Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Practice Diploma #1 /44

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Determine the smallest zero for y = 4sin3θ + 2 in the interval 2π ≤ θ ≤ 3π

a) 0.38 c) 6.66

b) 1.22 d) 7.50

____ 2. In high school, a shot put is thrown out of a circle with a radius of 3.5 feet. A curved wooden “stopboard? ”

is placed in an arc around part of this circle. The central angle is 65.5°. Determine the length of the curved “stopboard”.

a) 3.5 c) 4.5

b) 4.0 d) 5.0

____ 3. On Oct. 2, 2010, the tide at New Westminster reached a maximum height of 10.8 feet at midnight. At 9 am

the tide reached the next minimum height of 5.8 feet. Assuming the relationship is sinusoidal, what was the height of the tide at 7 am?a) 6.1 c) 8.7

b) 6.4 d) 9.9

____ 4. Solve: 7 = 2x + 1

a) -0.64 c) 1.81

b) 1.36 d) 3.81

____ 5. The population in a particular community is increasing at an annual rate of 6.5%. Assume this trend will

continue. In how many years will the present population of 12 000 grow to 32 000?

a) 15.5 c) 15.8

b) 15.6 d) 16.1

Name: ________________________ ID: A

2

____ 6. In a study which compared the pH of urine and tears, the following data was collected.

On average, how many times more alkaline are tears than urine?a) 1.3 c) 15.0

b) 1.5 d) 31.6

____ 7. A restaurant offers a selection of 4 different sandwiches, 3 different soups and 4 differentflavours of juice. In how many different ways can a person select one item from each category?

a) 11 c) 48

b) 18 d) 54

____ 8. Determine the 4th term in the expansion of 4x −y

2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃̃

8

a) −7168x5y

3c) 16x

4y

4

b) −128x5y

3d) 1120x

4y

4

____ 9. A family of 6 (2 parents and 4 children) sit in a row at a theatre. A parent must sit at either end with the 4 children between them. In how many ways can the family be seated?

a) 24 c) 120

b) 48 d) 720

____ 10. From a standard deck of 52 cards, how many 5-card hands can be formed containingat least 4 clubs?

a) 20592 c) 29172

b) 27885 d) 34320

____ 11. A hockey team has played 10 games and has a record of 5 wins, 3 losses and 2 ties.

In how many ways could this have happened if after the first 4 games the team? ’s recordwas 3 wins and a loss?a) 90 c) 360

b) 94 d) 630

____ 12. When a polynomial P(x) is divided by x + 3 , the remainder is 2. Which point must be on the graph of the

corresponding function y = P(x) .

a) −3.− 2( ) c) −3.2( )

b) −3.0( ) d) 3.2( )

Name: ________________________ ID: A

3

____ 13. Determine the range of the rational function graphed below.

a) all real numbers c) (−∞,2] , [2,∞)

b) (−∞,0] , [8,∞) d) (−∞,−1) , (−1,0) , [8,∞)

____ 14. The graph of y = f (x) is stretched horizontally by a factor of 1

4 . Determine the equation of the transformed

graph.

a) y =1

4f x( ) c) y = f

1

4x

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃

b) y = 4f x( ) d) y = f 4x( )

____ 15. The students at a graduation dinner are separated into groups to be seated at 10 different tables. The order in which these 10 groups will approach the buffet is to be determined randomly. In how many ways can this order be determined?

a) 1010c) 10 P10

b) 10C10 d) 10 × 10

____ 16. Consider the graph of y = −3cosπ x − 2( )

10+ 4 . Which statement is false?

