SAT Algebra Practice (with Explanations)
Algebra is the single largest sub-topic on SAT math. Work through these six questions, then read the full solution for each.
12 min read · Educational guide
Why algebra dominates SAT math
Roughly 35% of the math section is pure algebra: linear equations, systems of equations, and linear inequalities. Another 30% (advanced math) is algebra wearing a costume. If your algebra is sharp, you've already won half the section.
Practice set: 6 questions, fully worked
1. If 7n + 5 = 3n + 29, what is the value of n?
A) 4 B) 5 C) 6 D) 8
Subtract 3n from both sides: 4n + 5 = 29. Subtract 5: 4n = 24. Divide by 4: n = 6.
Answer: C
2. A printing company charges according to the equation C = 0.08p + 15, where C is the total cost in dollars for printing p pages. What does the number 15 represent?
A) The cost per page B) The cost to print 8 pages C) A flat setup fee independent of page count D) The maximum number of pages allowed
In y = mx + b form, b is the value when x = 0. With p = 0 pages, C = $15, which is a fixed setup fee charged before any pages are printed.
Answer: C
3. Solve the system: 4x + y = 22 and 3x − y = 13.
A) (3, 10) B) (4, 6) C) (5, 2) D) (7, −6)
Add the equations to eliminate y: 7x = 35, so x = 5. Substitute into the first equation: 4(5) + y = 22, so y = 2.
Answer: C
4. If 4(a − 1) + 6a = 10a + k for every value of a, what is the value of k?
A) −10 B) −4 C) 4 D) 10
Expand the left side: 4a − 4 + 6a = 10a − 4. The equation becomes 10a − 4 = 10a + k. The 10a terms cancel, leaving −4 = k, so k = −4.
Answer: B
5. If 5x + 2y = 36 and y = 8, what is the value of x?
A) 2 B) 4 C) 5 D) 7
Substitute y = 8: 5x + 16 = 36. Subtract 16: 5x = 20. Divide: x = 4.
Answer: B
6. A streaming service charges a one-time activation fee of $12 plus $9 per month of service. Which inequality represents the number of months m a subscriber can pay for while spending at most $93?
A) 9m + 12 ≤ 93 B) 12m + 9 ≤ 93 C) 9m − 12 ≤ 93 D) 9m + 12 ≥ 93
Total spend = 9m + 12. "At most" means ≤. So 9m + 12 ≤ 93, which solves to m ≤ 9.
Answer: A
What to drill next
- If you missed any of these, redo them by hand without looking at the explanation.
- Then do 10 more linear-equation questions from official material.
- Move on to our math strategy guide for backsolving and Desmos tactics.
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