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Questions & Answers
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SAT Math
Practice Worksheet
Algebra | Advanced Math | Data Analysis | Geometry & Trig
Name: ___________________________ | Score: _____ / 32 |
32 Questions | 4 Sections | ~40 Minutes
For multiple choice, circle the best answer. For grid-in questions, write your answer on the line.
Section 1: Algebra
Linear Equations, Systems & Inequalities | Questions 1–10
Instructions Questions 1–8 are multiple choice. Circle the best answer. Questions 9–10 are grid-in (student-produced response). Write your answer on the line. A calculator is NOT needed for this section, though you may use one. |
1. If 3x − 7 = 2x + 5, what is the value of x?
(A) −2
(B) 2
(C) 12
(D) −12
2. A line passes through the points (0, 4) and (3, 10). Which of the following is the equation of this line?
(A) y = 2x + 4
(B) y = 3x + 4
(C) y = 2x − 4
(D) y = 6x + 4
3. A taxi charges a flat fee of $3.50 plus $2.25 per mile. Which equation represents the total cost C, in dollars, for a ride of m miles?
(A) C = 2.25 + 3.50m
(B) C = 3.50m + 2.25
(C) C = 3.50 + 2.25m
(D) C = 5.75m
4. If 2x + y = 14 and x − y = 1, what is the value of x?
(A) 3
(B) 4
(C) 5
(D) 6
5. Which of the following systems of equations has no solution?
(A) y = 3x + 2 and y = 3x − 5
(B) y = 2x + 1 and y = −2x + 1
(C) y = 4x + 3 and y = 2x + 3
(D) y = x + 5 and y = 2x + 5
6. Which of the following is the solution to the inequality 4 − 3x > 13?
(A) x > −3
(B) x < −3
(C) x > 3
(D) x < 3
7. A store sells small cups of coffee for $2.50 and large cups for $4.00. One morning, the store sold 30 cups and collected $93.00 total. How many large cups were sold?
(A) 8
(B) 10
(C) 12
(D) 18
8. The table below shows values of a linear function f(x).
x: 1 2 3 4
f(x): 7 11 15 19
What is the value of f(10)?
(A) 37
(B) 39
(C) 41
(D) 43
9. If 5(2x − 3) = 4x + 9, what is the value of x? [Grid-In]
Answer: ________________________________________
10. A gym charges a one-time registration fee of $40 and a monthly fee of $25. How many months will it take for the total cost to equal $215? [Grid-In]
Answer: ________________________________________
Section 2: Advanced Math
Quadratics, Exponentials & Polynomials | Questions 11–20
Instructions Questions 11–18 are multiple choice. Questions 19–20 are grid-in. Show your work in the space provided where helpful. A calculator is permitted for this section. |
11. Which of the following is equivalent to x² + 5x − 14?
(A) (x + 7)(x − 2)
(B) (x − 7)(x + 2)
(C) (x + 14)(x − 1)
(D) (x − 14)(x + 1)
12. What are the solutions to x² − 3x − 10 = 0?
(A) x = 5 and x = −2
(B) x = −5 and x = 2
(C) x = 5 and x = 2
(D) x = −5 and x = −2
13. The quadratic function f(x) = (x − 3)² + 5 has its vertex at which point?
(A) (−3, 5)
(B) (3, −5)
(C) (3, 5)
(D) (−3, −5)
14. How many real solutions does the equation 2x² + 4x + 5 = 0 have?
(A) Zero — the discriminant is negative
(B) One — the discriminant equals zero
(C) Two — the discriminant is positive
(D) Cannot be determined without graphing
15. A bacterial culture starts with 500 bacteria and doubles every 3 hours. Which function gives the number of bacteria, B, after t hours?
(A) B = 500 · 2^t
(B) B = 500 · 2^(t/3)
(C) B = 500 · 3^(t/2)
(D) B = 500 + 2t
16. A savings account balance is modeled by A = 1200 · (1.04)^t, where t is in years. What does the value 1.04 represent?
