Algebra
1
Select the difference of (2x2 – 3x3)
– (9x2 – 7x3).
- A.
–3x6
- B.
–3x5
- C.
–7x2 – 10x3
- D.
–7x2 + 4x3
2
Simplify the following expression. 8(8x + 3)
- A.
64x + 24
- B.
64x + 3
- C.
88x
- D.
16x + 11
3
Select the product of (7x – 6)(2x + 7).
- A.
14x2 – 37x – 42
- B. 51x – 42
- C. 14x2 + 37x – 42
D. 9x + 1
4
Simplify the following expression. (x + 8)3
- A.
512x3
- B.
x3 + 512
- C.
x3 + 24x2 + 192x + 512
- D.
x3 + 24
5
Select the product of (7x + 2)(7x – 2).
- A.
49x2 – 4
- B.
49x2 – 28x – 4
- C.
14x2
- D.
14x
6
Select the product of (4x + 5)(x2 – 2x + 2).
- A.
4x3 – 3x2 – 2x + 10
- B.
9x2 – 18x + 18
- C.
4x3 – 13x2 – 18x + 10
- D.
x2 + 2x + 7
7
Select the product of (-2x3y)(x5y5).
- A.
2x8y6
- B.
-2x8y6
- C.
-2x15y2
- D.
2x15y5
8
Select the product of (3x – 7)(3x – 7).
- A.
9x2 + 49
- B.
9x2 + 42x + 49
- C.
9x2 – 49
- D.
9x2 – 42x + 49
9
Select the product of (2x+5) • (5x – 2)
- A.
10x² + 21x – 10
- B.
10x² + 29x – 10
- C.
7x² + 21x – 10
- D.
10x² – 10
10
Select the difference of (2x² – 5x + 13) – (4 – 4x).
- A.
x² + 9
- B.
2x² – x + 9
- C.
2x² – 9x + 17
- D.
2x² + x – 9
11
Factor the expression. x2 + 17x + 72
- A.
(x + 1)(x + 72)
- B.
(x + 9)(x + 8)
- C.
(x – 9)(x – 8)
- D.
Prime Polynomial
12
Factor the expression. x2 – 17x + 30
- A.
(x – 2)(x – 15)
- B.
(x – 6)(x – 5)
- C.
(x – 6)(x + 5)
- D.
Prime Polynomial
13
Factor the expression. x2 – 51x + 144
- A.
(x – 12)2
- B.
(x – 9)(x – 16)
- C.
(x – 3)(x – 48)
- D.
Prime Polynomial
14
Factor the expression. 35x2 + 34x + 8
- A.
(7x – 4)(5x – 2)
- B.
(7x + 4)(5x + 2)
- C.
(35x + 2)(x + 4)
- D.
Prime Polynomial
15
Factor the expression. 27x2 + 45x + 12
- A.
3(3x – 1)(3x – 4)
- B.
3(3x + 1)(3x + 4)
- C.
(27x + 1)(x + 12)
- D.
Prime Polynomial
16
Factor the expression. -40x2 – 47x – 12
- A.
-(8x – 3)(5x + 4)
- B.
-(8x + 3)(5x + 4)
- C.
(-8x + 3)(5x + 4)
- D.
Prime Polynomial
17
Factor the expression. x2 + 2x + 48
- A.
(x + 1)(x + 48)
- B.
(x + 8)2
- C.
(x + 8)(x + 6)
- D.
Prime Polynomial
18
Factor the expression. 64x2 – 25
- A.
(8x + 5)(8x – 5)
- B.
(8x + 5)2
- C.
(8x – 5)2
- D.
Prime Polynomial
19
Factor the expression. y2 + 6xy + 9x2
- A.
(y – 3x)²
- B.
(y + 3x)²
- C.
(y + 3x)(y – 3x)
- D.
Prime Polynomial
20
20.
Factor the expression. -125x³ + 1
- A.
(-5x + 1)(25x² + 5x + 1)
- B.
(5x + 1)³
- C.
(-5x – 1)(25x² – 5x + 1)
- D.
Prime Polynomial
21
Simplify the following rational expression.
x2−16×2−3x−4×2− 16×2− 3x−4
- A.
x−4x+1x−4x+1
- B.
3x
- C.
x+4x+1x+4x+1
- D.
cannot be simplified
22
Select the product.
9x−2⋅7x−59x−2⋅7x−5
- A.
63x−763x−7
- B.
16x−59×2−7x+1016x−59×2− 7x+ 10
- C.
63×2−7x+1063×2−7x+10
- D.
16×2−7x+10
24
Select the quotient:
x+3x−1÷x2+xx−1x+3x−1÷x2+xx−1
- A.
x+3x(x+1)x+3x(x+1)
- B.
x+3(x−1)2x+3(x−1)2
- C.
1x1x
- D.
x3+4×2+3x(x−1)2
25
25.