I The amplitude is 3

II The period is 10

III The phase shift is 2 to the right

IV The vertical displacement is 4 up

a) I c) III

b) II d) IV

Name: ________________________ ID: A

4

____ 17. Solve: cos x =3

2, 0 ≤ x < 2π

a)π

6,11π

6c)

π

3,2π

3

b)π

6,5π

6d)

π

3,5π

3

____ 18. Determine an expression for all angles coterminal with a standard position angle measuring

120°. Express your answer in radians.

a)5π

6+ πn, n is an integer c)

5π

6+ 2πn, n is an integer

b)2π

3+ πn, n is an integer d)

2π

3+ 2πn, n is an integer

____ 19. Determine the exact value of tan75°

a) 2 + 3 c)5 + 3

4

b) −2 − 3 d)3 + 3

3

____ 20. A point with an x value of 2 lies on the circle with a radius of 5 . This point also lies on

the terminal arm of θ in standard position. Determine the value of sec? θ .

a)5

2c)

2

5

b) 5 d)1

5

____ 21. Determine all the restrictions for the expression tanx

cos x − 1

a) cos x ≠ 0 c) sinx ≠ 0,cos x ≠ 1

b) cos x ≠ 1 d) cos x ≠ 0,cos x ≠ 1

____ 22. Solve sinx = −cos x, −π ≤ x ≤ π

a) −π

4.

3π

4c)

3π

4.

7π

4

b)π

4.

3π

4d)

3π

4.

5π

4

____ 23. Simplify the following expression csc x − sinx

sec x − cos x

a) cot2x c) tan2

x

b) cot3x d) tan3

x

Name: ________________________ ID: A

5

____ 24. The graph of y = 2sinb x − c( ) + 1 is shown below. Determine a value of c.

a) −π c)π

4

b) 2 d)2π

7

____ 25. Solve 23x − 1= 82x + 1

a) x = −4

3c) x = −

2

3

b) x = −1 d) x = −3

4

____ 26. Express logx

2

10y3

in terms of logx and logy

a) 2logx − 1 − 3logy c) 2logx − 10 − 3logy

b) 2logx − 1 + 3logy d) 2logx − 10 + 3logy

____ 27. Evaluate log3 27

a)2

9c)

3

2

b)2

3d)

9

2

____ 28. Which statement must be true for f x( ) = log 1

2x when x 2 > x 1 ?

a) f x 1ÊËÁÁ ˆ

¯˜̃ > f x 2

ÊËÁÁ ˆ

¯˜̃ c) f x 1

ÊËÁÁ ˆ

¯˜̃ > 0, f x 2

ÊËÁÁ ˆ

¯˜̃ < 0

b) f x 2ÊËÁÁ ˆ

¯˜̃ > f x 1

ÊËÁÁ ˆ

¯˜̃ d) f x 2

ÊËÁÁ ˆ

¯˜̃ > 0, f x 1

ÊËÁÁ ˆ

¯˜̃ < 0

Name: ________________________ ID: A

6

____ 29. For which graph is the relation and its inverse both functions?

a) c)

b) d)

____ 30. The graph of y = f x( ) as shown below is transformed to x = f yÊËÁÁ ˆ

¯˜̃ . Determine all the invariant points.

a) 0,3ÊËÁÁ ˆ

¯˜̃ c) 2,−1Ê

ËÁÁ ˆ

¯˜̃

b) 1,1ÊËÁÁ ˆ

¯˜̃ d) 1,1Ê

ËÁÁ ˆ

¯˜̃ and 2,−1Ê

ËÁÁ ˆ

¯˜̃

Name: ________________________ ID: A

7

____ 31. The graph of y = f x( ) is shown below.

Which graph represents the graph of y = f 2 x − 3( )ÊËÁÁ ˆ

¯˜̃ + 4

a) c)

b) d)

____ 32. The point P 4,6ÊËÁÁ ˆ

¯˜̃ lies on the graph of y = f x( ) . Which point must lie on the graph of y = −

1

2f

1

2x + 2

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ ?

a) 7,−3ÊËÁÁ ˆ

¯˜̃ c) 1,−3Ê

ËÁÁ ˆ

¯˜̃

b) 4,−3ÊËÁÁ ˆ

¯˜̃ d) −2,−3Ê

ËÁÁ ˆ

¯˜̃

Name: ________________________ ID: A

8

____ 33. Consider the following transformations on the graph of y = f x( )

I y = f x + 2( )

II y = 2f x( )

III y = f −x( )

IV y = −f x( )

Which transformations will have no effect on the zeros of the original graph of y = f x( )?

