Name: ________________________ Class: ___________________ Date: __________ ID: A 1 Pre-Calculus / Trigonometry Summer Review Packet Multiple Choice Identify 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, ) È Î Í Í Í c. , Ê Ë Á 7) b. , Ê Ë Á 7] d. 7, Ê Ë Á ) 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) x 2 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]
Transcript
Name: ________________________ Class: ___________________ Date: __________ ID: A
1
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
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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
8
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
9
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
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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.
