Preparing for the SAT Math section requires more than just strategies—you need real practice with SAT-style questions. Below is a full-length Math practice set modeled after the SAT exam. Use it to test your skills, identify weak areas, and get comfortable with pacing. You can also download the PDFs (scroll to the end of the post) and print them out for a self-test.

How to Use This Practice Set

• Time yourself strictly to mimic SAT pacing.

• Attempt without a calculator for Section A.

• Review wrong answers carefully and identify patterns in your mistakes.

• Record your score and retake later to check improvement.

SAT Math Practice Test: Full-Length Section with Answers

This practice test has two sections:

• No Calculator (20 questions | 25 minutes)

• Calculator (38 questions | 55 minutes)

Try to simulate real testing conditions. After finishing, check the answer key and review your mistakes.

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Section A: No Calculator (20 Questions)

1. Solve for x: $3x+7=25$
2. If $2y–5=15$, what is y?
3. A line passes through (2, 3) and (6, 7). What is its slope?
4. Evaluate: f(x)=2×2–3x+1f(x) = 2x^2 – 3x + 1f(x)=2x2–3x+1. Find $f(2)$.
5. If x+4=5\sqrt{x + 4} = 5x+4​=5, what is x?
6. The solution to $5x–2=3x+6$ is:
7. Expand: $(x+2)(x–3)$.
8. If $3a=18$, then a = ?
9. A system of equations: $x+y=10$, $x–y=2$. Find x and y.
10. Simplify: 3x2y6xy\frac{3x^2y}{6xy}6xy3x2y​.
11. The vertex of y=(x–2)2+3y = (x – 2)^2 + 3y=(x–2)2+3 is:
12. If x2=49x^2 = 49x2=49, x = ?
13. What is the slope of a line perpendicular to $y=2x+3$?
14. If $4x+3=19$, find x.
15. Simplify: (2×2)(3×3)(2x^2)(3x^3)(2x2)(3x3).
16. If $x–y=7$ and $x+y=13$, find x.
17. Solve: $2(x–3)=10$.
18. A triangle has angles 30°, 60°, and 90°. If the shortest side = 5, what is the hypotenuse?
19. The equation of a line parallel to y=–12x+3y = –\tfrac{1}{2}x + 3y=–21​x+3 passing through (0, 4) is:
20. If $f(x)=3x–2$, find f(–1).

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Section B: Calculator (38 Questions)

21. A shirt costs $50. It is discounted 30% and then taxed 8%. What is the final price?
22. A car travels 120 miles in 2 hours. At the same speed, how long for 300 miles?
23. A right triangle has legs 5 and 12. Find the hypotenuse.
24. A parabola passes through (0, 4), (1, 2), (2, 4). Find the quadratic equation.
25. If line of best fit is $y=0.5x+2$, what is y when x = 8?
26. A student scored 80, 85, 90. What is the mean?
27. If 2×2–5=112x^2 – 5 = 112x2–5=11, solve for x.
28. A circle has radius 7. Find its circumference ($\pi =3.14$).
29. In a survey, 60% like tea, 25% like coffee, 15% like both. What % like neither?
30. Solve: x2–6x+9=0x^2 – 6x + 9 = 0x2–6x+9=0.
31. A data set has median 10. Which number keeps the median unchanged: 1, 5, 10, or 20?
32. If simple interest = P × R × T / 100, find interest for $2000 at 5% for 3 years.
33. A rectangle has length 8, width 6. Find diagonal.
34. A car depreciates 10% per year. If value now is $20,000, what will it be in 2 years?
35. Solve: $|2x–5|=7$.
36. A bag has 3 red, 2 blue, 5 green balls. Probability of drawing a blue?
37. If sin θ = 0.6, cos θ = ? (0° < θ < 90°).
38. A school has ratio boys:girls = 3:2. If 120 students total, how many girls?
39. Solve: 2x+34=1\frac{2}{x} + \frac{3}{4} = 1x2​+43​=1.
40. A function g(x) = x² – 4. What is g(–3)?
41. A ladder leans against a wall making angle 60°. Ladder = 10 ft. Height it reaches?
42. Monthly rent is $1200. Annual cost = ?
43. If $y=3x–4$, what is y when x = –2?
44. A train leaves at 2 pm at 60 mph. Another at 3 pm at 80 mph. When will faster train catch up?
45. Compound interest formula: A=P(1+r/n)ntA = P(1 + r/n)^{nt}A=P(1+r/n)nt. Find A for P = 1000, r = 0.08, n = 1, t = 2.
46. A triangle has sides 6, 8, 10. Is it right triangle?
47. If $f(x)=2x+1$, find f(3) + f(–1).
48. Solve inequality: $3x–7>5$.
49. A fair die is rolled. Probability of even number?
50. If slope of line is –3 and it passes through (0, 5), write equation.
51. The average of 4 numbers is 12. Their sum = ?
52. Solve: x2–16=0x^2 – 16 = 0x2–16=0.
53. A class has 40 students. 60% are girls. How many girls?
54. The graph of y = |x| is shifted up 3 units. Write new equation.
55. Find roots of x2–2x–15=0x^2 – 2x – 15 = 0x2–2x–15=0.
56. The volume of a cylinder is πr2h\pi r^2 hπr2h. For r = 3, h = 10, find volume.
57. If 2x=322^x = 322x=32, find x.
58. A polygon has interior angles sum = 900°. How many sides?

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Answer Key (Condensed)

No Calculator (1–20):

1. 6, 2) 10, 3) 1, 4) 3, 5) 21, 6) 4, 7) x2–x–6x^2 – x – 6x2–x–6, 8) 6, 9) (6, 4), 10) x/2, 11) (2, 3), 12) ±7, 13) –½ → perpendicular slope = 2, 14) 4, 15) 6x⁵, 16) x = 10, 17) 8, 18) 10, 19) y = –½x + 4, 20) –5.

Calculator (21–58):
21) $37.80, 22) 5 hrs, 23) 13, 24) y = x² – 2x + 4, 25) 6, 26) 85, 27) x = ±√8, 28) 43.96, 29) 30%, 30) x = 3, 31) 10, 32) $300, 33) 10, 34) $16,200, 35) x = 6 or –1, 36) 2/10 = 1/5, 37) 0.8, 38) 48, 39) x = 8, 40) 5, 41) 8.66, 42) $14,400, 43) –10, 44) 6 pm, 45) $1166.40, 46) Yes (Pythagoras holds), 47) 8, 48) x > 4, 49) 3/6 = ½, 50) y = –3x + 5, 51) 48, 52) ±4, 53) 24, 54) y = |x| + 3, 55) x = 5, –3, 56) 282.6, 57) 5, 58) 7 sides.

 

Download PDFs to Print

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SAT_Math_Practice_Test_Answers_Full

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