SAT Math quiz

SAT Algebra Quizzes

Practice 10 SAT Algebra questions involving linear equations, linear functions, equations in two variables, systems of equations, inequalities, slope, parallel lines, tables, and interpreting linear relationships. Use hints when needed and review the explanation after each answer.

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1 Question 1 of 10

Not answered

Solve for x: 5(2x - 7) = 3x + 14

Hint: Distribute 5 first, then move the x-terms to one side and constants to the other.

Explanation: Distribute: 10x - 35 = 3x + 14. Subtract 3x: 7x - 35 = 14. Add 35: 7x = 49. Divide by 7, so x = 7.

2 Question 2 of 10

Not answered

A storage company models the monthly cost C, in dollars, for storing b boxes by C = 28 + 6.5b. What does 6.5 represent in this model?

Hint: In a linear model, the coefficient of the variable is the rate of change.

Explanation: The coefficient of b is 6.5, so the cost increases by $6.50 for each additional box stored. It represents the cost per stored box.

3 Question 3 of 10

Not answered

The equation 4x + 2y = 18 represents a line in the xy-plane. What is the slope of the line?

Hint: Rewrite the equation in the form y = mx + b.

Explanation: Subtract 4x: 2y = -4x + 18. Divide by 2: y = -2x + 9. Therefore, the slope is -2.

4 Question 4 of 10

Not answered

The system 2x + y = 11 and x - y = 1 has solution (x, y). What is the value of x + y?

Hint: Add the equations to eliminate y, then substitute back.

Explanation: Add the equations: 3x = 12, so x = 4. Substitute into x - y = 1: 4 - y = 1, so y = 3. Therefore, x + y = 7.

5 Question 5 of 10

Not answered

How many solutions does the system 6x - 9y = 15 and 2x - 3y = 5 have?

Hint: Compare the two equations after multiplying the second equation by 3.

Explanation: Multiplying 2x - 3y = 5 by 3 gives 6x - 9y = 15, which is exactly the first equation. Both equations represent the same line, so the system has infinitely many solutions.

6 Question 6 of 10

Not answered

A school club has a budget of at most $300 for an event. The room fee is $84, and the club must pay $18 for each participant. What is the greatest number of participants the club can afford?

Hint: Write 84 + 18p ≤ 300 and solve for p.

Explanation: The inequality is 84 + 18p ≤ 300. Subtract 84: 18p ≤ 216. Divide by 18: p ≤ 12. The greatest whole-number number of participants is 12.

7 Question 7 of 10

Not answered

Which point does NOT satisfy the inequality 3x + 2y ≤ 18?

Hint: Substitute each ordered pair into the left side of the inequality.

Explanation: For (5, 2), 3(5) + 2(2) = 15 + 4 = 19, and 19 is not less than or equal to 18. The other three points satisfy the inequality.

8 Question 8 of 10

Not answered

Which equation represents the line parallel to 2x - 5y = 15 and passing through the point (5, 4)?

Hint: Parallel lines have equal slopes. First rewrite 2x - 5y = 15 in slope-intercept form.

Explanation: Rewrite the given line: -5y = -2x + 15, so y = (2/5)x - 3. A parallel line has slope 2/5. Using (5, 4): 4 = (2/5)(5) + b = 2 + b, so b = 2. The equation is y = (2/5)x + 2.

9 Question 9 of 10

Not answered

A linear function f has values f(-2) = 9, f(1) = 3, and f(4) = -3. What is f(7)?

Hint: Find the constant rate of change from one input-output pair to the next.

Explanation: When x increases by 3, f(x) decreases by 6, so the slope is -6/3 = -2. The function is f(x) = -2x + 5. Therefore, f(7) = -14 + 5 = -9.

10 Question 10 of 10

Not answered

Two phone plans have monthly costs A = 18 + 0.14m and B = 30 + 0.10m, where m is the number of minutes used. For how many minutes do the plans cost the same amount?

Hint: Set the two expressions for monthly cost equal to each other.

Explanation: Set 18 + 0.14m = 30 + 0.10m. Subtract 0.10m: 18 + 0.04m = 30. Subtract 18: 0.04m = 12. Divide by 0.04: m = 300.

Your result

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SAT Algebra strategy board

SAT Algebra is the linear-relationships domain: equations, functions, systems, and inequalities

These 10 questions stay inside the SAT Algebra domain. They practice solving and interpreting linear equations, reading linear models, rewriting equations in two variables, analyzing systems, checking inequalities, finding parallel lines, and moving between tables and equations.

1-variable equations

Linear functions

2-variable equations

Systems

Inequalities

Linear equation compression

Distribute once, collect once, then isolate the variable

The first quiz question looks longer than it is because the linear structure is hidden inside parentheses.

Transform

5(2x − 7) = 3x + 14

10x − 35 = 3x + 14

7x = 49

x = 7

Check

x = 7

Left: 5(14 − 7) = 35

Right: 21 + 14 = 35

Both sides agree ✓

Linear model anatomy

Separate the starting value from the rate of change

Storage model C = 28 + 6.5b

A SAT question may ask what a coefficient means instead of asking you to calculate anything.

28 = fixed starting monthly fee

6.5 = dollars added per stored box

b = number of stored boxes

Line language

Slope can be hidden in standard form, a table, or a parallel-line condition

Rewrite before reading slope

4x + 2y = 18 becomes y = −2x + 9.

The slope is −2, not 4 or 9.

Parallel means same slope

A line parallel to 2x − 5y = 15 must keep slope 2/5.

Then use the required point to determine the intercept.

System scanner

Before solving a system, ask what kind of intersection is possible

SAT Algebra can test the solution itself or whether a system has zero, one, or infinitely many solutions.

No solutionparallel lines with different intercepts

One solutiontwo different lines intersect once

Infinitely manyboth equations describe the same line

Inequality boundary

“At most” includes the boundary value

For the club budget, 84 + 18p ≤ 300 gives p ≤ 12. The greatest affordable whole-number value is therefore 12.

Representation switch

The same linear relationship may appear as a table, equation, graph, or real-world model

Tablex rises by 3 while f(x) falls by 6

Rateslope = −6 / 3 = −2

Equationf(x) = −2x + 5

SAT Algebra traps

Most distractors come from a structural mistake that still produces a reasonable-looking number

Coefficient vs interceptIn C = 28 + 6.5b, 6.5 is the rate; 28 is the starting value.

Equivalent equationsIf one system equation is a multiple of the other, they can represent the same line.

Inequality testingA point must satisfy the entire inequality after both coordinates are substituted.

Skill diagnostic

Use the 10-question result to identify which SAT Algebra skill needs practice

1-variablesolve and interpret linear equations

Functionsrate, input-output, model meaning

2-variableslope, standard form, parallel lines

Systemssolution pairs and number of solutions

Inequalitiesboundaries, contexts, solution points

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