Must-Know Algebra Exam Questions

Welcome to Collegly.com! Whether you’re prepping for your next exam or just brushing up on algebra, these 10 algebra exam questions will help you master key concepts and boost your confidence.

Question 1:

Simplifying Expressions
Simplify the expression:
3×2−5x+8−(2×2−4x+6)3x^2 – 5x + 8 – (2x^2 – 4x + 6)3x2−5x+8−(2x2−4x+6)
Answer: x2−x+2x^2 – x + 2x2−x+2

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Question 2:

Solving Linear Equations
Solve for $x$:
$4x-7=2x+9$
Answer: $x=8$

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Question 3:

Factoring Quadratic Expressions
Factor the quadratic expression:
x2−5x+6x^2 – 5x + 6x2−5x+6
Answer: $(x-2)(x-3)$

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Question 4:

Solving Systems of Equations
Solve the system of equations:

2x+3y=7x−y=1\begin{aligned} 2x + 3y &= 7 \\ x – y &= 1 \end{aligned}2x+3yx−y​=7=1​

Answer: $x=2$, $y=1$

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Question 5:

Exponential Equations
Solve for $x$:
2x+1=162^{x+1} = 162x+1=16
Answer: $x=3$

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Question 6:

Simplifying Rational Expressions
Simplify the expression:
3×2−12×2−4x\frac{3x^2 – 12}{x^2 – 4x}x2−4x3x2−12​
Answer: 3(x+2)x\frac{3(x + 2)}{x}x3(x+2)​

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Question 7:

Solving Quadratic Equations by the Quadratic Formula
Solve using the quadratic formula:
x2−3x−10=0x^2 – 3x – 10 = 0x2−3x−10=0
Answer: $x=5$, $x=-2$

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Question 8:

Inequalities
Solve the inequality:
$5x-2>3x+6$
Answer: $x>4$

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Question 9:

Graphing Linear Equations
Given the equation $y=2x-3$, what is the slope and y-intercept?
Answer: Slope = 2, Y-intercept = -3

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Question 10:

Word Problem
A rectangle’s length is 3 times its width. If the perimeter of the rectangle is 48 units, what is the width?
Answer: Width = 6 units