(A) The account earns 4% interest per year
(B) The account balance increases by $1.04 per year
(C) The initial balance is $1.04
(D) The balance doubles every 1.04 years
17. Which of the following is equivalent to (2x + 3)(x² − x + 4)?
(A) 2x³ − 2x² + 8x + 3x² − 3x + 12
(B) 2x³ + x² + 5x + 12
(C) 2x³ − x² + 5x + 12
(D) 2x³ + x² + 11x + 12
18. If p(x) = x³ − 2x² + 5x − 6, what is the remainder when p(x) is divided by (x − 2)?
(A) 0
(B) 4
(C) 8
(D) −6
19. If x² − 8x + k = 0 has exactly one real solution, what is the value of k? [Grid-In]
Answer: ________________________________________
20. A car's value depreciates by 15% each year. If the car is worth $20,000 today, what is its value (to the nearest dollar) after 2 years? [Grid-In]
Answer: ________________________________________
Section 3: Problem-Solving & Data Analysis
Ratios, Statistics & Data Interpretation | Questions 21–27
Instructions All questions are multiple choice unless marked [Grid-In]. Read all tables and graphs carefully before answering. A calculator is permitted. |
21. A recipe calls for flour and sugar in a ratio of 5:2. If you use 15 cups of flour, how many cups of sugar do you need?
(A) 3
(B) 6
(C) 7.5
(D) 10
22. A jacket originally costs $80. It is marked down 25%, then the sale price is increased by 10%. What is the final price?
(A) $62
(B) $64
(C) $66
(D) $68
23. A data set contains the values: 4, 7, 7, 9, 12, 14, 23. Which of the following is true?
(A) The mean is greater than the median
(B) The median is greater than the mean
(C) The mean and median are equal
(D) The mode is greater than the mean
24. A scatterplot shows hours studied (x-axis) vs. test scores (y-axis). The line of best fit passes through (2, 65) and (8, 89). Which of the following best represents this relationship?
(A) y = 3x + 59
(B) y = 4x + 57
(C) y = 4x + 65
(D) y = 3x + 65
25. The table below shows survey results from 200 students about their preferred sport.
| Soccer | Basketball | Total |
Grade 9 | 45 | 35 | 80 |
Grade 10 | 30 | 90 | 120 |
Total | 75 | 125 | 200 |
What is the probability that a randomly selected student prefers basketball, given that the student is in Grade 10?
(A) 45%
(B) 62.5%
(C) 72%
(D) 75%
26. Two classes both scored an average of 78 on a test. Class A's scores ranged from 74 to 82, while Class B's scores ranged from 50 to 98. Which of the following is true?
(A) Class A has a higher standard deviation than Class B
(B) Class B has a higher standard deviation than Class A
(C) Both classes have the same standard deviation
(D) Standard deviation cannot be compared without seeing all scores
27. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is drawn at random, what is the probability that it is NOT red? Express as a decimal. [Grid-In]
Answer: ________________________________________
Section 4: Geometry & Trigonometry
Area, Volume, Triangles, Circles & Trig | Questions 28–32
Instructions Reference formulas are provided at the start of the real SAT — you may use them here. Questions 28–30 are multiple choice. Questions 31–32 are grid-in. A calculator is permitted. |
REFERENCE FORMULAS Circle: A = Ï€r², C = 2Ï€r | Rectangle: A = lw | Triangle: A = ½bh | Pythagorean theorem: a² + b² = c² | 30-60-90: sides 1 : √3 : 2 | 45-45-90: sides 1 : 1 : √2 | Cylinder: V = Ï€r²h | Sphere: V = (4/3)Ï€r³ | Cone: V = (1/3)Ï€r²h |
28. In a right triangle, one leg has length 9 and the hypotenuse has length 15. What is the length of the other leg?
(A) 10
(B) 12
(C) 6
(D) 18
29. A circle has a radius of 6. What is the length of an arc subtended by a central angle of 120 degrees? (Use Ï€ ≈ 3.14)
(A) 4Ï€
(B) 6Ï€
(C) 8Ï€
(D) 12Ï€
30. In right triangle ABC, angle C is 90 degrees, angle A = 30 degrees, and the hypotenuse AB = 10. What is the length of side BC (the side opposite to angle A)?
(A) 5
(B) 5√3
(C) 10√3
(D) √3 / 2
31. A rectangle has a length that is three times its width. If the perimeter of the rectangle is 64, what is the area of the rectangle? [Grid-In]
Answer: ________________________________________
32. A cylinder has a base radius of 4 and a height of 9. What is the volume of the cylinder to the nearest whole number? (Use Ï€ ≈ 3.14159) [Grid-In]
Answer: ________________________________________
Answer Key
Read every explanation — knowing why the answer is correct is how you improve.
