The schedule for the course can be viewed on the website at

Transcription

1 MCT4C: Exam Review The schedule for the course can be viewed on the website at All topics are on the exam except for: 1) long/synthetic division (Unit 3 Lesson 6, 7 & 11) and 2) Factor theorem (Unit 3, Lesson 8). You will not need to use the Factor theorem on the exam. I will provide you with the: Quadratic Formula, Sine Law, Cosine Law & Compound Interest formula. You may use a scientific calculator and your powers chart (if you wish to). Review Questions 1. Evaluate the following expressions. a) b) c) d) e) f) g) h) i) j) k) 2. Factor the following expressions. a) b) c) d) 3. Simplify the following expressions. a) b) c) 4. Solve for the variable in following equations. If necessary, express in simplest radical form. You should not round answers in any question here. a) b) c) d) e) f) g)

2 5. Solve the following. Round your final answer only. (2 decimal places) a) b) 6. Sketch the graphs of the following equations. Label the x and y-intercepts for each graph, any asymptotes or other key points depending on the type of graph. a) b) c) d) e) f) g) 7. After various tests it is found that the safe stopping distance, d, in metres, for a boat travelling on calm water at v km/h is given by a) At what speed can the boat travel and still stop safely in 15 m? b) What is the safe stopping distance of a boat travelling 12 km/h? 8. Suppose that a video game company can sell 1500 video games for a price of $45 each. Research suggests that for every $5 increase in price, the company will sell 100 less games. What price will maximize the company s revenue? 9. In 2001, Roy bought an antique slide rule for $25. It is estimated that this item will increase in value by approximately 3% per year. a) Find the approximate value of the slide rule in b) When will the slide rule be worth $50? c) If Roy keeps the slide rule for 50 years what will it be worth? 10. How long will it take for a $1200 investment to double in value if it is deposited into an account that pays 4.5%/a compounded monthly? 11. Suppose that the current population of city is 139,000 and decreasing at a rate of 0.9% per year. a) What will the population of the city be in 5 years? b) How long before the city population is below 100,000 people? 12. The coordinates of point P on the terminal arm of angle in standard position are P(-3, -6). Determine exact values for all 6 trigonometric ratios. Then solve for 13. If find the possible measures for: a) and b).

3 14. A Ferris wheel at a carnival has a diameter of 18m and a lowest point at 2m above the ground. The Ferris wheel moves counter-clockwise at a constant speed. Amy boards the Ferris wheel and starts a stopwatch as soon as the Ferris wheel begins to move. She reaches a maximum height when the stopwatch reads 10 seconds. She reaches her minimum height when the stopwatch reads 26 seconds. a) Define a function that will model Amy s height on the Ferris. b) Find Amy s height when the stopwatch reads 40 seconds. 15. Find an equation for the curves shown below. a) b) 16. Solve each triangle below. a) b) B C 28 cm 23 cm B A cm 43 C A 33 cm 17. Find the area of triangle ABC in question 16a) above. 18. The profit of a company is given by the function where P is profit (in thousands) and t is number of years since the company opened. When did the company make a profit? 19. Calculate the area of the segment below chord AB created by a central angle C. C 14 cm 110⁰ 14 cm A B

4 20. Environmentalists track the population of wolves in a certain area over a period of time. They determine that the population, P of wolves can be modeled using the function: P ( t) 100sin[22.5t] 350, where t is the number of years since the beginning of the study. a) Sketch a graph showing this function. Your graph should include at least 2 cycles. b) State the domain and range of this function. 21. Two ATVs are used to pull a crate. Ropes are attached to the crate of the ATV as shown. Find the magnitude and direction of the resultant force. 22. A sign that weighs 3.7 kg hangs from a horizontal pole. Two cables are used to support the sign as shown below. Find the tension in each wire. (hint: force of gravity = 9.8N/kg) 51⁰ 68⁰

5 ANSWERS 1. a) b) c) d) 4375 e) 3 f) -3 g) h) 3 i) 3 j) 1 k) 2 2. a) (2n 3) (2n + 3) (n 2) b) 2x (x 8) (x + 3) c) (2x + 1) (3x 2) d) (x 1) (x + 1) (x + 3) 3. a) b) c) 16 19x 4. a) b) x = -5, 1 c) x = -9/4 d) x = 2 e) x =2, x = -1, x = -2 f) g) x = 210⁰ or 330⁰ 5. a) 4.92 b)

6 7. a) 45 km/h b) 6.8m 8. $60 per game 9. a) $38 b) in 23.5 years c) $ years (185 months) 11. a)132, 857 b) In 36.4 years a) b) 135⁰ or 315⁰ 14. a) (there are other possible answers) b) 19.3m 15. a) y = -2cos[1/2x] +3 b) 16. a) <B = 81⁰, c = 26.2cm, a = 31.9cm b) A = 56⁰, B = 43⁰, C = 81⁰ between years N, 25⁰ N (left cable), 15.5 N (right cable)