Name: ________________________ Class: ___________________ Date: __________ ID: A 1 alg 2 spring2013 review 1 Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Evaluate the expression for the given value of the variable(s). ____ 1. 5a + 5b; a =-6, b =-5 a. –55 b. 55 c. 5 d. –5 ____ 2. 4(3h - 6) 1 + h ; h =-2 a. 32 b. 48 c. -48 d. 30 ____ 3. 4b - 4 | |+ 3 - b 2 | | | | + 2b 3 ; b = 2 a. 19 b. 17 c. –11 d. 21 ____ 4. -x 2 - 4x - 4; x = –3 a. 3 b. –1 c. 11 d. –17 ____ 5. The expression -16t 2 + 1800 models the height of an object t seconds after it has been dropped from a height of 1800 feet. Find the height of an object after falling for 4.8 seconds. a. 2168.64 ft b. 1431.36 ft c. 1723.2 ft d. 7698.24 ft Simplify by combining like terms. ____ 6. 4c - 4d + 8c - 3d a. 12c 7d b. 12c - 7d c. -12c - 7d d. -7c 12d ____ 7. -3(-4y + 3) + 7y a. 19y - 9 b. 10y c. -19y 3 d. -19y - 9 ____ 8. Find the perimeter of the figure. Simplify the answer. x + y x y x x x 2 2 4 a. 9x + 2y b. 10x + y c. 10x + 2y d. 9x + 3y
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Name: ________________________ Class: ___________________ Date: __________ ID: A
1
alg 2 spring2013 review 1
Multiple ChoiceIdentify the letter of the choice that best completes the statement or answers the question.
Evaluate the expression for the given value of the variable(s).
____ 1. 5a + 5b; a = −6, b = −5a. –55 b. 55 c. 5 d. –5
____ 2. 4(3h − 6)
1 + h; h = −2
a. 32 b. 48 c. −48 d. 30
____ 3. 4b − 4| | + 3 − b 2||
|| + 2b 3; b = 2
a. 19 b. 17 c. –11 d. 21
____ 4. −x2 − 4x − 4; x = –3a. 3 b. –1 c. 11 d. –17
____ 5. The expression −16t2 + 1800 models the height of an object t seconds after it has been dropped from a height of 1800 feet. Find the height of an object after falling for 4.8 seconds.a. 2168.64 ft b. 1431.36 ft c. 1723.2 ft d. 7698.24 ft
Simplify by combining like terms.
____ 6. 4c − 4d + 8c − 3da. 12c + 7d b. 12c − 7d c. −12c − 7d d. −7c + 12d
____ 7. −3(−4y + 3) + 7ya. 19y − 9 b. 10y c. −19y + 3 d. −19y − 9
____ 8. Find the perimeter of the figure. Simplify the answer.
x + y
x
y
x
x
x
2
2
4
a. 9x + 2y b. 10x + y c. 10x + 2y d. 9x + 3y
Name: ________________________ ID: A
2
Solve the equation.
____ 9. 3y + 20 = 3 + 2y
a. −1
17b. 7
2
3c. 23 d. −17
____ 10. 1
4r −
1
16+
1
2r =
1
2+ r
a. 94
b.7
4c. −
9
4d. −
7
4
____ 11. −5y − 9 = −(y − 1)
a. −1
2b. −2
1
2c. −2 d. −
2
5
____ 12. 6(x − 0.8) − 0.2 5x − 4( ) = 6a. –0.5 b. –2 c. 0.5 d. 2
____ 13. 3x + 5| | = 1
a. x = 2 or x = −11
3c. x = 2 or x = −2
b. x = 2 or x = −4 d. x = −11
3 or x = −2
____ 14. 3 3x + 4| | − 7 = 5
a. x = 8
9 or x = −
2
9c. x =
8
9 or x = −2
2
3
b. x = 0 or x = −22
3d. x =
8
9 or x = 0
Solve the equation or formula for the indicated variable.
____ 15. S = 5r2t, for t
a. t = S5
− r b. t = 25rS
c. t = r2 − 5S d. t = S5r2
____ 16. T = 2UE
, for U
a. U = T − E2
b. U = T + E2
c. U = 2T − E d. U = TE2
Name: ________________________ ID: A
3
____ 17. The formula for the time a traffic light remains yellow is t = 18
s + 1, where t is the time in seconds and s is
the speed limit in miles per hour.a. Solve the equation for s.b. What is the speed limit at a traffic light that remains yellow for 4.5 seconds?
a. s = 8t − 8; s = 28 mi/h c. s = 8t − 1; s = 35
b. s = 8t; s = 36 mi/h d. s = 18
t − 1; s = 28 mi/h
Solve for x. State any restrictions on the variables.
