Pre-Calculus / Trigonometry Summer Review · PDF filePre-Calculus / Trigonometry Summer Review Packet Multiple Choice Identify the choice that best completes the statement or answers

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

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Pre-Calculus / Trigonometry Summer Review Packet

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

Use interval notation to describe the interval of real numbers.

1. x 7

a. 7,)ÈÎÍÍÍ c. ,Ê

ËÁÁ 7)

b. ,ÊËÁÁ 7] d. 7,Ê

ËÁÁ )

2. x > 12 or x 9

a. (,9] (12,) c. (,9] (12,)b. (,9) (12,) d. [9,12)

3. Find the domain and range of the function f(x) x2 8.

a. domain: (, )range: (8, )

b. domain: [8, )range: [8, )

c. domain: [8, )range: (8, )

d. domain: (, )range: [8, )

4. Use the graph below to find the domain and range.

a. D: (–4, 1], (2, 8] R: (–9, 1.4]

b. D: [–4, 1], [2, 8] R: [–9, 1.4]

c. D: (–4, 1), (2, 8) R: (–9, 1.4)

d. D: (–4, 8] R: (–9, 1.4]

Name: ________________________ ID: A

2

Use the graph to determine the domain and range of the relation, and whether the relation is a function.

5.

a. Domain: {x| 8, 8}; Range: all real numbers; No, it is not a function.b. Domain: {x| 8 x ; Range: all real numbers; Yes, it is a function.c. Domain: {x| 8 x ; Range: all real numbers; No, it is not a function.d. Domain: {x| 8 x ; Range: {y| 12 x ; Yes, it is a function.

6. Use the graph of f(x) to estimate f(–2).

a. f(–2) = 1 b. f(–2) = –1 c. f(–2) = 2 d. f(–2) = 0

7. Solve the system of equations by graphing. y 11x 6 y 6x 11

a. (–1, 5) b. (1, 7) c. (5, 1) d. (1, 5)

8. Solve the system of equations by using substitution. 8x + 7y = 18 3x – 5y = 22

a. (–2, 4) b. (3, –2) c. (4, –2) d. (4, 0)

Name: ________________________ ID: A

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9. Solve the system of equations by using elimination. 3p + 9q = 6 5p 5q 30

a. (6, –1) b. (3.75, 2) c. (5, 0.5) d. (5, –1)

10. Solve the system of equations.

3x 3y 3z 3

3y 3

5x 6y 4

a. x 2, y -1, z 0ÊËÁÁ

ˆ¯̃̃ c. x 4, y 3, z 2Ê

ËÁÁˆ¯̃̃

b. x 1,y 0, z 1ÊËÁÁ

ˆ¯̃̃ d. x 3, y 2, z 1Ê

ËÁÁˆ¯̃̃

11. Solve the system of inequalities by graphing.

y 3x 9

y 9x 8

a. c.

b. d.

Name: ________________________ ID: A

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Perform the indicated operation for the given matrices.

12. If A =

3 8 2

1 5 2

9 3 4

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

and B =

9 2 6

2 5 5

3 5 2

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

, find A + B.

a.

14 9 6

1 11 9

11 2 5

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

b.

12 10 4

1 10 7

12 2 6

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

c.

11 12 5

7 9 6

14 0 4

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

d.

12 8 2

0 8 6

15 9 2

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇˙̇̇˙̇

13. 3 4 2

2 8

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇ 2 0 6

8 2

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

a.12 6

2 8

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

b.12 6

10 20

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

c.0 6

2 8

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

d.4 4

6 6

È

Î

ÍÍÍÍÍÍÍÍÍÍÍÍ

˘

˚

˙̇̇˙̇̇˙̇̇˙̇̇

14. i47

a. i b. 1 c. i d. 1

15. 11 i( ) 3 15i( )a. 14 14i b. 4 4i c. 12 12i d. 14 16i

16. 8 10i( )(5 8i)

a. 40 14i 80 b. 120 14i c. 40 14i 80i2 d. 88 50i

17. 3

6 7i

a.1885

2185

i b.685

785

i c.1813

2113

i d.1885

2185

i

18. Consider f(x) 2x 2 8x 3. Determine whether the function has a maximum or minimum value. Then find the value of the maximum or minimum.a. maximum; –2 c. minimum; –2b. minimum; –5 d. maximum; –5

Name: ________________________ ID: A

5

19. Graph f(x) x 2 3x 3 by making a table of values.a. c.

b. d.

