MCT4C Practice Final Exam

KNOWLEDGE SECTION

1. Solve each triangle below. a) b)

B C 28 cm

23 cm B

33 cm 56° A 43° A 38 cm C

2. Sketch the graph of on a clearly labelled graph, showing nice points to demonstrate your understanding.

3. Find the resultant force vector given the following;

4. Find the horizontal and vertical components following vector. Draw them in.

5. Simplify the expression

6. Evaluate (a) log 2 16 (b) log 6 1 c) log 8 4  log 8 16

7. Factor each expression. a) b) c) 푥3 − 3푥 − 2

8. Without the use of technology, sketch the graph of

9. Solve for all unknown values.

APPLICATION SECTION

10. The coordinates of point P on the terminal arm of angle X in standard position are P(-3, -6). Determine exact values for all 6 trigonometric ratios. Then solve for X.

11. If find the possible measures for: a) and b) tan 퐴 = −2.34.

12. Find the amplitude, period, phase shift, vertical displacement then the equation for the following trig functions:

13. 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.

14. The number of Canadian cellular phone subscribers, s, has grown according to the formula s 1300001.45n , where n is the number of years since 1987.

(a) At this rate, how many phone subscribers will there be in 2002? (b) When will the number of phone subscribers reach 10 million?

15. Solve the following exponential equations using the most appropriate method. a) 7푥 = 15 b) 4푥+1 = 32푥

16. Consider the function 푓(푥) = 푥3 + 3푥2 − 4푥 − 12. a) State the degree of the function, the y-intercept and describe the end behaviours. b) Calculate f(2) and describe what your calculation tells you about the graph of y = f(x). c) Solve the polynomial equation 푥3 + 3푥2 − 4푥 − 12 = -12 . d) Show all of this information on a sketch of y = f(x).

17. A rectangular prism will have width, length and height in the ratio 1:2:4. The volume is 1 L exactly. Find the dimensions.

THINKING SECTION

18. A ferris wheel with a radius of 7m makes one revolution every 16 seconds. The bottom of the wheel is 1.5m above the ground. a) Draw a graph to show how a persons height above ground varies with time. b) Find the equation of this function, assuming it is a cosine function.

19. Sketch the graphs of 푦 = 4 cos 30푥 and 푦 = 2푥 on the same set of axes. How many solutions to the equation 4 cos(30푥) = 2푥 are there in the domain 0 ≤ 푥 ≤ 3? Explain briefly. Estimate the solution(s).

20. A cubic function has zeros –3, -1 and 2. The y intercept of its graph is 12. Determine the equation of the function.

21. How many of these objects could you mold from a vat of liquid plastic that is in a cylindrical container with height 2.5 m and diameter 2 m?