____ 18. ax + bx + 9 = 7
a. x = 2a + b
; a ≠ b c. x = 7a + b + 9
; a + b ≠ −9
b. x = 7a + b + 9
; a ≠ 0,b ≠ −9 d. x = −2a + b
; a ≠ −b
____ 19. A rectangle is 3 times as long as it is wide. The perimeter is 60 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary.a. 7.5 cm by 22.5 cm c. 20 cm by 60 cmb. 7.5 cm by 52.5 cm d. 15 cm by 22.5 cm
Solve the inequality. Graph the solution set.
____ 20. 2 + 2k ≤ 8a. k ≥ 3
0 2 4 6 80–2–4–6–8
c. k ≤ 3
0 2 4 6 80–2–4–6–8
b. k ≤ 5
0 2 4 6 80–2–4–6–8
d. k ≥ 5
0 2 4 6 80–2–4–6–8
____ 21. 2r – 9 ≥ –6
a. r ≤ 11
2
0 2 4 6 80–2–4–6–8
c. r ≥ 11
2
0 2 4 6 80–2–4–6–8
b. r ≥ −71
2
0 2 4 6 80–2–4–6–8
d. r ≤ −71
2
0 2 4 6 80–2–4–6–8
Name: ________________________ ID: A
4
____ 22. –4k + 5 ≤ 21a. k ≥ –4
0 2 4 6 80–2–4–6–8
c. k ≤ –4
0 2 4 6 80–2–4–6–8
b. k ≥ −61
2
0 2 4 6 80–2–4–6–8
d. k ≤ −61
2
0 2 4 6 80–2–4–6–8
____ 23. 2(4y – 5) < –10a. y > 0
0 2 4 6 80–2–4–6–8
c. y < 0
0 2 4 6 80–2–4–6–8
b. y < −5
8
0 2 4 6 80–2–4–6–8
d. y > −5
8
0 2 4 6 80–2–4–6–8
____ 24. 2(2m – 5) – 6 > –36
a. m < −61
4
0 2 4 6 80–2–4–6–8
c. m < –5
0 2 4 6 80–2–4–6–8
b. m > –5
0 2 4 6 80–2–4–6–8
d. m > −61
4
0 2 4 6 80–2–4–6–8
____ 25. 4(3b – 5) < –31 + 12b
a. no solutions
0 2 4 6 80–2–4–6–8
c. b > −11
24
0 2 4 6 80–2–4–6–8
b. b < −11
24
0 2 4 6 80–2–4–6–8
d. all real numbers
0 2 4 6 80–2–4–6–8
Name: ________________________ ID: A
5
____ 26. 26 + 6b ≥ 2(3b + 4)
a. all real numbers
0 2 4 6 80–2–4–6–8
c. b ≥ 11
2
0 2 4 6 80–2–4–6–8
b. b ≤ 11
2
0 2 4 6 80–2–4–6–8
d. no solutions
0 2 4 6 80–2–4–6–8
Solve the problem by writing an inequality.
____ 27. If the perimeter of a rectangular picture frame must be less than 200 in., and the width is 36 in., what must the height h of the frame be?a. h < 64 in. b. h > 128 in. c. h > 64 in. d. h < 128 in.
Solve the compound inequality. Graph the solution set.
____ 28. 5x + 10 ≥ 10 and 7x – 7 ≤ 14a. x ≥ 4 or x ≤ 1
0 2 4 6 80–2–4–6–8
c. x ≥ 4 or x ≤ 3
0 2 4 6 80–2–4–6–8
b. x ≥ 0 and x ≤ 1
0 2 4 6 80–2–4–6–8
d. x ≥ 0 and x ≤ 3
0 2 4 6 80–2–4–6–8
____ 29. 4x – 5 < –17 or 5x + 6 > 31
a. x < –3 or x > 5
0 2 4 6 80–2–4–6–8
c. x < –3 or x > 72
5
0 2 4 6 80–2–4–6–8
b. x < −51
2 or x > 7
2
5
0 2 4 6 80–2–4–6–8
d. x < −51
2 or x > 5
0 2 4 6 80–2–4–6–8
____ 30. −2 ≤ 2x − 4 < 4a. 0 ≤ x < − 2
0 2 4 6 80–2–4–6–8
c. 1 ≤ x < 0
0 2 4 6 80–2–4–6–8
b. 1 ≤ x < 4
0 2 4 6 80–2–4–6–8
d. 3 ≤ x < 6
0 2 4 6 80–2–4–6–8
Name: ________________________ ID: A
6
____ 31. The perimeter of a square garden is to be at least 22 feet but not more than 36 feet. Find all possible values for the length of its sides.a. 11 < x < 18 c. 5.5 ≤ x ≤ 9b. 5.5 < x < 9 d. 11 ≤ x ≤ 18
____ 32. Students tested the acidity of the campus pond over a three-day period. On Monday and Tuesday, the pH values were 6.75 and 7.86. Find the range of pH values for Wednesday’s reading that will result in a mean pH greater than 7.1 and less than 7.6.a. 7.01 < x < 7.5 c. 21.3 < x < 22.8b. 16.69 < x < 8.19 d. 10.65 < x < 11.4
Solve the equation. Check for extraneous solutions.
