SAT Algebra
Practice Questions
Algebra accounts for roughly 35% of Math questions. Its linear equations, functions, systems, and inequalities also support work in the other Math domains.
About Algebra
Algebra questions test your ability to set up and solve equations in one or two variables, interpret linear functions in context, and reason about inequalities. The test emphasizes translating real-world scenarios into mathematical models: expect word problems about rates, costs, ages, or distances that you must convert into equations before solving. Misreading the requested quantity or making an arithmetic slip can change an otherwise sound setup.
The digital test routes Module 2 from your performance across all of Math Module 1, not from one domain alone. Algebra can appear in both modules, so focus on clean, step-by-step solving habits rather than mental shortcuts that invite errors.
One useful skill in this chapter is interpreting linear equations and functions in context. Rather than asking you to simply solve for x, the test often asks what the slope or y-intercept of a line represents in a given scenario, or what value of a parameter makes a system have no solution. These questions require understanding what the algebra represents, not just applying a solving procedure.
What You'll Practice
- Solving linear equations and isolating a variable in one step or multiple steps
- Writing and solving linear equations from word-problem scenarios
- Interpreting slope and intercept in context (rates, starting values)
- Solving systems of two linear equations by substitution or elimination
- Setting up and solving linear inequalities, including compound inequalities
- Graphing linear relationships and identifying key features from equations
Why Algebra Matters for Your Score
Algebra is one of the two largest Math domains, with about 13–15 questions on a typical test form. Modeling with equations, interpreting linear relationships, and solving systems also support later Advanced Math work, so an Algebra error log can reveal gaps that affect more than one domain.
Algebra Subtopics
Each subtopic page combines its available practice questions with concept explanations, common mistakes, and strategy tips tailored to that specific skill.
Linear Equations in One Variable
Solving equations with a single unknown, from simple one-step problems to multi-step equations with fractions and parentheses.
Linear Equations in Two Variables
Interpreting and writing equations relating two quantities, including converting between equation forms and identifying key features like slope and intercepts.
Linear Functions
Understanding linear functions as rules mapping inputs to outputs, evaluating them, and interpreting function notation in real-world models.
Systems of Two Linear Equations
Finding the intersection of two lines by substitution or elimination, and analyzing when systems have no solution or infinitely many solutions.
Linear Inequalities in One or Two Variables
Solving and graphing inequalities, interpreting solution sets, and modeling real-world constraints with inequality expressions.
Algebra Sample Questions
More questionsPick an answer and hit Check Answer to see the detailed explanation. Questions are from easy, medium, and hard difficulty levels.
If 4x - 7 = 17, what is the value of x?
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Correct answer: C. x = 6
Explanation
Add 7 to both sides: 4x = 24. Divide both sides by 4: x = 6. Checking: 4(6) - 7 = 24 - 7 = 17. ✓
A line passes through the points (2, 5) and (6, 13). What is the y-intercept of this line?
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Correct answer: C. y = 1
Explanation
Slope m = (13-5)/(6-2) = 8/4 = 2. Using point (2, 5) in y = 2x + b: 5 = 2(2) + b, so b = 1. The y-intercept is 1.
For the linear function f, f(a) = 12 and f(a + 4) = 28. What is f(a - 3)?
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Correct answer: D. 0
Explanation
The slope is (f(a+4) - f(a))/(4) = (28-12)/4 = 16/4 = 4. So f decreases by 4 for each unit decrease in x. From f(a) = 12, going 3 units left: f(a-3) = 12 - 4(3) = 12 - 12 = 0.
If y = 2x + 1 and y = 4x - 5, what is the value of x?
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Correct answer: D. x = 3
Explanation
Set the two expressions for y equal: 2x + 1 = 4x - 5 → 6 = 2x → x = 3.
What is the largest integer value of x that satisfies 4x - 3 < 2x + 9?
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Correct answer: A. 5
Explanation
Solve: 4x - 3 < 2x + 9 → 2x < 12 → x < 6. The largest integer less than 6 is 5.
If ax + 6 = 3x + b has infinitely many solutions, which of the following must be true?
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Correct answer: B. a = 3 and b = 6
Explanation
For infinitely many solutions, the equation must be an identity (always true). This requires the coefficients of x to match (a = 3) and the constants to match (6 = b, so b = 6). Any other combination gives one solution or no solution.
A line has slope 3 and passes through the point (0, -2). Which equation represents this line?
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Correct answer: B. y = 3x - 2
Explanation
The line passes through (0, -2), so the y-intercept is -2. With slope 3, the equation in slope-intercept form is y = 3x + (-2) = 3x - 2.
If f(x) = 4x + c and f(3) = 19, what is f(-2)?
Show explanation
Correct answer: D. -1
Explanation
From f(3) = 19: 4(3) + c = 19 → 12 + c = 19 → c = 7. So f(x) = 4x + 7. Then f(-2) = 4(-2) + 7 = -8 + 7 = -1.
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Strategy Tips for Algebra
Translate before you compute
For word problems, write out the equation in full before doing any arithmetic. Label your variable explicitly (e.g., 'let h = hours worked') so you catch unit mismatches and avoid solving for the wrong quantity.
Check solutions in the original equation
After solving, plug your answer back in. This takes ten seconds and catches sign errors or arithmetic slips that are otherwise invisible—especially important for equations with fractions or negatives.
Know the three system outcomes cold
A system of two linear equations has one solution (lines intersect), no solution (parallel lines, same slope different intercept), or infinitely many solutions (same line). Recognizing these from coefficients—without actually solving—saves significant time on test questions that test this concept directly.
Use answer choices strategically on inequalities
When an inequality question asks which value satisfies the system, plug the answer choices into the inequality rather than solving algebraically. This is often faster and sidesteps sign-flip errors from dividing by a negative.
Frequently Asked Questions — Algebra
How many Algebra questions are on the test?
College Board's current content-domain range assigns Algebra about 35% of the Math section, or roughly 13–15 of the 44 questions. The exact mix can vary by test form.
Do I need to memorize the slope formula?
Yes. The slope formula m = (y2 - y1) / (x2 - x1) and the slope-intercept form y = mx + b are essential. The test does not provide a reference sheet for algebraic formulas, so these must be automatic. You should also know standard form Ax + By = C and how to convert between forms quickly.
Can I use the graphing calculator on Algebra questions?
Yes—the test provides a built-in graphing calculator for the entire Math section. For linear equations and systems, graphing both lines and finding the intersection point is often faster than algebraic solving, especially if the numbers are messy. Practice using the calculator efficiently during your prep.
What is the hardest Algebra concept on the test?
Systems with parameters can require an extra conceptual step. Questions such as 'for what value of k does the system have no solution?' depend on the conditions for parallel lines—equal slopes with different intercepts—rather than on solving for one intersection point.
Should I solve algebra questions algebraically or use the answer choices?
Both approaches are valid. Backsolving can be efficient when the choices are clean numbers; direct algebra is usually clearer for variable expressions or abstract problems. Practice both, then choose the approach that makes the given structure easiest to verify.
Other Math Topics
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