Ch. 3 Review. Name: Class: Date: Short Answer

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1 Name: Class: Date: ID: A Ch. 3 Review Short Answer 1. A developer wants to subdivide a rectangular plot of land measuring 600 m by 750 m into congruent square lots. What is the side length of the largest possible square? 2. One neighbour cuts his lawn every 8 days. Another neighbour cuts her lawn every 10 days. Suppose both neighbours cut their lawns today. How many days will pass before both neighbours cut their lawns on the same day again? 14. Factor: 3b b Complete: (a + 6)(a ) = a 2 + a Which multiplication sentence does this set of algebra tiles represent? 3. Determine the perfect square whole number closest to How many perfect square whole numbers are between 5000 and 6000? 5. An aquarium approximates a cube with surface area 1014 square feet. Water was poured into the empty aquarium at a rate of 6 cubic feet per minute. To the nearest minute, how long did it take to fill the aquarium? 6. Factor the binomial 44a + 99a Factor the trinomial 4 8n + 12n Factor the trinomial 33b b Factor the trinomial 24c 3 d 40c 2 d 2 32cd Which set of algebra tiles represents 3x 2 + x + 4? 18. Expand and simplify: (6p + 3)(5p 6) 19. Factor: 25x x Factor: 4 9z 13z Factor: 96w w Expand and simplify: (6x y)(3x + 8y) (2x 3y) Simplify the expression 23w 3 5w 2 x + 8wx 2 8w 3 13wx w 2 x, then factor. 11. Expand and simplify: (4 r)(7 r) 12. Factor: t 2 + 9t Factor: 24 2x + x 2 1

2 Name: ID: A 23. Each shape is a rectangle. Write a polynomial, in simplified form, to represent the area of the shaded region. 26. Factor: 16p 2 81q Factor: 49s 2 112st + 64t Factor: 3z 4 768z Identify this polynomial as a perfect square trinomial, a difference of squares, or neither. 9a 2 + 9a Write the prime factorization of Factor: 121a a Factor: 36 60r + 25r Determine the greatest common factor of 56 and Determine the least common multiple of 48, 72, and 108. Problem 33. Jordan wants to cut a rectangular carpet with dimensions 32 cm by 80 cm into squares of equal size. a) What is the side length of the largest possible square Jordan can cut? b) How many squares can she cut from carpet? 36. Find the area of the rectangle. 34. Calculate the volume of the largest possible sphere that can fit in a cube with volume cm 3. Give the volume to the nearest tenth of a cubic centimetre. Explain your steps. 35. A square is drawn inside a circle with radius 11x. a) Write an expression for the area of the shaded region. b) Factor the expression. 2

3 Ch. 3 Review Answer Section SHORT ANSWER m days h 6 min 6. 11a(4 + 9a) 7. 4(1 2n + 3n 2 ) 8. 11(3b 2 9b 7) 9. 8cd(3c 2 + 5cd + 4d 2 ) 10. 5w(3w 2 + 5wx x 2 ) r + r (t + 12)(t 3) 13. ( 6 + x)(4 + x) 14. 3(b + 1)(b 6) 15. (a + 6)(a 2) = a 2 + 4a (2x + 2)(2x + 2) p 2 21p (25x + 8)(x + 2) 20. (4 13z)(1 + z) 21. 6(8w 1)(2w + 7) x xy 17y x x (11a + 5) (6 5r) (4p + 9q)(4p 9q) 27. (7s 8t) z 2 (z + 16)(z 16) 29. Neither

4 PROBLEM 33. a) The shorter side of the carpet measures 32 cm. So, the side length of the square must be a factor of 32. The longer side of the carpet measures 80 cm. So, the side length of the square must be a factor of 80. So, the side length of the square must be a common factor of 32 and 80. The side length of the largest square will be the greatest common factor of 32 and 80. Check to see which factors of 32 are also factors of 80. The factors of 32 are: 1, 2, 4, 8, 16, 32 The factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 The greatest common factor of 32 and 80 is 16. The side length of the largest possible square is 16 cm. b) Find the number of squares Jordan can cut from the carpet: Area, A, of the carpet: A = lw A = (32 cm)(80 cm) A = 2560 cm 2 Area, A, of the largest possible square is: A = lw A = (16 cm)(16 cm) A = 256 cm 2 Divide the area of the carpet by the area of the largest possible square cm cm 2 = 10 Jordan can cut 10 squares from the carpet. 2

5 34. To determine the volume of the sphere, first determine the edge length of the cube. The edge length, e, of a cube is equal to the cube root of its volume. 3 e = e = 13 The radius, r, of the largest sphere that will fit in the cube is one-half of the edge length of the cube. r = 1 2 (13) r = 6.5 Use the formula for the volume of a sphere. V = 4 3 πr 3 V = 4 3 π(6.5)3 V = Τhe volume of the largest possible sphere that can fit in the cube is approximately cm 3. 3

6 35. a) The area of the shaded region is the area of the circle minus the area of the square. Use the formula for the area of a circle. A = πr 2 A = π(11x) 2 A = 121πx 2 To determine the area of the square, first determine the side length, s, of the square. Use the Pythagorean Theorem in right ABC. s 2 = AB 2 + BC 2 s 2 = (11x) 2 + (11x) 2 s 2 = 121x x 2 s 2 = 242x 2 s = 242x 2 Use the formula for the area, A, of a square. A = s 2 Ê ˆ A = 242x 2 Ë Á A = 242x 2 2 The area, A, of the shaded region is:. A = 121πx 2 242x 2 b) 121πx 2 242x 2 = 121x 2 (π 2) 36. Use the formula for the area, A, of a rectangle. A = l w A = ( 5b 6) ( 3b 2) Use the distributive property. A = 5b(3b 2) + ( 6)(3b 2) A = 15b 2 10b 18b + 12 A = 15b 2 28b + 12 The area of the rectangle is 15b 2 28b + 12 square units. 4

Determine the surface area of the following square-based pyramid. Determine the volume of the following triangular prism. ) + 9.

Determine the surface area of the following square-based pyramid. Determine the volume of the following triangular prism. ) + 9. MPM 1D Name: Unit: Measurement Date: Calculating and of Three Dimensional Figures Use the Formula Sheet attached to help you to answer each of the following questions. Three problems are worked out for