MPM1D Exam Review Chapter 5 Slope

MPM1D Exam Review Chapter 5 – Slope

1. Alexei works during the weekends at a restaurant, earning $10.50 per hour. His pay varies directly with the time, in hours. a) Choose appropriate letters for variables and make a table of values showing Alexei’s pay for 0h, 1h, 2h, 3h, and 4h. b) Graph the relationship. c) Write an equation in the form y  kx .

2. Matt bikes 50km to a friend’s home. The distance, d, in kilometres, varies directly with the time, t, in hours. a) Find an equation relating distance and time if it takes 1.5 hours to travel 24 kilometres. b) What does the constant of variation represent in this problem? c) Use the equation to determine how long it will take Matt to reach his friend’s house.

3. Loreena has $50 in her piggy bank, but withdraws $2.50 each day to buy a chocolate milk and muffin at the cafeteria. Create a table of values, a graph, and an equation to represent the amount of money remaining in her piggy bank each day.

4. The amount of juice varies directly with the amount of water used to prepare it. Tommy used 2L of water to make 2.5L of juice. a) Explain why it makes sense for this relation to be a direct variation. b) Write an equation relating the amount of juice made to the amount of water needed.

5. Identify each of the following as direct variation, partial variation, or neither.

2 2 1 a) y  5x  2 b) C    d c) y  1 x d) y  x  5 e) y   x  3 6 x y 6. a) Complete the table of values on the right, given that y varies partially with respect to x. 0 5 b) Identify the initial value and constant of variation from the table, and use them to 1 9 write an equation in the form y  mx  b . 2 3 17 7. A company is having business cards printed. The cost to design the cards is $25. There s 4 an additional charge of $0.04 per business card printed. 37 a) Identify the fixed cost and variable cost. b) Write an equation representing this relationship. c) Use your equation to determine the total cost of 500 business cards. d) Use your equation to determine the number of business cards that can be purchased for $225.

8. Calculate the slope of each line segment.

C H D E F 9. Calculate the slope of the line through each pair of points. a) (-2, 5) and (4, -8) b) (-7, 8) and (4, 8) c) (32, 630) and (58, 1020)

10. Dalton was biking towards his home at a constant speed. After two hours of cycling he was 55km from home. After 4.5 hours of cycling he was 17.5 km from home. How fast is he cycling?

11. For safety reasons, an extension ladder should have a slope between 6.3 and 9.5 when it is placed against a wall. Determine if the following ladders are within the safe range. a) A ladder reaches 4m up the wall, while the foot of the ladder is 0.5m from the wall. b) A ladder reaches 3m up the wall, while the foot of the ladder is 0.6m from the wall.

12. Determine whether each relation is linear or non-linear. If the relation is linear, determine an equation to represent the relation.

a) x y b) x y c) x y d) x y 0 5 0 14 0 21 3 -15 1 11 1 8 3 13 4 -12 2 17 2 3 6 5 5 -9 3 23 3 -1 9 -3 6 -6 4 29 4 -4 12 -11 7 -3

13. The distance-time graph to the right shows two cyclists that are travelling at the same time. a) Calculate the speed of each cyclist. b) What does the point of intersection of the two lines represent?

Chapter 5 Exam Review – Solutions 1a) 0, $10.50, $21.00, $31.50, $42.00 c) y=10.50x 2a) d=16t b) speed c) 3.125 hours 3) Equation: A  2.50d  50 4a) (0,0) is part of the relation, meaning that 0L of water will make 0L of juice b) J  1.25W 5a) partial b) direct c) partial d) neither e) partial 6a) (2, 13), (4, 21), (8, 37) b) initial value: 5, constant of variation: 4, equation: y  4x  5 7a) fixed cost: $25, variable cost: $0.04 per card b) C  0.04n  25 c) $45 3 1 13 d) 5000 8) AB: CD:  EF: 0 GH: undefined 9a)  b) 0 c) 15 10) 15 km/h 11a) safe b) unsafe 2 4 6 8 12a) linear, y  6x  5 b) non-linear c) linear, y   x  21 d) linear, y  3x  24 13a) A: 10km/h B: 20km/h 3 b) The point where cyclist B passes cyclist A.