____ 33. 4 4 − 3x| | = 4x + 6
a. x =5
8or x =
11
8c. x =
5
8or x =
11
4
b. x =11
8or x =
1
4d. x = −
5
8or x =
11
4
Solve the inequality. Graph the solution.
____ 34. 2x + 3| | ≥ 19a. x ≤ −22 or x ≥ 16
0 10 20 30 400–10–20–30–40
c. x ≤ −11 or x ≥ 8
0 5 10 15 200–5–10–15–20
b. x ≤ −8 or x ≥ 8
0 5 10 15 200–5–10–15–20
d. x ≥ −11 or x ≤ 8
0 5 10 15 200–5–10–15–20
____ 35. 2 x + 14
|||
||| < 9
a. −43
8 < x < 4
3
8
0 2 4 60–2–4–6
c. x < −43
8 or x > 4
3
8
0 2 4 60–2–4–6
b. −43
4 < x < 4
1
4
0 2 4 60–2–4–6
d. x < −43
4 or x > 4
1
4
0 2 4 60–2–4–6
Name: ________________________ ID: A
7
____ 36. Write the ordered pairs for the relation. Find the domain and range.
____ 38. Find the domain and range of the relation and determine whether it is a function.
O 2 4–2–4 x
2
4
–2
–4
y
a. Domain: all real numbers; range: all real numbers; yes, it is a functionb. Domain: x > 0; range: y > 0; yes, it is a function.c. Domain: positive integers; range: positive integers; no, it is not a function.d. Domain: x ≥ 0; range: y ≤ 0; no, it is not a function.
____ 39. Use the vertical-line test to determine which graph represents a function.
a.
O 2 4–2–4 x
2
4
–2
–4
yc.
O 2 4–2–4 x
2
4
–2
–4
y
b.
O 2 4–2–4 x
2
4
–2
–4
yd.
O 2 4–2–4 x
2
4
–2
–4
y
Name: ________________________ ID: A
9
____ 40. For f x( ) = 5x + 1, find f −4( ).a. –19 b. 1 c. –21 d. 21
____ 41. Suppose f x( ) = 4x − 2 and g x( ) = −2x + 1.
Find the value of f 5( )
g −3( ).
a. 15
9b. 2
4
7c. −2 d. 2
Graph the absolute value equation.
____ 42. y = x + 4| |a.
O 4 8–4–8 x
4
8
12
16
–4
yc.
O 4 8–4–8 x
4
8
–4
–8
–12
y
b.
O 4 8–4–8 x
4
8
12
16
–4
yd.
O 4 8–4–8 x
4
8
12
16
–4
y
Name: ________________________ ID: A
10
____ 43. y = − 2x + 3| |a.
O 4 8–4–8 x
4
–4
–8
–12
–16
yc.
O 4 8–4–8 x
4
–4
–8
–12
y
b.
O 4 8–4–8 x
4
8
12
–4
–8
yd.
O 4 8–4–8 x
4
–4
–8
–12
–16
y
____ 44. What is the vertex of the function y = − 3x + 2| | − 4?
a. (−2
3, –4) b. (
2
3, –4) c. (
2
3, 4) d. (−
2
3, 4)
Name: ________________________ ID: A
11
____ 45. The graph models a train’s distance from a river as the train travels at a constant speed. Which equation best represents the relation?
RiverHours Before River Hours After River
Mile
s F
rom
Riv
er
2 4–2–4
20
40
60
80
100
a. y = x| | + 60 b. y = x + 60| | c. y = 60x| | d. y =1
60x
||||
||||
____ 46. Write the equation for the translation of y = x| |.
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
a. y = x + 4| | b. y = x| | + 4 c. y = x| | − 4 d. y = x − 4| |
Name: ________________________ ID: A
12
____ 47. Graph the equation of y = |x| translated 4 units up.a.
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
yc.