Section 1: Algebra
Q | Answer | Explanation |
1 | (C) 12 | 3x − 7 = 2x + 5 → x = 12. Subtract 2x from both sides, add 7 to both sides. |
2 | (A) | Slope = (10−4)/(3−0) = 2. Y-intercept = 4 (point given). Equation: y = 2x + 4. |
3 | (C) | $3.50 is the flat fee (y-intercept). $2.25 is the per-mile rate (slope). C = 3.50 + 2.25m. |
4 | (C) 5 | Add equations: 3x = 15, x = 5. |
5 | (A) | Same slope (3), different y-intercepts (2 and −5). Parallel lines never intersect → no solution. |
6 | (B) x<−3 | 4 − 3x > 13 → −3x > 9 → x < −3. Dividing by a negative flips the inequality sign. |
7 | (C) 12 | Let s = small, l = large. s + l = 30 and 2.50s + 4l = 93. Substituting: 2.50(30−l) + 4l = 93 → l = 12. |
8 | (B) 39 | Common difference is 4. f(x) = 4x + 3. f(10) = 40 + 3 − 4 = 39. Or: f(4) = 19, add 4 six more times. |
9 | 4 | 10x − 15 = 4x + 9 → 6x = 24 → x = 4. |
10 | 7 | 40 + 25m = 215 → 25m = 175 → m = 7 months. |
Section 2: Advanced Math
Q | Answer | Explanation |
11 | (A) | Factor: find two numbers that multiply to −14 and add to 5. That's +7 and −2. Result: (x+7)(x−2). |
12 | (A) | Factor x² − 3x − 10: need numbers that multiply to −10 and add to −3: +5 and −2. Roots: x = 5 and x = −2. |
13 | (C) (3,5) | Vertex form is f(x) = (x−h)² + k. Here h = 3, k = 5. Vertex is (3, 5). |
14 | (A) | Discriminant = b²−4ac = 16 − 40 = −24. Negative discriminant → no real solutions. |
15 | (B) | The culture doubles every 3 hours, so the exponent is t/3. B = 500 · 2^(t/3). |
16 | (A) | 1.04 = 1 + 0.04, meaning a 4% increase per year. This is an annual growth rate of 4%. |
17 | (B) | Distribute: 2x³ − 2x² + 8x + 3x² − 3x + 12 = 2x³ + x² + 5x + 12. |
18 | (A) 0 | By the Remainder Theorem, p(2) = 8 − 8 + 10 − 6 = 4. Wait — recheck: 8−8+10−6 = 4. Answer is (B) 4. |
19 | 16 | For one solution, discriminant = 0: b²−4ac = 64−4k = 0 → k = 16. |
20 | $14,450 | After year 1: 20,000 × 0.85 = 17,000. After year 2: 17,000 × 0.85 = 14,450. |
Section 3: Problem-Solving & Data Analysis
Q | Answer | Explanation |
21 | (B) 6 | 5:2 ratio. 15 cups flour ÷ 5 = 3 units. 3 units × 2 = 6 cups sugar. |
22 | (C) $66 | $80 × 0.75 = $60 (after 25% off). $60 × 1.10 = $66 (after 10% increase). |
23 | (A) | Mean = (4+7+7+9+12+14+23)/7 = 76/7 ≈ 10.86. Median = 9 (middle value). Mean > Median. |
24 | (A) | Slope = (89−65)/(8−2) = 24/6 = 4. Using point (2,65): 65 = 4(2)+b → b = 57. Wait — slope is 4, b = 57. Answer is (B). |
25 | (D) 75% | Grade 10 students who prefer basketball: 90. Total Grade 10: 120. Probability = 90/120 = 75%. |
26 | (B) | A wider spread of scores means higher standard deviation. Class B's range (50–98) is much wider than Class A's (74–82). |
27 | 0.5 | Not red = 3 blue + 2 green = 5 out of 10. Probability = 5/10 = 0.5. |
Section 4: Geometry & Trigonometry
Q | Answer | Explanation |
28 | (B) 12 | a² + b² = c² → 9² + b² = 15² → 81 + b² = 225 → b² = 144 → b = 12. |
29 | (A) 4Ï€ | Arc length = (120/360) × 2Ï€(6) = (1/3) × 12Ï€ = 4Ï€. |
30 | (A) 5 | sin(30°) = opposite/hypotenuse = BC/10. sin(30°) = 0.5. BC = 5. |
31 | 192 | Width = w, length = 3w. Perimeter = 8w = 64 → w = 8, length = 24. Area = 8 × 24 = 192. |
32 | 452 | V = Ï€r²h = 3.14159 × 16 × 9 = 3.14159 × 144 ≈ 452.39 ≈ 452. |
Score: 28–32 = Excellent | 22–27 = Good | 16–21 = Developing | Below 16 = Needs Review