AQR Final Exam Review Fall, 2014 Solve using the addition and

Name: ______________________________________________
AQR Final Exam Review
Fall, 2014
Solve.
Solve using the addition and multiplication principles
together.
1) 9m + 7 = 3 - 3m
2)
1
3
p- p=2
4
8
15) A lamp shade has the geometric form as
shown. The total surface area of a lamp shade
with a slant height s and top and bottom base
radii of r2 and r1 is given by
r1 2 + r2 2 + r1 s + r2s. Find an equivalent
expression for the total surface area by
factoring out a common factor.
3) 45(x - 180) = 90
4) -2x + 7(2x - 6) = -24 - 6x
Solve for the given letter.
1
5) A = bh for h
2
6) S = 2 rh + 2 r2 for h
Factor.
16) 2m(3 - m) + 9n(3 - m)
7) A = P(1 + nr) for n
17) x3 + 5x2 + 7x + 35
Multiply.
8) (3p - 1)(9p2 + 3p + 1)
18) x2 + 12x + 36
9) (w - 10)2
19) x2 y2 - 36
10) (p + 13q)(p - 13q)
20) y2 - 49
11) (s + t + 4)(s + t - 4)
21) 125s3 + 1
Factor.
12) 3x3 + 6x
22) 1000p3 - 1
13) 20m 9 + 4m 7 + 10m 4
23) x2 - x - 30
Factor out a factor with a negative coefficient.
14) -15u4 - 10u3 + 25u
24) x2 + 5xy - 14y2
25) 5x2 - 5x - 30
26) x3 - x 2 - 12x
27) 2x2 + 17x + 30
1
Simplify the expression. Leave answers with exponents.
8
m7
43)
n9
28) 15y2 + 32y + 16
29) 6x2 - 26x - 20
Evaluate the expression.
44) 1251/3
30) 6x3 + 17x2 + 12x
31) 9x2 + 18xy + 8y2
Perform the indicated operations. Write answers using
only positive exponents. Assume variables represent
positive real numbers.
3
x 1/2 y3
45)
y3/2
Solve the equation.
32) 36n 2 + 18n = 0
33) 5k2 - 14k - 3 = 0
Simplify.
34) x2 + 8x - 20 = 0
46)
3 216
64
35) (x + 1)(x - 3) = 5
Write rational exponents in radical notation and radicals
in rational exponential notation.
47) 644/3
Simplify by removing a factor equal to 1.
y2 + 12y + 35
36)
y2 + 13y + 40
37)
Write in radical form. Assume all variables represent
positive real numbers.
48) (7py2 )1/5
y2 - 5y - 36
y2 - 4y - 45
Write in exponential form. Assume all variables are
positive real numbers.
6
49) x5
m 2 - 16m
38)
16 - m
39)
r2 - 9
5r + 15
Simplify.
50)
Evaluate the expression without a calculator.
40) 4 -3
Simplify the expression. Write the answer without
negative exponents.
98
41)
9 -3
-4
42) (x-3 y6 )
2
6 7
5
Answer Key
Testname: AQR FINAL EXAM REVIEW FALL 2014
1) -
1
3
2) -16
3) 182
4) 1
5) h =
2A
b
6) h =
S - 2 r2
2 r
7) n =
A-P
Pr
8) 27p3 - 1
9) w2 - 20w + 100
10) p2 - 169q2
11) s2 + 2st + t2 - 16
12) 3x(x2 + 2)
13) 2m 4 (10m 5 + 2m 3 + 5)
14) -5u(3u3 + 2u2 - 5)
15) (r1 2 + r2 2 + sr1 + sr2 )
16) (2m + 9n)(3 - m)
17) (x + 5)(x2 + 7)
18) (x + 6)2
19) (xy + 6)(xy - 6)
20) (y + 7)(y - 7)
21) (5s + 1)(25s2 - 5s + 1)
22) (10p - 1)(100p2 + 10p + 1)
23) (x + 5)(x - 6)
24) (x + 7y)(x - 2y)
25) 5(x + 2)(x - 3)
26) x(x + 3)(x - 4)
27) (2x + 5)(x + 6)
28) (3y + 4)(5y + 4)
29) 2(3x + 2)(x - 5)
30) x(3x + 4)(2x + 3)
31) (3x + 2y)(3x + 4y)
1
32) - , 0
2
33) -
1
,3
5
34) -10, 2
35) 4, -2
y+ 7
36)
y+ 8
37)
y+ 4
y+ 5
3
Answer Key
Testname: AQR FINAL EXAM REVIEW FALL 2014
38) -m
r-3
39)
5
40)
1
64
41) 9 11
x12
42)
y24
43)
m 56
n 72
44) 5
45) x3/2 y9/2
3
46)
2
47)
3
644
5
7py2
49) x5/6
42
5
50)
48)
4

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