The SAT math section tests four content areas: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. Most questions are multiple choice, and some ask you to enter your own answer. These 15 practice questions are written in that style but are all original, so they are a warm-up and a skills check rather than a copy of any official test. They are not produced by or affiliated with the College Board.
You will find linear equations and systems, function notation, quadratics and factoring, percents, averages, exponential growth, circles and triangles. For each one, try it on paper first, then check your answer and read the worked solution, even when you got it right, because it may show a faster method. On test day, two habits save the most points: substitute your answer back into the original equation, and reread the question to make sure you found what it asked for (the width, not the length). If a topic keeps costing you marks, a full worksheet on it is one click away.
Choose an option or type your answer, then press Check. Capital letters and extra spaces do not matter in typed answers, and units are optional.
Answer: A) 12
Subtract 3x from both sides: x - 7 = 5. Add 7: x = 12. Check: 4(12) - 7 = 41 and 3(12) + 5 = 41.
Answer: 5 (also accepted: a = 5, a=5)
Add the two equations to eliminate b: 3a = 15, so a = 5. (Then b = 1, and 2(5) + 1 = 11 checks.)
Answer: A) 6
Substitute x = 4: 16 - 12 + 2 = 6.
Answer: 36 (also accepted: $36, 36.00)
20% off means you pay 80%. 0.8 x 45 = 36, so the sale price is $36.
Answer: A) x = 2 and x = 3
Find two numbers that multiply to 6 and add to -5: -2 and -3. So (x - 2)(x - 3) = 0, giving x = 2 or x = 3.
Answer: 5
Slope = (6 - (-4)) / (2 - 0) = 10 / 2 = 5.
Answer: B) x² + 6x + 9
(x + 3)(x + 3) = x² + 3x + 3x + 9 = x² + 6x + 9.
Answer: 7
Area = πr², so πr² = 49π. Divide by π: r² = 49, so r = 7.
Answer: A) (2, 5)
Set them equal: 2x + 1 = -x + 7, so 3x = 6 and x = 2. Then y = 2(2) + 1 = 5. The point is (2, 5).
Answer: 7
Let the width be w, so the length is w + 3. Perimeter: 2w + 2(w + 3) = 34, so 4w + 6 = 34, 4w = 28 and w = 7.
Answer: A) 21
The five numbers add up to 5 x 18 = 90. The four known numbers add up to 69. The fifth number is 90 - 69 = 21.
Answer: 4000 (also accepted: 4,000)
9 years is 3 doubling periods. 500 x 2³ = 500 x 8 = 4,000 rabbits.
Answer: D) 80
The angles add to 180: 9x = 180, so x = 20. The largest angle is 4x = 80 degrees.
Answer: 10 (also accepted: x = 10, x=10)
Use a common denominator: x/3 = 2x/6, so 2x/6 + x/6 = 3x/6 = x/2. Then x/2 = 5, so x = 10.
Answer: B) 6
One real solution means the discriminant is zero: k² - 4(1)(9) = 0, so k² = 36 and k = 6 (taking the positive value). Then x² + 6x + 9 = (x + 3)².
Many problems ask for one quantity after you solve for another. If you find x but the question asks for 2x + 1, you are not done.
(x + 3)² is x² + 6x + 9, not x² + 9. Multiply it out as (x + 3)(x + 3).
20% off $45 means paying 80% of $45, which is $36. Subtracting 20 dollars instead of 20 percent is a common slip.
x² - 5x + 6 = (x - 2)(x - 3), so the solutions are x = 2 and x = 3, not -2 and -3. Check by substituting.
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Algebra (linear equations and systems), Advanced Math (quadratics, exponentials and functions), Problem-Solving and Data Analysis (ratios, percents and statistics) and Geometry and Trigonometry.