Patterns and Relations Unit Review

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1 Patterns and Relations Unit Review 1. In the equation, determine the value of R when w = 13.. The pattern in this table continues. Write an equation that relates the number of squares to the figure number. Figure Number, f Number of Squares, s The cost of a taxi ride is the sum of a fixed cost of $.50 for the first kilometre, plus $1.75 for each additional kilometre. a) Write an equation that relates the cost of a taxi ride, F dollars, to the distance travelled, n. b) Determine the cost of a 8-km taxi ride.. Here is a pattern made with toothpicks. The pattern continues. Figure 1 Figure Figure 3 a) Write an equation that relates the number of toothpicks, N, to the figure number, n. b) How man toothpicks are needed for figure 80? 5. Which graphs represent a linear relation? x 1 R 3 5 Q P. Which equations represent a linear relation? i iv)

2 7. a) Which table of values represents a linear relation? i x x x b) Write an equation that represents the linear relation. 8. a) Create a table of values for the linear relation. Use,, 0,, for values of x.. x 0 9. Create a table of values for the linear relation, then graph the relation. Use values of x from 0 to. x

3 x A helicopter is at a height of 100 m when it starts descending to land. The helicopter s height changes at an average rate of 10 m/min. a) Write an equation that relates the height of the helicopter, H metres, to the time since the helicopter began its descent, t minutes. b) What is the height of the helicopter 9 min after it began its descent? 11. Graph the equation. 0 x 1. Graph the following lines on the same grid. Label the lines.

4 0 x 13. Graph these equations on the same grid. What shape is formed b the lines? i iv) 0 x 1. Graph the following lines on the same grid. What shape do the form? i

5 x 15. a) Graph the straight line that passes through the points (0, 10), (3, 7), and (10, 0) x b) Write an equation to describe the line. 1. Match each equation with a graph on the grid below. i

6 Graph A Graph B Graph C 0 x 17. Match each equation with a graph on the grid below. i iv) 10 8 Graph D Graph C Graph A Graph B 0 x Which graph on this grid has the equation x + = 3?

7 8 Graph A Graph B Graph C 0 x 19. Match each equation with a graph on the grid below. i 1 8 B A x C This graph represents a linear relation. a) Estimate the value of when x = 7. b) Estimate the value of x when = 5.

8 x 8 1. This graph represents a linear relation. a) Estimate the value of when. b) Estimate the value of x when x This graph shows the gas consumption rate of a car. a) Estimate the volume of gas required to travel 30 km. b) Estimate the distance the car can travel on 0 L of gas.

9 Consumption (L) 70 Gas Consumption Distance (km) 3. A large white square represents an x -tile, a black rectangle represents a x-tile, and a small white square represents a 1-tile. What polnomial does this collection of algebra tiles represent?. What algebra tiles would ou use to model the polnomial? 5. Which of the following expressions are polnomials? i iv). Is each expression a monomial, binomial, or trinomial? a) b) x c) d) e) 7. Name the coefficients, variable, degree, and constant term in the polnomial. 8. Identif the degree of each polnomial.

10 a) b) c) d) e) 9. Write a polnomial that matches this description: variable: p; degree: ; binomial; constant: Identif the polnomials that can be represented b the same set of algebra tiles. i iv) v) 31. A large white square represents an x -tile, a large black square represents a x -tile, a white rectangle represents an x-tile, a black rectangle represents a x-tile, a small white square represents a 1-tile, and a small black square represents a 1-tile. Match each polnomial with its corresponding algebra tile model. i iv) v) v Model A Model B Model C Model D Model E

11 Model F 3. A large white square represents an x -tile, a large black square represents a x -tile, a white rectangle represents an x-tile, and a black rectangle represents a x-tile. Write the simplified polnomial. 33. Combine like terms. Sketch algebra tiles if it helps. 3. Group like terms. 35. Simplif: 3. A white rectangle represents an x-tile, a black rectangle represents a x-tile, a small white square represents a 1-tile, and a small black square represents a 1-tile. Write the polnomial sum modelled b this set of tiles A large white square represents an x -tile, a large black square represents a x -tile, a small white square represents a 1-tile, and a small black square represents a 1-tile. Write the polnomial sum modelled b this set of tiles. +

12 38. Add: 39. Add: 0. Add:. 1. Write the perimeter of this equilateral triangle as a polnomial in simplest form. 9x + 5. Subtract: 3. Subtract:. Subtract: 5. Subtract:. Subtract: 7. Subtract: 8. A white rectangle represents an x-tile and a small white square represents a 1-tile. Write the multiplication sentence modelled b this set of algebra tiles. Determine the product. 9. Multipl: 50. Divide: 51. Here is a student s solution for this question:

13 Identif the errors in the solution. 5. A large white square represents an x -tile, a white rectangle represents an x-tile, and a small white square represents a 1-tile. Write a division sentence that is modelled b these algebra tiles. 53. Divide: 5. Multipl: 55. Divide: 5. Here is a student s solution for this question: Divide: Identif an errors in the solution. 57. Here is a student s solution for this question: Multipl: Identif an errors in the solution.

14 58. Determine the product: 59. Determine the quotient: 0. Solve: 1. Solve:. Solve: 3. Solve:. Here is a student s solution for this question: Solve: Identif an errors in the solution. 5. Solve:, c 0. Fort-four divided b a number is 11. Write, then solve an equation to determine the number. 7. Solve: 8. Solve: 9. Solve: 70. Write numbers that are solutions of this inequalit: 71. Write an inequalit whose solution is graphed on the number line x

15 7. Which of these numbers is a solution of?.5,.7,.1,.3, Graph the solution of on a number line w 7. Graph the solution of m 3 1 on a number line m 75. Which operation will ou perform on each side of the inequalit to isolate the variable? 7. Which operation will ou perform on each side of the inequalit to isolate the variable? 77. Solve: 78. Solve: 79. Solve, then graph this inequalit: x 80. Solve, then graph this inequalit: Solve, then graph this inequalit: x 8. Claire has $18. She wants to bu a book and a magazine. The book costs $13.8. How much can Claire spend on a magazine? a) Choose a variable, then write an inequalit that can be used to solve this problem. b) Solve the problem. 83. State whether ou would reverse the inequalit sign to solve each inequalit. a) b) c)

16 d) 8. Solve: 85. Write, then solve an inequalit to show how man magazines ou would have to sell at $ each to raise at least $ Solve. Graph the solution Solve: 88. Solve: 89. Solve: 90. When 3 times a number is subtracted from 15, the result is less than 9. Write and solve an inequalit to determine the number.

5.1 Modelling Polynomials

5.1 Modelling Polynomials FOCUS Model, write, and classify polynomials. In arithmetic, we use Base Ten Blocks to model whole numbers. How would you model the number 234? In algebra, we use algebra tiles