Math 9 Review (Chapters 5 and 7) Problem 1. Brenda rides her bike to work. She must travel 12 blocks to leave her neighbourhood. Once she leaves her neighbourhood, she must travel 2100 m along a main road to get to her job. a) Write an expression to show the distance, in metres, she must travel to get to work. If each block in her neighbourhood is 150 m long, represent her total trip to work using a single term. 2. The perimeter of the triangle below can be represented by the polynomial. What is the missing side length? 3. Calculate the perimeter of the triangle shown. 4. A farm hand can move n bales of hay per hour when he is fresh. When he gets tired, however, he moves 5 fewer bales of hay per hour. One day, he works 3 h at top speed, then another 4 h at the slower speed. Write an expression to show how many bales of hay he moved. Simplify your answer. 5. Helen is fencing off two areas for her rabbits and her chickens. The length of one area is 2 m more than double its width. The length of the other area is 3 m less than its width. a) If the width of both areas is the same, write an expression to describe how much fencing she will require to fence both areas. If the width of both areas is 6 m, how much fencing will she need? 6. To raise money for new uniforms, the school volleyball team held a bake sale where they sold cookies, squares, and muffins. The number of cookies sold is twice the square of the number of muffins sold. Only 10 squares were sold. a) Write an expression to represent the total number of baked goods sold at the bake sale. A month after the first bake sale, the team had another bake sale which was much more successful. This time they sold three times as much of each baked good as they sold in the first bake sale. Use a simplified expression to show the number of baked goods they sold during this sale. c) How many more items did they sell at the second bake sale? Show your thinking. 7. a) Create a model to represent the addition and subtraction of the following polynomials.
Simplify the model. 8. a) Create a model to represent the addition of the following polynomials. Simplify the model. 9. Simplify the following expression by collecting like terms. 10. Karen sells her crafts on the Internet. When shipping her crafts, she charges a flat fee for the package plus a set amount for each small item and a different set amount for each large item. Her shipping rates are all based on the fee for a small item. The flat fee is 3 times the square of the small-item fee, while the charge for a large item is 1 less than twice the small-item fee. a) Write and simplify an expression for shipping one large and one small item. Write and simplify an expression for shipping two small items and three large items. c) If the charge for a small item is $2, what would be the cost of shipping the package described in part? 11. Write a simplified expression for the area of the triangle. 12. A garden has the dimensions shown. a) Determine an expression to represent the area of the garden. What is the area of the garden if x = 6 m?
Math 9 Review (Chapters 5 and 7) Answer Section PROBLEM 1. ANS: Examples: a) Let b represent 1 block in metres. Brenda travels m to work. Express the distance on the main road as a number of blocks. Total distance She travels 26b to work. PTS: 1 DIF: Difficult+ OBJ: Section 5.2 NAT: PR6 TOP: Equivalent Expressions KEY: expression term 2. ANS: Example: The missing side length is. PTS: 1 DIF: Average OBJ: Section 5.3 NAT: PR5 KEY: polynomial subtraction perimeter 3. ANS: The perimeter is. PTS: 1 DIF: Easy OBJ: Section 5.3 NAT: PR5 KEY: polynomial subtraction perimeter 4. ANS: Number of bales moved per hour when fresh. Number of bales moved per hour when tired. He moved bales. PTS: 1 DIF: Average OBJ: Section 5.3 NAT: PR5 KEY: expression variable
5. ANS: Example: a) Perimeter of area Helen will need m of fencing. Helen will need 58 m of fencing. PTS: 1 DIF: Difficult OBJ: Section 5.3 NAT: PR6 KEY: expression 6. ANS: Example: a) Number of muffins sold is represented by m. Number of cookies sold = Number of squares sold = 10 There were baked goods sold. Number of baked goods sold There were c) They sold baked goods sold at the second bake sale. more items at the second bake sale. PTS: 1 DIF: Difficult+ OBJ: Section 5.3 NAT: PR5 KEY: expression 7. ANS: a) PTS: 1 DIF: Difficult OBJ: Section 5.2 NAT: PR6 TOP: Equivalent Expressions KEY: model expression polynomial 8. ANS: a)
PTS: 1 DIF: Average OBJ: Section 5.2 NAT: PR6 TOP: Equivalent Expressions KEY: model expression polynomial 9. ANS: PTS: 1 DIF: Average OBJ: Section 5.3 NAT: PR6 KEY: expression polynomial simplify 10. ANS: a) Fee for small item = c Fee for large item = Fee for package = The cost of shipping this package can be expressed as. The cost of shipping this package can be expressed as. c) The cost of shipping this package would be $25. PTS: 1 DIF: Difficult+ OBJ: Section 5.2 Section 5.3 NAT: PR5 PR6 TOP: Equivalent Expressions Adding and Subtracting Polynomials KEY: expression simplify 11. ANS: An expression for the area of the triangle is 4x 5x 2.
PTS: 1 DIF: Average OBJ: Section 7.2 NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a binomial by a monomial area simplify 12. ANS: a) An expression for the area of the garden is. The area of the garden is 102 m 2. PTS: 1 DIF: Difficult OBJ: Section 7.2 NAT: PR7 TOP: Multiplying Polynomials by Monomials KEY: multiplying a polynomial by a monomial area model