a) I and II only c) II and IV only

b) II and III only d) III and IV only

____ 34. Which of the following functions are polynomial functions?

I y = x3

− 2x2

+ x + 3

IIy = x

3−

2

x2

− x + 3

III y = x3

− 2x1.5

+ x + 3

IVy = x

3−

1

2x

2− x + 3

a) III only c) I and IV only

b) IV only d) II and III only

____ 35. Which sketch best represents the graph of y = ax3

− bx2

+ cx + 24 if a < 0 ?

a) c)

b) d)

Name: ________________________ ID: A

9

____ 36. The graphs of y = f x( ) and y = g x( ) are graphed below. Which graph represents y = f x( ) + g x( ) ?

a) c)

b) d)

____ 37. Which three expressions are factors of 9x3

− 36x2

− 4x + 16?

I x − 4

II x + 4

III 3x − 2

IV 3x + 2

a) I, II, III only c) I, III, IV only

b) I, II, IV only d) II, III, IV only

Name: ________________________ ID: A

10

____ 38. Given the graph of y = f x( ) as shown, determine the graph of y = f x( ) .

a) c)

b) d)

____ 39. Given f x( ) = x + 2 and g x( ) = x2

+ 3x − 1, determine the value of f g 3( )ÊËÁÁ ˆ

¯˜̃ .

a) 16 c) 19

b) 17 d) 39

Name: ________________________ ID: A

11

____ 40. As a furniture salesperson, Chacci gets a 3% commission on all his weekly sales above

$5000. Which row in the table shows the composite function that will determine his

commission if x represents his weekly sales if f x( ) represents the amount eligible for commission, g x( )

represents the amount earned as commission.

a) f x( ) = 5000 − x ; g x( ) = 0.03x ; and the composite function is f g x( )ÊËÁÁ ˆ

¯˜̃

b) f x( ) = x − 5000 ; g x( ) = 0.03x ; and the composite function is f g x( )ÊËÁÁ ˆ

¯˜̃

c) f x( ) = 5000 − x ; g x( ) = 0.03x ; and the composite function is g f x( )ÊËÁÁ ˆ

¯˜̃

d) f x( ) = x − 5000 ; g x( ) = 0.03x ; and the composite function is g f x( )ÊËÁÁ ˆ

¯˜̃

____ 41. Consider the graphs of the function f x( ) = x2 and g x( ) = f x( ) . Which answer correctly describes the

domain and range of g x( )

a) D: x ∈ ℜ and R: y ∈ ℜ

b) D: has restrictions and R: has restrictions

c) D: has restrictions and R: y ∈ ℜ

d) D: x ∈ ℜ and R: has restrictions

____ 42. Determine the range of the function y = 3x − 9 + 2

a) y ≥ 0 c) y ≥ 3

b) y ≥ 2 d) y ≥ 9

____ 43. The function f x( ) = log4 x + 2( ) is stretched horizontally by a factor of 2 and translated 3 units upward to

produce g x( ) . Which function below is the correct equation for this transformed function.

a) g x( ) = log4 32x + 128( ) c) g x( ) = 2log4 x + 2( ) + 3

b) g x( ) = log4

1

2x + 5

Ê

Ë

ÁÁÁÁÁÁ

ˆ

¯

˜̃˜̃˜̃ d) g x( ) = 2log4 64x + 128( )

Name: ________________________ ID: A

12

____ 44. Which of the following best represents the graph of the rational function y =x

x2

− 4x?

a) c)

b) d)

ID: A

1

Practice Diploma #1 /44

Answer Section

MULTIPLE CHOICE

1. D

2. B

3. B

4. C

5. B

6. D

7. C

8. A

9. B

10. C

11. C

12. C

13. B

14. D

15. C

16. B

17. A

18. D

19. A

20. A

21. D

22. A

23. B

24. D

25. A

26. A

27. C

28. A

29. A

30. B

31. D

32. B

33. C

34. C

35. A

36. A

37. C

38. A

39. C

ID: A

2

40. D

41. D

42. B

43. A

44. D