 angles that add up to 90˚ 10. Supplementary angles are 2 angles that add up to 180˚ 11. Vertically opposite angles are 2 angles are the same degree and the make an “X”. 12. Alternate interior angles are 2 angles are the same degree and the make an “Z”. 13. They can only be formed when there are 2 parallel lines. 14. a) Angle <1 = 90˚ <2 = 60˚ <3 = 30˚ <4 = 90˚ <5 = 60˚ Reason Corner of a rectangle is 90˚ All angles in a triangle add up to 180˚ ( 30˚ + 90˚ + 60˚ = 180˚) Alternate interior angle Corner of a rectangle is 90˚ All angles in a triangle add up to 180˚ ( 30˚ + 90˚ + 60˚ = 180˚) OR Complementary angle (30˚ + 60˚ = 90˚) b) Angle <1 = 120˚ <2 = 30˚ <3 = 30˚ <4 = 75˚ <5 = 60˚ Reason Supplementary angle (60˚ + 120˚ = 180˚) All angles in a triangle add up to 180˚ ( 30˚ + 120˚ + 30˚ = 180˚) Alternate interior angle Complementary angle (15˚ + 75˚ = 90˚) All angles in a triangle add up to 180˚ ( 30˚ + 75˚ + 75˚ = 180˚) Ch. 11 1. i) Length = 5 m Width = 10dm = 1 m Height = 220 cm = 2.2 m Area = 36.4 m² Volume = 11 m³ 2. Box 1 will cost $10 x 36.4 = $364 Box 2 will cost $10 x 62 = $620 So box 1 will be cheaper to paint. Ch. 12 4 11 4 b) P(M or T) = 11 c) P(N) = 0 1. a) P(a vowel) = ii) Length = 3 m Width = 2 m Height = 50 dm = 5 m Area = 62 m² Volume = 30 m³ 2. 1st draw 2nd draw 100 tickets 2 prizes 99 tickets 1 prize P(prize) = 2 1 = 100 50 P (prize, prize ) = P(prize) = 1 99 1 1 1 X = is the probability of winning the 2 prizes 4950 50 99 3. a) Since you are the 1st person, you start with 50 lollipops in the bag. 1st draw 2nd draw 50 lollipops 20 red 20 blue 10 green 10 1 P(green) = = 50 5 49 lollipops 20 red 20 blue 9 green 20 P(blue) = 49 P(green, blue) = b) 1 20 20 4 X = = is the probability of getting a green and a blue. 5 49 245 49 Since you are the 2st person, you start with 48 lollipops in the bag, because the 1st person already took out 2 blue lollipops 1st draw 2nd draw 48 lollipops 20 red 18 blue 10 green 47 lollipops 20 red 18 blue 9 green 18 P(blue) = 47 P(green) = 10 5 = 48 24 P(green, blue) = 5 18 15 90 X = = is the probability of getting a green and a blue. 24 47 1128 188