SAIT Pre-calculus Self-diagnostic Test Page 1

SAIT Pre-calculus Self-diagnostic Test 2012

Welcome to the pre-calculus self-test. Take this test to see if you are ready for MATH 235 or

MATH 238. The answer key is at the end of this test.

1. 2 9 3x x

True

False

2. 32332 22 xxxx

True

False

3. sin x2 is the same as sin

2x

True

False

4. The x intercept for the line represented by

the equation 3 4 7 0x y is

a. 7

,03

b. 7

0,3

c. 7

,03

d. 7

,04

e. 7

0,3

SAIT Pre-calculus Self-diagnostic Test Page 2

5. (cos x)2 is the same as cos

2x

True

False

6. xsin

1 is the same as arcsinx. Arcsinx means the inverse function.

True

False

7.

2sinsin

xx

x

True

False

8.

222

222

x

x

x

True

False

9. 11

1

yx

yx

True

False

SAIT Pre-calculus Self-diagnostic Test Page 3

10. 12

2

x

x

True

False

11. 2

12

x y z

z y x

True

False

12. 3

1

2 x is the same as

a.

1

32x

b.

1

32x

c.

1

3

2

x

d.

1

3

2

x

13. (x2 + y)

2 = x

4 + y

2

True

False

SAIT Pre-calculus Self-diagnostic Test Page 4

14. xx

tan3

3tan

True

False

15. If simplified the expression 1

6 10 216c d is equivalent to:

a. 3 54c d

b. 3 58c d

c. 6.5 10.54c d

d. None of the above

16. If simplified the expression 3

8 32c d

is equivalent to:

a. 24 96c d

b. 5 66c d

c. 5 68c d

d. 24 98c d

e. None of the above

17. f(x) = x2 + 2x then f(x+1) is

a. 2 4 3x x

b. 2 4x x

c. 2 2 3x x

d. 2 4 4x x

e. 2 4 2x x

18. 2 5

3 1 7

x

x

then x is

a. 2

b. 3

c. 4

d. 5

e. 6

SAIT Pre-calculus Self-diagnostic Test Page 5

19. In factored form 2R(R+r) – (R+r)2

is (R+r)(R-r)

True

False

20. When simplified 2

3 13 1

xx

x

is:

a. 3 1 2

3 1

x x

x

b. 2 3

3 1

x

x

c. 2 1

3 1

x

x

d. 4 3

3 1

x

x

21. When simplified

sr

sr

r

1

is:

a. 1

r s

r s

b. ( )

1

r r s

r s

c. 22r

r s

d. 2

r s

SAIT Pre-calculus Self-diagnostic Test Page 6

22. When adding 4

3

2

x

x

x

x

the answer is :

a. 2

2 4

x x

x

b. 2

2

4 2

8

x x

x

c. 2

2

4 2

2 8

x x

x x

d. 2

2 (2 1)

2 8

x x

x x

23. Perform the operation and simplify. xx

5

3

22

a. 2

2

2 15

3

x

x

b. 17

3x

c. 2

3

2 15

3

x

x

d. 2

15 2

3

x

x

24. Circle the correct answer

a.3

2

3 2

1x

x

b. 3

2

3 2

1x

x

c. 2

3

3 2

1x

x

d. 2

3

3 2

1x

x

SAIT Pre-calculus Self-diagnostic Test Page 7

25. The algebraic expression 2

2

5 3

2 4

x x

zx y

can be simplified to

5 3

2 4

x

z y

True

False

26. Circle the correct answer

a. 2 2 2sin 2 sin 4x x

b. 2 2sin 2 sin 4x x

c. 2 2sin 2 sin 2x x

d. 2 2sin 2 sin 4x x

27. The fraction

x

y

z is the same as :

a. xz

y

b. x

yz

c. none of the above

28. The fraction x

y

z

is the same as :

a. xz

y

b. xy

z

c. none of the above

SAIT Pre-calculus Self-diagnostic Test Page 8

29. Circle the correct answer:

a. 2

2 3

3

4 64 6 5

5

x yx y x

x

b. 5 3

2 3

3

4 6 54 6 5

x x yx y x

x

c. 2

2 3

3

4 6 54 6 5

x yx y x

x

d. none of the above

30. The y intercept of the graph represented by 4 5 8 0x y is

a. 0,1.6

b. 0, 2

c. 0,2

d. 1.6,0

e. 2,0

31. The expression 5 2

2 4

3

2

x y

x y when simplified is:

a. 3

2

6x

y

b. 7

2

3

2

x

y

c. 3

2

3

2

x

y

d. 2

3

2

3

y

x

SAIT Pre-calculus Self-diagnostic Test Page 9

Questions 32 to 35 are based on the graphs shown below.

Please examine the graphs carefully before answering the questions.

SAIT Pre-calculus Self-diagnostic Test Page 10

SAIT Pre-calculus Self-diagnostic Test Page 11

Questions 32 to 35 are based on the graphs shown above.

Please examine the graphs carefully before answering the questions.

32. The graph of y x is represented by

a. Graph 1

b. Graph 2

c. Graph 3

d. Graph 4

e. Graph 5

e. Graph 6

f. Graph 7

g. Graph 8

33. The graph of y x is represented by

a. Graph 1

b. Graph 2

c. Graph 3

d. Graph 4

e. Graph 5

e. Graph 6

f. Graph 7

g. Graph 8

SAIT Pre-calculus Self-diagnostic Test Page 12

34. The graph of 2 y x is represented by

a. Graph 1

b. Graph 2

c. Graph 3

d. Graph 4

e. Graph 5

e. Graph 6

f. Graph 7

g. Graph 8

35. Solve for x the equation 21 2x x x

a. 2 0x and x

b. 1 0x and x

c. 3 1x and x

d. 1 0x and x

e. 1 1x and x

SAIT Pre-calculus Self-diagnostic Test Page 13

Answer Key

If you get less than 25 out of 35 correct answers, you might find taking MATH 123 Mathematics

Refresher course a good investment. Alternatively, purchase your textbook for MATH 235 and

work through the first 12 chapters as a review.

1. False

2. False

3. False

4. a

5. True

6. False

7. False

8. False

9. True

10. False

11. True

12. d

13. False

14. False

15. a

16. d

17. a

18. d

19. True

20. b

21. d

22. d

23. d

24. d

25. False

26. c

27. b

28. a

29. b

30. a

31. b

32. g

33. a

34. b

35. d