Name:

Time Allowed: 80 minutes Total Value: 40 marks Number of Pages: 8

Instructions: Non-programmable, non-graphing calculators are permitted. No other aids allowed. Check that your test paper has no missing, blank, or illegible pages. Note that test questions appear on both sides of the paper. Answer in the spaces provided. Show all your work. Insu¢ cient justi…cation will result in a loss of marks.

1. [3 marks] Let A =

2 1

4 1

3 2

, B=

1 3

0 1

2 1

Determine each of the following: (a) 3A B

1 and C = 4 4 1

2

2 0 1

3 0 25. 3

(b) BC

1

2. [3 marks] Simplify each of the following expressions. 2x3 y (xy 4 ) 2 3 2

(a)

(b)

x2

x2 4 6x2 3x 2 + 7x + 10 + 3x 10 x

3. [3 marks] Solve the following inequality for x. State your answer using interval notation. 2 x 3 x 2

2

4. [3 marks] Solve the system of linear equations if it is consistent, or prove that there is no solution if the system is inconsistent: 2y + z 4x 5z 10x + 4y + 8z x = = = 2 1 4

5. [2 marks] A business-copier repair company charges a …xed amount F , plus an hourly rate R for a service call. A customer is billed $159 for a one-hour service call and $287 for a three-hour service call. Determine the …xed amount and the hourly rate the company charges for a service call.

3

6. [2 marks] Determine an equation of the line which has a x-intercept of 3 and passes through the point (5; 1).

7. [2 marks] Consider the parabola given by y = 2x2 (a) Determine the x-intercepts of the parabola.

8x

1.

(b) Determine the coordinates of the parabola’ vertex. s

4

8. [4 marks] Consider the functions f (x) =

p x+3 and g (x) = x x2 4

3.

(a) State the domain of f and the domain of g.

(b) Determine f (2 + h) and simplify the resulting expression.

(c) Determine (f

g) (x) and then evaluate (f

g) (12).

5

9. [6 marks] Solve each of the following equations for x. (a) 36x 5

= 27x+1

(b) 2e3x

1

= 23

(c) log2 (x + 4) = 3

6

10. [3 marks] Evaluate each of the following expressions exactly (calculator answers will receive no marks): (a) 5 log64 4 (b) 32 log3 6 log3 9

11. [2 marks] (a) Which of the following graphs represents the function f (x) = 7 4 x

?

y

2 1

y

2 1

-3

-2

-1 -1 -2

1

2

x

3

-3

-2

-1 -1 -2

1

2

x

3

A

2 1

B

2 1

y

y

-3

-2

-1 -1 -2

1

2

x

3

-3

-2

-1 -1 -2

1

2

x

3

C Answer: ________

D

From the graph,

x! 1

lim

7 4

x

= _________

(b)

Consider the graph of a function y = g (x) given to the right. Evaluate:

y

5 4 3

(i) lim g (x) =

x!2

2 1

(ii) lim g (x) =

x!5

2 -1

4

6

x

8

7

12. [6 marks] Determine the derivative of each of the following functions. (a) f (x) = x2 2x + 5 p x

(b) g (x) = (2x + 3)

5

ln 4

x + 2x3

(c) h (x) =

ex

3

23 4x x2 + 1

8