20. Find f(t 6) for f(x) 2x 2 9x 1.

a. 2t2 33t 125 c. 2t2 33t 125b. –125 d. 2t2 33t 125

21. Factor: 3t2 10t 8a. 3t 6( ) t 4( ) c. primeb. 3t 4( ) t 2( ) d. (3t + 4)( t + 2)

22. Factor: g 2 9g 22a. x 2( ) x 11( ) c. x 23( ) x 1( )b. x 4( ) x 13( ) d. x 2( ) x 11( )

23. Solve the equation x 2 9x 20 0.

a. 4,5 c. 4,5b. 4, 5 d. 4,5

Name: ________________________ ID: A

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24. Solve x 2 2x 15 by completing the square.

a. 3, –5 b. 6, –2 c. 5, –15 d. 4, –15

25. Find the exact solution of x 2 3x 40 by using the Quadratic Formula.

a. 5, 8 b. 8, 5 c. 10, 16 d. 40, 43

26. Find the exact solution of x 2 3x 7 0 by using the Quadratic Formula.

a.3 37

2,

3 37

2c.

3 19

2,3 19

2

b.3 12

2,3 12

2d.

3 37

2,3 37

2

27. Simplify the expression: 16a 10

a. 16a 10 b. 16a 5 c. 4a 10 d. 4a 5

28. Simplify 25x 20 y14 .

a. 5x 10y 7 c. 5x 20 y 14

b. 12.5x 20 y 14 d. 12.5x 10 y 7

29. Simplify 81a 32 b 204 .

a. 20.25a 32 b 20 c. 3a 8 b 5

b. 3a 32 b 20 d. 20.25a 8 b 5

30. Simplify 72x 5 y12 .

a. 6y 6 2x 5 c. 6x 2 y 6 x

b. 6 2x 5 y12 d. 6x 2 y 6 2x

31. Simplify the expression. x

4

7 x3

7

x

1

7

a. x

7

8b. x

6

7c. x

7

6d. x

8

7

Name: ________________________ ID: A

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32. Use the graph below to identify the y-intercept and zeros.

a. y-intercept: 20zeros: No zeros

c. y-intercept: 20zeros: 2, –2 ,2.24,2.24

b. y-intercepts:2, –2 ,2.24,2.24zero: 20

d. y-intercept: –20zeros: 2, –2 ,2.24,2.24

Simplify the given expression. Assume that no variable equals 0.

33. 19x6 y11ÊËÁÁÁ

ˆ¯˜̃̃ 6xy5ÊËÁÁÁ

ˆ¯˜̃̃

a. 114x5 y 16 c.114y 16

x 5

b.13y 16

x 5 d. 114x7 y24

34. 14x 4xy 14ÊËÁÁÁ

ˆ¯˜̃̃ 4x10 y7ÊËÁÁÁ

ˆ¯˜̃̃

a. 224x11y110 c.14y 21

x 9

b.224y 21

x 9 d. 224x9 y 21

Name: ________________________ ID: A

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35. 32x 18 y 10

16x 9 y 20

Ê

Ë

ÁÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃̃

2

a. 2x 9 y 20 c.4x 9

y 10

b.4x 18

y 20 d. 4x 18 y20

36. 20a 7b 6

ab 3

Ê

Ë

ÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃

2b 2

4a 3b 8

Ê

Ë

ÁÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜̃

a. 10a 3 b 3 b.5a 3

b 3 c.10a 3

b 3 d.1

10a 3 b 3

37. 3

xy 2

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜

3

a.x 3y 6

27b.

x 3y 3

27c.

x 3y 6

3d.