Select the sum:
x2x−4+16x2x−4+16
- A.
1212
- B.
x12(x−2)x12(x−2)
- C.
2x−13x−62x−13x−6
- D.
x12x−24
26
Select the value of xx that is a solution for this equation:
- 5x=2x+3
- A.
-5
- B.
157157
- C.
5
- D.
15
27
An object 3.6 feet tall casts a shadow that is 10.8 feet long. How long in feet would the shadow be for an object which is 18.6 feet tall?
- A.
11.4 feet
- B.
6.2 feet
- C.
25.8 feet
- D.
55.8 feet
28
Simplify the expression:
527‾‾‾√35273
- A.
5353
- B.
5√33533
- C.
53√3533
- D.
527
29
Simplify the expression. (7 – ) + 5
- A.
11
- B.
12 – 6
- C.
7 + 24
- D.
5 + 7
30
Simplify the expression:
51+3√51+3
- A.
−52−52
- B.
5454
- C.
53√−5253−52
- D.
5−3‾√
31
Solve for xx in the equation x2 – 3x – 18 = 0.
- A.
{-3, -6}
- B.
{3, -6}
- C.
{-3, 6}
- D.
{3, 6}
32
Consider the equations:
f(x)=−5x−1f(x)=−5x−1 and g(x)=2x2g(x)=2×2
Select the solution for (f+g)(x)(f+g)(x).
- A.
2x² + 5x + 1
- B.
50x² – 20x + 2
- C.
2x² – 5x – 1
- D.
-10x² – 1
33
Consider the equations:
f(x)=−5x−1f(x)=−5x−1 and g(x)=2x2g(x)=2×2
Select the solution for (fg)(x)(fg)(x).
- A.
2x² + 5x + 1
- B.
50x² – 20x + 2
- C.
2x² – 5x – 1
- D.
-10x3 – 2x2
34
Select the x-coordinate of the vertex of the parabola defined by the function f(x) = -7x2 + 9x +6.
- A.
–
- B.
6
- C.
- D.
–
35
Determine the equation of g(x) that results from translating the function f(x) = x2 + 5 upward 11units.
- A.
g(x) = (x + 16)2
- B.
g(x) = (x + 11)2 + 5
- C.
g(x) = x2 – 6
- D.
g(x) = x2 + 16
36
Determine the equation of g(x) that results from translating the function f(x) = (x + 8)2 to the right 10units.
- A.
g(x) = (x – 2)2
- B.
g(x) = (x + 18)2
- C.
g(x) = (x + 8)2 – 10
- D.
g(x) = (x + 8)2 + 10
37
Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -2x2 + 4x + 9.
- A.
{–0.22, 0.44}
- B.
{-2, 4}
- C.
{–2.00, –4.50}
- D.
{–1.35, 3.35}
38
Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -2x2 + 3x + 7.
- A.
{2.77, –1.27}
- B.
{-2, 3}
- C.
{–1.50, –3.50}
- D.
{–0.29, 0.43}
38
Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -8x2 + 2x + 2.
- A.
{–0.39, 0.64}
- B.
{-8, 2}
- C.
{–0.25, –0.25}
- D.
{–4.00, 1.00}
Select the values of xx that are solutions to the inequality 0>x2+7x−30>x2+7x−3.
- A.
x∈(−7−61√2,−7+61√2)x∈(−7−612,−7+612)
- B.
x∈[−7−61√2,−7+61√2]x∈[−7−612,−7+612]
- C.
x∈(−∞,−7−61√2)∪(−7+61√2,∞)x∈(−∞,−7−612)∪(−7+612,∞)
- D.
x∈(−∞,−7−61√2]∪[−7+61√2,∞)
41
Given the function f(x)=5x+4f(x)=5x+4, find its inverse.
- A.
f−1(x)=(x−5)4f−1(x)=(x−5)4
- B.
f−1(x)=x5−4f−1(x)=x5−4
- C.
f−1(x)=(x−4)5f−1(x)=(x−4)5
- D.
f−1(x)=x4−5
42
Simplify the logarithm log2(32)log2(32). Select the correct solution.
- A.
5
- B.
16
- C.
30
- D.
32
43
Select the first five terms in the arithmetic sequence an = 4n, starting with n =1.
- A.
{, , , , }
- B.
{1, 2, 3, 4, 5}
- C.
{5, 6, 7, 8, 9}
- D.
{4, 8, 12, 16, 20}
44
Select the first five terms in the geometric sequencean=(3)n−1an=(3)n−1, starting with n=1n=1.
- A.
{3, 9, 27, 81, 243}
- B.
{1, 3, 9, 27, 81}
- C.
{1, 3, 6, 9, 12}
- D.
{3, 6, 9, 12, 15}
45
Select the sum of the series. ∑4k=1k2∑k=14k2
- A.
9
- B.
30
- C.
31
- D.
100
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