Below are 30 sample quiz questions—with answers and brief explanations—that cover key
topics in College Algebra, Pre-Calculus, and Calculus I, II, & III. These questions can serve as a
review tool and gauge your understanding of fundamental concepts.
College Algebra
1. Solve for xx:
Solve the linear equation:
3x−7=2x+5.3x - 7 = 2x + 5.
A) x=12x = 12
B) x=−12x = -12
C) x=2x = 2
D) x=−2x = -2
Answer: A) x=12x = 12
Explanation: Subtract 2x2x from both sides: x−7=5x - 7 = 5, then add 7 to both sides: x=12x =
12.
2. Solve the quadratic equation by factoring:
x2−5x+6=0.x^2 - 5x + 6 = 0.
A) x=1x = 1 and x=6x = 6
B) x=2x = 2 and x=3x = 3
C) x=−2x = -2 and x=−3x = -3
D) x=5x = 5 and x=−1x = -1
Answer: B) x=2x = 2 and x=3x = 3
Explanation: Factor as (x−2)(x−3)=0(x-2)(x-3)=0 so x=2x=2 or x=3x=3.
3. Simplify the exponential expression:
25⋅2324.\frac{2^{5} \cdot 2^{3}}{2^{4}}.
A) 242^4
B) 252^5
C) 262^6
D) 272^7
, Answer: C) 262^6
Explanation: Multiply in the numerator: 25+3=282^{5+3} = 2^8; then divide by 242^4:
28−4=242^{8-4} = 2^4.
[Correction:] Actually, 25+3=282^{5+3} = 2^8 and 28−4=242^{8-4}=2^4. The correct answer
should be 242^4.
Revised Answer: A) 242^4
4. Solve the absolute value equation:
∣2x−3∣=5.|2x - 3| = 5.
A) x=4x = 4 or x=−1x = -1
B) x=4x = 4 only
C) x=−1x = -1 only
D) x=1x = 1 or x=−4x = -4
Answer: A) x=4x = 4 or x=−1x = -1
Explanation: 2x−3=52x - 3 = 5 gives x=4x=4; 2x−3=−52x - 3 = -5 gives x=−1x=-1.
5. Simplify the rational expression:
x2−9x2−6x+9.\frac{x^2 - 9}{x^2 - 6x + 9}.
A) x−3x−3\frac{x-3}{x-3}
B) x+3x−3\frac{x+3}{x-3}
C) x−3(x−3)2\frac{x-3}{(x-3)^2}
D) (x−3)(x+3)(x−3)2\frac{(x-3)(x+3)}{(x-3)^2}
Answer: D) (x−3)(x+3)(x−3)2\frac{(x-3)(x+3)}{(x-3)^2}
Explanation: Factor numerator as (x−3)(x+3)(x-3)(x+3) and denominator as (x−3)2(x-3)^2.
Simplification (cancel one factor x−3x-3) gives x+3x−3\frac{x+3}{x-3} for x≠3x \neq 3.
6. Solve the system of equations:
{2x+3y=12,x−y=1.\begin{cases} 2x + 3y = 12,\\[1mm] x - y = 1. \end{cases}
A) x=3, y=2x=3, \, y=2
B) x=4, y=3x=4, \, y=3
C) x=2, y=1x=2, \, y=1
D) x=5, y=4x=5, \, y=4
topics in College Algebra, Pre-Calculus, and Calculus I, II, & III. These questions can serve as a
review tool and gauge your understanding of fundamental concepts.
College Algebra
1. Solve for xx:
Solve the linear equation:
3x−7=2x+5.3x - 7 = 2x + 5.
A) x=12x = 12
B) x=−12x = -12
C) x=2x = 2
D) x=−2x = -2
Answer: A) x=12x = 12
Explanation: Subtract 2x2x from both sides: x−7=5x - 7 = 5, then add 7 to both sides: x=12x =
12.
2. Solve the quadratic equation by factoring:
x2−5x+6=0.x^2 - 5x + 6 = 0.
A) x=1x = 1 and x=6x = 6
B) x=2x = 2 and x=3x = 3
C) x=−2x = -2 and x=−3x = -3
D) x=5x = 5 and x=−1x = -1
Answer: B) x=2x = 2 and x=3x = 3
Explanation: Factor as (x−2)(x−3)=0(x-2)(x-3)=0 so x=2x=2 or x=3x=3.
3. Simplify the exponential expression:
25⋅2324.\frac{2^{5} \cdot 2^{3}}{2^{4}}.
A) 242^4
B) 252^5
C) 262^6
D) 272^7
, Answer: C) 262^6
Explanation: Multiply in the numerator: 25+3=282^{5+3} = 2^8; then divide by 242^4:
28−4=242^{8-4} = 2^4.
[Correction:] Actually, 25+3=282^{5+3} = 2^8 and 28−4=242^{8-4}=2^4. The correct answer
should be 242^4.
Revised Answer: A) 242^4
4. Solve the absolute value equation:
∣2x−3∣=5.|2x - 3| = 5.
A) x=4x = 4 or x=−1x = -1
B) x=4x = 4 only
C) x=−1x = -1 only
D) x=1x = 1 or x=−4x = -4
Answer: A) x=4x = 4 or x=−1x = -1
Explanation: 2x−3=52x - 3 = 5 gives x=4x=4; 2x−3=−52x - 3 = -5 gives x=−1x=-1.
5. Simplify the rational expression:
x2−9x2−6x+9.\frac{x^2 - 9}{x^2 - 6x + 9}.
A) x−3x−3\frac{x-3}{x-3}
B) x+3x−3\frac{x+3}{x-3}
C) x−3(x−3)2\frac{x-3}{(x-3)^2}
D) (x−3)(x+3)(x−3)2\frac{(x-3)(x+3)}{(x-3)^2}
Answer: D) (x−3)(x+3)(x−3)2\frac{(x-3)(x+3)}{(x-3)^2}
Explanation: Factor numerator as (x−3)(x+3)(x-3)(x+3) and denominator as (x−3)2(x-3)^2.
Simplification (cancel one factor x−3x-3) gives x+3x−3\frac{x+3}{x-3} for x≠3x \neq 3.
6. Solve the system of equations:
{2x+3y=12,x−y=1.\begin{cases} 2x + 3y = 12,\\[1mm] x - y = 1. \end{cases}
A) x=3, y=2x=3, \, y=2
B) x=4, y=3x=4, \, y=3
C) x=2, y=1x=2, \, y=1
D) x=5, y=4x=5, \, y=4
