Top 50 SAT Math Questions You Must Practice

Preparing for the SAT can feel overwhelming, but the math section doesn’t have to be. The SAT Math section tests your ability to apply mathematical concepts to solve real-world and academic problems. To help you succeed, we’ve compiled 50 SAT math questions with answers and step-by-step explanations. These questions cover all the major topics you’ll encounter on the exam, making this a one-stop resource for your practice.

📌 Why Practice SAT Math Questions?

• The SAT Math section accounts for 50
• Questions are designed to test conceptual understanding, not just memorization.
• Practicing with real-style questions helps build speed, accuracy, and confidence.

The section is divided into:

1. No Calculator Section (25 minutes, 20 questions)
2. Calculator Section (55 minutes, 38 questions)

📊 SAT Math Topics Breakdown

1. Heart of Algebra (linear equations, systems, inequalities)
2. Problem Solving and Data Analysis (ratios, percentages, probability, statistics)
3. Passport to Advanced Math (quadratics, higher-order equations, functions)
4. Additional Topics (geometry, trigonometry, complex numbers)

🔢 Top 50 SAT Math Questions with Answers

We’ll divide them into categories for easier learning.

Heart of Algebra (Q1–Q15)

Q1. Solve for x: 2x + 5 = 15

Solution:
Subtract 5 from both sides: 2x = 10.
Divide both sides by 2 to get x = 5.
Answer: x = 5

Q2. If 3x – 7 = 11, what is x?

Solution:
Add 7 to both sides: 3x = 18.
Divide by 3: x = 6.
Answer: x = 6

Q3. A line passes through (2, 3) with slope 4. Find its equation.

Solution:
Use point-slope form y – y1 = m(x – x1): y – 3 = 4(x – 2).
Simplify: y = 4x – 8 + 3 = 4x – 5.
Answer: y = 4x – 5

Q4. Solve: 5x – 3 = 2x + 12

Solution:
Subtract 2x from both sides:
3x – 3 = 12.
Add 3: 3x = 15.
Divide by 3: x = 5.
Answer: x = 5

Q5. If 2x + y = 10 and x – y = 2, solve for x and y.

Solution:
From x – y = 2
⇒ y = x – 2.
Substitute into first: 2x + (x – 2) = 10
⇒ 3x – 2 = 10
⇒ 3x = 12
⇒ x = 4.
Then y = 4 – 2 = 2.
Answer: (x, y) = (4, 2)

Q6. Which is the slope of line 2y – 6x = 10?

Solution:
Solve for y:
2y = 6x + 10
⇒ y = 3x + 5.
Slope m = 3.
Answer: slope = 3

Q7. Solve: 4x + 9 = 2x + 3

Solution:
Subtract 2x:
2x + 9 = 3.
Subtract 9: 2x = -6.
Divide: x = -3.
Answer: x = -3

Q8. A system of equations: y = 2x + 1 and y = –x + 4. Find intersection.

Solution:
Set equal: 2x + 1 = -x + 4
⇒ 3x = 3
⇒ x = 1.
Then y = 2(1) + 1 = 3.
Answer: (x, y) = (1, 3)

Q9. Solve inequality: 2x – 3 > 7

Solution:
Add 3:
2x > 10
⇒ divide by 2: x > 5.
Answer: x > 5

Q10. If 5x + 2y = 20 and x = 2, find y.

Solution:
Substitute x = 2
10 + 2y = 20
⇒ 2y = 10 ⇒ y = 5.
Answer: y = 5

Q11. Solve: 7x – 4 = 3x + 8

Solution:
Subtract 3x:
4x – 4 = 8.
Add 4: 4x = 12
⇒ x = 3.
Answer: x = 3

Q12. If slope = 1/2 and passes through (0, 4), find equation.

Solution:
(0,4) is y-intercept.
Equation: y = (1/2)x + 4.
Answer: y = 0.5x + 4

Q13. Solve: x/3 + 2 = 5

Solution:
Subtract 2:
x/3 = 3
⇒ x = 9.
Answer: x = 9

Q14. Solve: 2(x – 3) = 10

Solution:
Expand: 2x – 6 = 10
⇒ 2x = 16
⇒ x = 8.
Answer: x = 8

Q15. Solve: 6x + 4 = 28

Solution:
6x = 24
⇒ x = 4.
Answer: x = 4

Problem Solving & Data Analysis (Q16–Q30)

Q16. A bag has 4 red and 6 blue balls. Probability of picking red?

Solution:
Total = 10, favorable = 4
⇒ probability = 4/10 = 0.4 or 2/5.
Answer: 2/5 or 0.4

Q17. A survey: 60

Solution:
0.60 × 200 = 120.
Answer: 120 students

Q18. If price increases by 20

Solution:
Increase = 0.20 × 50 = 10
⇒ new price = 50 + 10 = 60.
Answer: $60

Q19. Average of 5, 7, 9?

Solution:
(5 + 7 + 9)/3 = 21/3 = 7.
Answer: 7

Q20. Ratio of boys to girls = 3:2. If 30 boys, find girls.

Solution:
Let girls = x. 3/2 = 30/x
⇒ 3x = 60
⇒ x = 20.
Answer: 20 girls

Q21. A class has 40

Solution:
0.40 × 200 = 80.
Answer: 80 males

Q22. A die is rolled. Probability of even number?

Solution:
Even faces = {2,4,6}
⇒ 3/6 = 1/2.
Answer: 1/2

Q23. A car travels 120 miles in 3 hours. Speed?

