Mercy High School – Summer Math ReviewName___________________________________
Students Entering Algebra 2
Write each as an algebraic expression.
1) 7 more than w is 37
2) the quotient of a and 8 is greater than or equal to 50
3) u decreased by 4 is equal to 8
4) n increased by 5 is greater than 45
5) w increased by 9 is equal to 13
6) the difference of n and 7 is less than 50
Evaluate each using the values given.
7) x − (4 − y) − 1; use x = 3, and y = 4
8) z(3 ÷ 3 + x); use x = 2, and z = 6
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9) k ÷ 5 − (h − h); use h = 3, and k = 5
10) 3 − (c + b); use b = 6, and c = 4
11) ( y(z + x)) ÷ 6; use x = 6, y = 3, and z = 2
12) y + 3 − z ÷ 4; use y = 1, and z = 4
13) (m + p 2 ) ÷ 2; use m = 6, and p = 2
14) 3m − n ÷ 4; use m = 6, and n = 4
3
15) p ÷ 5 + mp; use m = 5, and p = 5
Solve each equation.
16) 5(1 + 8n) = 125
17) 8(3 + 5x) = 264
18) 3(1 − 4x) − 8 = 91
19) 2(−3 + 8n) − 2n = −6(1 + 8n)
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20) 8( x + 6) − 2 = −5 − 5(6x + 5)
21) 4(k + 7) = 7(k − 2)
Write the slope-intercept form of the equation of the line described.
22) through: (−1, −5), parallel to y = 8x + 2
1
23) through: (5, 5), perp. to y = − x + 4
2
Write the slope-intercept form of the equation of each line.
24)
y
4
2
−5 −4 −3 −2 −1
1
2
3
4
5 x
−2
−4
Write the slope-intercept form of the equation of each line given the slope and y-intercept.
4
25) Slope = , y-intercept = −1
5
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Write the slope-intercept form of the equation of the line through the given points.
26) through: (0, −5) and (5, −1)
Solve each compound inequality and graph its solution.
27) 8x > 24 or x + 4 < 2
28) −9 ≤ −8 + v < −6
Solve each inequality and graph its solution.
29)
9 + 8v
≥2
4
Solve each system by elimination.
30) 5x − 2 y = 2
−8x − 5 y = 5
31) 0 = 5y − 2x + 19
−9x + 27 = −3y
Solve each system by substitution.
32) −7x − 6 y = 15
y = −5x + 9
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Simplify. Your answer should contain only positive exponents.
33)
35)
(−2a 4b −1) 0
−2 0
0 −3
2 2
34)
(2u) 3
−2a b ⋅ −a b
(−a −4b 4) 2 ⋅ 2a 3b 3
37) −
b
−3
2nm
36)
4
(2m −1) 4 ⋅ 2n −1
(−2a 3b 0) 2
4 2
2a b ⋅ −a
3
38)
−2 4
2u v ⋅ −u v
−2
0 3
x ⋅ −x y
( x −4 y 4) 3
Factor each completely.
39) n 2 − 2n − 48
40) v 2 − 15v + 56
41) x 2 − x
42) 3n 2 + 10n
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43) 5n 2 − 19n − 30
44) 9n 2 + 71n − 90
45) 21r 3 − 24r 2 + 56r − 64
46) 5n 3 − 7n 2 + 40n − 56
Simplify each expression.
47)
4p + 4
3p
+
10 p − 10
3
48)
3p
5p
−
3 p + 18 p
2
49)
8(2k + 9) 3(2k + 9)
÷
8k
3
50)
n + 3 8n(n + 3)
÷
7
7(n − 3)
51)
2
(n − 2)(n + 7) (n − 2)(n + 7)
8n 2
÷
n + 10
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Simplify.
52) 2 24 −
24
54) − 6 (3 − 2 6 )
53) 2 45 − 3 45
4
55)
2+
3
Find the value of each trigonometric ratio to the nearest ten-thousandth.
56) cos A
57) sin A
C
C
25
A
25
A
24
7
B
24
B
7
58) tan Z
X
35
Z
21
28
Y
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Find the missing side. Round to the nearest tenth.
59)
60)
17
x
27°
x
11
74°
61)
18
35°
x
62) Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school
sold 5 senior citizen tickets and 8 child tickets for a total of $44. The school took in $39 on the
second day by selling 6 senior citizen tickets and 5 child tickets. Find the price of a senior citizen
ticket and the price of a child ticket.
Simplify each expression.
63) (5x 4 + 4x 3 − 8) + (1 + 3x 3 − 2x 4 )
64) (4n 2 + 3 + 2n 4 ) + (3 − 7n 2 − 2n 3 )
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Answers to Students Entering Algebra 2
1) w + 7 = 37
a
≥ 50
8
6) n − 7 < 50
10) 17
14) 17
18) {−8}
22) y = 8x + 3
2)
5) w + 9 = 13
9) 1
13) 5
17) {6}
21) {14}
4
25) y = x − 1
5
27) x > 3 or x < −2 :
3) u − 4 = 8
4) n + 5 > 45
7) 2
11) 4
15) 26
19) {0}
23) y = 2x − 5
8) 18
12) 3
16) {3}
20) {−2}
1
24) y = x − 3
4
4
26) y = x − 5
5
−6 −5 −4 −3 −2 −1 0
1
2
3
4
4
5
6
7
5
6
28) −1 ≤ v < 2 :
−5 −4 −3 −2 −1 0
1
2
3
1
17
29) v ≥ − or v ≤ −
:
8
8
−7 −6 −5 −4 −3
30) (0, −1)
31) (2, −3)
v6
4u 3
x 15
38) − 9
y
42) n(3n + 10)
46) (n 2 + 8)(5n − 7)
34) −
50)
54)
58)
62)
64)
−2 −1 0
2b 14
a5
39) (n + 6)(n − 8)
35)
43) (5n + 6)(n − 5)
5 p2 − 3 p + 2
47)
5( p − 1)
n−3
n + 10
51)
8n
8n 2
−3 6 + 12
55) 8 − 4 3
1.3333
59) 11.4
senior citizen ticket: $4, child ticket: $3
2n 4 − 2n 3 − 3n 2 + 6
1
2
3
4
5
32) (3, −6)
2a 4
b2
40) (v − 8)(v − 7)
a2b3
2
m8n2
37) −
16
41) x( x − 1)
44) (n + 9)(9n − 10)
2 − 5 p 2 − 30 p
48)
2( p + 6)
52) 2 6
45) (3r 2 + 8)(7r − 8)
1
49)
k
53) −3 5
56) 0.2800
60) 7.7
63) 3x 4 + 7x 3 − 7
57) 0.2800
61) 14.7
36) −
33)
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