27

x 3y6

38. Simplify: 2xy(3xy 3 5xy 7y 2 )

a. 6x 2 y 4 10x 2 y2 14xy 3 c. 6x 2 y 4 5x 2 y 2 7x2 y 3

b. 6x 2 y 4 5xy 7y 2 d. 6x 2 y 4 10xy 14y 2

39. Find f gÊËÁÁ

ˆ¯̃̃ x( ) for the following functions.

f x( ) 6x 2 9x 8

g x( ) 4x 6

a. 10x 2 15x 8 c. 6x 2 13x 8b. 10x 3 15x 8 d. 6x 2 13x 14

40. Find (f g) x( ) for the following functions.f x( ) 12x 15

g x( ) 20x 2 2x 30

a. 20x 2 10x 15 c. 20x2 10x 15b. 32x 2 2x 15 d. 20x 2 10x 15

41. Find f gÊËÁÁ

ˆ¯̃̃ x( ) for the following functions.

f x( ) 3x 2 4x 5

g x( ) 11x 3

a. 33x3 53x 2 43x 15 c. 33x3 53x 2 12x 70b. 33x 3 9x 2 87x 15 d. 33x3 53x 2 43x 15

Name: ________________________ ID: A

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42. Find fg

Ê

Ë

ÁÁÁÁÁÁÁ

ˆ

¯

˜̃̃˜̃̃˜

x( ) for the following functions.

f x( ) 20x 3 4x 2 10x 13

g x( ) 12x 2 7

a.20x3 4x 2 10x 13

12x2 7, x 7

12c.

20x3 4x 2 10x 13

12x2 7, x 7

12

b.20x3 4x 2 10x 13

12x2 7, x 2 7

12d.

20x3 4x 2 10x 13

12x2 7, x 2 7

12

43. Find g û hÈÎÍÍÍ

˘˚˙̇̇ x( ) and [h û g](x).

g x( ) 7x

h x( ) 5x3 9x 2 2x 2

a. [g û h](x) 35x 4 63x 3 14x 2 14x

[h û g](x) 1715x 4 441x 3 14x 2 2x

b. [g û h](x) 35x 3 63x 2 14x 14

[h û g](x) 1715x 3 441x 2 14x 2

c. [g û h](x) 35x3 63x2 14x 14

[h û g](x) 1715x 3 441x 2 14x 2

d. [g û h](x) 35x 3 63x 2 14x 14

[h û g](x) 1715x 3 441x 2 14x 14

Find the inverse of the given function.

44. f x( ) 5x 1110

a. f 1 x( ) 5x 1011

c. f 1 x( ) 10x 115

b. f 1 x( ) 5x 1011

d. f 1 x( ) 10x 115

45. Determine whether each pair of functions are inverse functions.1) f x( ) 8x 5

g x( ) 18

(x 5)

2) f(x) 3x 12

g(x) 3x 12

a. Both 1 and 2 are inverse functions.b. Only 1 is an inverse function.c. Only 2 is an inverse function.d. Neither 1 nor 2 is an inverse function.

Name: ________________________ ID: A

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46. Find x.

a. 22 b. 2 286 c. 1144 d. 1594

47. Find x and y.

a. x 45, y 13.1 c. x 30, y 13.1 2

b. x 30, y 13.1 d. x 45, y 13.1 2

48. Find x and y.

a. x 24 3, y 24 c. x 24, y 24 3

b. x 12 3, y 12 d. x 12, y 12 3

Name: ________________________ ID: A

11

49. Find x and y.

a. x 1.5 3, y 1.5 c. x 3, y 3 3

b. x 3 3, y 3 d. x 1.5, y 1.5 3

50. Find the values of the six trigonometric functions for angle , when AC 25 and BC 20.

a. sin = 53

, cos = 54

, csc = 35

, sec = 45

, tan = 34

, and cot = 43

.

b. sin = 45

, cos = 35

, csc = 54

, sec = 53

, tan = 43

, and cot = 34

.

c. sin = 53

, cos = 34

, csc = 35

, sec = 45

, tan = 43

, and cot = 54

.

d. sin = 45

, cos = 35

, csc = 53

, sec = 54

, tan = 43

, and cot = 43

.