Solution:
Speed = distance/time = 120/3 = 40 mph.
Answer: 40 mph

Q24. If simple interest is $200 on $1000 at 10

Solution: SI = PRT ⇒ 200 = 1000 × 0.10 × t
⇒ 200 = 100t ⇒ t = 2 years.
Answer: 2 years

Q25. If mean of 6 numbers is 8, total sum?

Solution: Sum = mean × count = 8 × 6 = 48.
Answer: 48

Q26. If 25

Solution: 0.25x = 50
⇒ x = 50/0.25 = 200.
Answer: x = 200

Q27. A train moves 300 miles in 5 hours. Average speed?

Solution: 300/5 = 60 mph.
Answer: 60 mph

Q28. If 3 pens cost $6, cost of 5 pens?

Solution: Unit cost = 6/3 = 2
⇒ 5 × 2 = $10.
Answer: $10

Q29. A spinner has 8 equal sections. Probability of landing on 1 section?

Solution: 1/8 = 0.125.
Answer: 1/8

Q30. If a student answered 45/50 correctly, percentage score?

Solution: (45/50) × 100 = 90 Answer: 90

Passport to Advanced Math (Q31–Q40)

Q31. Solve: x² −9=0

Solution: (x – 3)(x + 3) = 0 ⇒ x = ±3.
Answer: x = ±3

Q32. Solve: x² −5x+6=0

Solution: (x – 2)(x – 3) = 0 ⇒ x = 2 or 3.
Answer: x = 2, 3

Q33. Solve: 2x² – 8 = 0

Solution: 2x² = 8
⇒ x² = 4
⇒ x = ±2.
Answer: x = ±2

Q34. If f(x) = 2x + 3, find f(5)

Solution: f(5) = 2(5) + 3 = 13.
Answer: 13

Q35. Solve: (x−4)(x+2)=0

Solution: x = 4 or x = -2.
Answer: x = 4, -2

Q36. If g(x)=x²+2x,  find g(−3)?

Solution: g(-3) = 9 – 6 = 3.
Answer: 3

Q37. Solve: x² – 16 = 0

Solution: (x – 4)(x + 4) = 0 ⇒ x = ±4.
Answer: x = ±4

Q38. Solve: (x + 1)(x – 5) = 0

Solution: x = -1 or x = 5.
Answer: x = -1, 5

Q39. Solve: x² + 6x + 9 = 0

Solution:
Recognize perfect square: x² + 6x + 9 = (x + 3)² .
So (x + 3)² = 0
⇒ x = -3 (double root).
Answer: x = -3

Q40. Solve: 3x² = 27

Solution: x² = 9 ⇒ x = ±3.
Answer: x = ±3

Geometry & Trigonometry (Q41–Q45)

Q41. Area of rectangle: length=10, width=5

Solution: Area = length × width = 10 × 5 = 50.
Answer: 50

Q42. Perimeter of square with side=6

Solution: Perimeter = 4 × side = 4 × 6 = 24.
Answer: 24

Q43. Area of circle with radius = 7 (π = 3.14)

Solution: Area = πr² = 3.14 × 49 = 153.86.
Answer: 153.86

Q44. Pythagoras: Hypotenuse if legs = 3 and 4

Solution: c = √(3² + 4²) = √(9 + 16) = √25 = 5.
Answer: 5

Q45. sin θ if opposite = 5, hypotenuse = 13

Solution: sin θ = opposite/hypotenuse = 5/13.
Answer: 5/13

Mixed & Word Problems (Q46–Q50)

Q46. A tank fills in 6 hrs. In 1 hr, what fraction filled?

Solution: Fraction filled in 1 hour = 1/6.
Answer: 1/6

Q47. If speed=60 mph, time=2 hrs, distance?

Solution: Distance = speed × time = 60 × 2 = 120 miles.
Answer: 120 miles

Q48. If 2 pencils cost $1, how many with $5?

Solution: Unit cost = $0.50 ⇒ 5 ÷ 0.5 = 10 pencils.
Answer: 10 pencils

Q49. If x

Solution: (x/100) × 200 = 50 ⇒ 2x = 50 ⇒ x = 25.
Answer: 25

Q50. If a = 3 and b = 4, find a² + b² 

Solution: 3² + 4² = 9 + 16 = 25.
Answer: 25

 

✅ Final Tips for SAT Math Success

1. Know the formulas: SAT provides some, but memorize key ones.
2. Practice mental math: Save calculator time for complex problems.
3. Eliminate wrong answers: Use process of elimination.
4. Manage time: Don’t get stuck on one question.
5. Review mistakes: Learn from practice tests.

📖 Conclusion

Mastering SAT Math requires consistent practice, focus on weak areas, and strategic preparation. The 50 questions above cover every major concept tested on the SAT. Work through them carefully, understand the step-by-step solutions, and you’ll build the confidence you need to maximize your score.

 

📌 FAQs about SAT Math

Q1. How many math questions are on the SAT?
Ans. There are 58 math questions in total (20 no-calculator and 38 calculator).

Q2. What’s the best way to study SAT Math?
Ans. Practice topic by topic, review your mistakes, and take timed mock tests.

Q3. Can I rely only on formulas provided in the test booklet?
Ans. Some are given, but memorizing common formulas will save time.

Q4. What is considered a good SAT Math score?
Ans. A score above 700 is considered very strong, but it depends on your college goals.

Q5. How much time should I dedicate daily to SAT Math practice?
Ans. 1–2 hours of focused practice daily for 2–3 months is effective for most students.