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
b.
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
yd.
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
____ 48. Compare the graphs of the pair of functions. Describe how the graph of the second function relates to the graph of the first function.y = −2 x| | and y = −2 x| | − 3a. The second function is the graph of y = −2 x| | moved to the right 3 units.b. The second function is the graph of y = −2 x| | moved up 3 units.c. The second function is the graph of y = −2 x| | moved to the left 3 units.d. The second function is the graph of y = −2 x| | moved down 3 units.
Write an equation for the vertical translation.
____ 49. y = −2
9x| | − 7; 2 units down
a. y = −29
x| | − 9 c. y = −29
x| | − 2
b. y = −29
x| | − 2 d. y = −29
x| | + 9
Name: ________________________ ID: A
13
____ 50. Write an equation for the horizontal translation of y = x| |.
O 4 8–4–8 x
4
8
–4
–8
y
a. y = x + 4| | b. y = x − 4| | c. y = − x + 4| | d. y = − x − 4| |
Name: ________________________ ID: A
14
____ 51. The equation y = − x + 5| | describes a function that is translated from a parent function.a. Write the equation of the parent function. b. Find the number of units and the direction of translation.c. Sketch the graphs of the two functions.
a. y = x| |; 5 units right;
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
yc. y = x| |; 5 units left;
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
b. y = − x| |; 5 units right;
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
yd. y = − x| |; 5 units left;
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
____ 52. Write the equation that is the translation of y = x| | left 1 unit and up 2 units.a. y = x − 2| | − 1 c. y = x − 1| | + 2b. y = x + 1| | + 2 d. y = x + 2| | − 1
Name: ________________________ ID: A
15
____ 53. Graph the function y = x − 5| | − 4.a.
O 3 6–3–6 x
3
6
–3
–6
yc.
O 3 6–3–6 x
3
6
–3
–6
y
b.
O 3 6–3–6 x
3
6
–3
–6
yd.
O 3 6–3–6 x
3
6
–3
–6
y
Name: ________________________ ID: A
16
____ 54. Describe the relationship between the graph of y = x + 3| | − 4 and the graph of y = x| | in terms of a vertical and a horizontal translation. Then graph y = x + 3| | − 4.a. 3 units left and 4 units down;
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
yc. 3 units up and 4 units right;
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
b. 3 units right and 4 units down;
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
yd. 3 units down and 4 units left;
O 2 4 6–2–4–6 x
2
4
6
–2
–4
–6
y
Name: ________________________ ID: A
17
Graph the absolute value inequality.
____ 55. y < |x + 2| – 2a.
O 3 6–3–6 x
3
6
–3
–6
yc.
O 3 6–3–6 x
3
6
–3
–6
y
b.
O 3 6–3–6 x
3
6
–3
–6
yd.
O 3 6–3–6 x
3
6
–3
–6
y
Name: ________________________ ID: A
18
____ 56. y ≥ |x + 3| – 2a.
O 3 6–3–6 x
3
6
–3
–6
yc.
O 3 6–3–6 x
3
6
–3
–6
y
b.
O 3 6–3–6 x
3
6
–3
–6
yd.
O 3 6–3–6 x
3
6
–3
–6
y
Name: ________________________ ID: A
19
____ 57. –|x – 1| > y – 5a.
O 3 6–3–6 x
3
6
–3
–6
yc.
O 3 6–3–6 x
3
6
–3
–6
y
b.
O 3 6–3–6 x
3
6
–3
–6
yd.
O 3 6–3–6 x
3
6
–3
–6
y
Name: ________________________ ID: A
20
Write an inequality for the graph.
____ 58.
O 3 6–3–6 x
3
6
–3
–6
y
a. y ≤ |x + 3| – 1 c. y ≤ |x – 3| – 1b. y ≤ |x – 3| + 1 d. y ≥ |x – 3| – 1
Other
59. What is the maximum number of 3.5-to-5-min songs that can fill a 120-min CD? What is the minimum number? Write your answer as a compound inequality. Explain your reasoning.
59. ANS: 24 ≤ x ≤ 34; if all of the songs on the CD are the maximum length, 5 minutes long, then the minimum number of songs will fit on the CD. 120 divided by 5 is 24, so the CD can contain a minimum of 24 songs. The shortest possible song is 3.5 minutes. Since 120 divided by 3.5 is approximately 34.29, the CD can contain at most 34 complete songs.