A bike courier charges a flat $9 for a delivery plus $0.80 for each kilometer ridden. One delivery cost $29. How many kilometers was the ride?Answer: 25. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear equations in one variable. The answer is worked out from the numbers in the question.
A candle is 30 centimeters tall when lit and burns down at a steady 1.5 centimeters per hour. Which function gives its height h(t), in centimeters, t hours after it is lit?Answer: h(t) = 30 − 1.5t. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear functions. The answer is worked out from the numbers in the question.
A club needs at least $600. It has $135 and earns $15 for each car it washes. Which inequality gives the numbers of cars, c, that meet the goal?Answer: c ≥ 31. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear inequalities in one or two variables. The answer is worked out from the numbers in the question.
Show all 60 questions (57 more)
Algebra, continued
A food truck sells tacos for $3 each and bowls for $8 each. One evening it sold t tacos and b bowls for a total of $940. Which equation represents this?Answer: 3t + 8b = 940. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear equations in two variables. The answer is worked out from the numbers in the question.
A freight elevator can carry at most 1,800 pounds. A worker who weighs 190 pounds loads it with boxes of 46 pounds each. What is the greatest number of boxes the worker can ride with?Answer: 35. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear inequalities in one or two variables. The answer is worked out from the numbers in the question.
A line in the xy-plane is perpendicular to the line y = (2/5)x − 3 and passes through (4, 1). What is its equation?Answer: y = −(5/2)x + 11. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear equations in two variables. The answer is worked out from the numbers in the question.
A line in the xy-plane passes through (−3, 4) and (5, −2). What is the slope of the line?Answer: −3/4. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear equations in two variables. The answer is worked out from the numbers in the question.
Adult tickets cost $14 and child tickets cost $9. A group bought 11 tickets for $129. How many adult tickets did the group buy?Answer: 6. Source: College Board, SAT Math section, Types of Math Tested: Algebra, systems of two linear equations in two variables. The answer is worked out from the numbers in the question.
The equation 4(2x + 1) = 8x + k has infinitely many solutions. What is the value of k?Answer: 4. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear equations in one variable. The answer is worked out from the numbers in the question.
For what value of a does the system 6x − 4y = 10 and 9x + ay = 3 have no solution?Answer: −6. Source: College Board, SAT Math section, Types of Math Tested: Algebra, systems of two linear equations in two variables. The answer is worked out from the numbers in the question.
The function c(m) = 45 + 0.2m gives the cost, in dollars, of renting a van and driving it m miles. What does 0.2 represent?Answer: The cost in dollars of each mile driven. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear functions. The answer is worked out from the numbers in the question.
The function f is linear, with f(3) = 7 and f(8) = 27. What is f(0)?Answer: −5. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear functions. The answer is worked out from the numbers in the question.
The function g is defined by g(x) = −4x + 7. For what value of x is g(x) = −13?Answer: 5. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear functions. The answer is worked out from the numbers in the question.
How many solutions does the equation 3(x + 4) − x = 2x + 7 have?Answer: None. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear equations in one variable. The answer is worked out from the numbers in the question.
If 4x + 3y = 29 and x − 3y = −4, what is the value of x?Answer: 5. Source: College Board, SAT Math section, Types of Math Tested: Algebra, systems of two linear equations in two variables. The answer is worked out from the numbers in the question.
If 6(x − 2) = 2x + 16, what is the value of x?Answer: 7. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear equations in one variable. The answer is worked out from the numbers in the question.
In the xy-plane, the graph of y = f(x) is a line with slope −2 that crosses the x-axis at (5, 0). What is f(−1)?Answer: 12. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear functions. The answer is worked out from the numbers in the question.
Line k has the equation 5x − 2y = 30. At what point does line k cross the y-axis?Answer: (0, −15). Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear equations in two variables. The answer is worked out from the numbers in the question.
The solution to the system y = 3x − 5 and y = −x + 11 is (x, y). What is the value of x + y?Answer: 11. Source: College Board, SAT Math section, Types of Math Tested: Algebra, systems of two linear equations in two variables. The answer is worked out from the numbers in the question.
Which of the following is the solution to 11 − 3x > 26?Answer: x < −5. Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear inequalities in one or two variables. The answer is worked out from the numbers in the question.
Which point is a solution to the system of inequalities y ≥ 3x − 4 and y < −2x + 9?Answer: (1, 3). Source: College Board, SAT Math section, Types of Math Tested: Algebra, linear inequalities in one or two variables. The answer is worked out from the numbers in the question.
Advanced Math 21
A patch of moss covers 40 square centimeters and doubles in area every 5 weeks. Which function gives its area, in square centimeters, after w weeks?Answer: A(w) = 40 · 2^(w/5). Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear functions. The answer is worked out from the numbers in the question.
A stall's daily profit, in dollars, from selling a snack at a price of p dollars is P(p) = −4p² + 120p − 500. What is the greatest daily profit the model gives?Answer: $400. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear functions. The answer is worked out from the numbers in the question.
The expression x² + 10x + 7 can be written as (x + h)² + k. What is the value of k?Answer: −18. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, equivalent expressions. The answer is worked out from the numbers in the question.
For what value of c does the equation x² − 12x + c = 0 have exactly one real solution?Answer: 36. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear equations in one variable. The answer is worked out from the numbers in the question.
For x > 0, which expression is equivalent to √(50x³)?Answer: 5x√(2x). Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, equivalent expressions. The answer is worked out from the numbers in the question.
The function f is defined by f(x) = (x − 3)² − 16. For which values of x does f(x) = 0?Answer: −1 and 7. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear functions. The answer is worked out from the numbers in the question.
The function h is defined by h(x) = 3 · 4^x. What is the value of h(1/2)?Answer: 6. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear functions. The answer is worked out from the numbers in the question.
The graphs of y = x² − 3 and y = 2x + 5 meet at two points. What is the larger x-coordinate of the two?Answer: 4. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, systems of equations in two variables. The answer is worked out from the numbers in the question.
If f(x) = x³ − 4x, what is f(−2)?Answer: 0. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear functions. The answer is worked out from the numbers in the question.
If |4x − 6| = 10, what is the sum of the two solutions?Answer: 3. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear equations in one variable. The answer is worked out from the numbers in the question.
The number of subscribers to a newsletter is modeled by S(t) = 2,400(1.06)^t, where t is the number of months since its launch. What does 1.06 mean in this model?Answer: The count grows by 6% each month. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear functions. The answer is worked out from the numbers in the question.
What are all the solutions to √(2x + 3) = x?Answer: 3 only. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear equations in one variable. The answer is worked out from the numbers in the question.
What are the solutions to x² + 3x − 40 = 0?Answer: −8 and 5. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear equations in one variable. The answer is worked out from the numbers in the question.
What is the positive solution to 3x² + 10x − 8 = 0?Answer: 2/3. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear equations in one variable. The answer is worked out from the numbers in the question.
What is the solution to 3/(x − 1) = 2/(x + 4)?Answer: −14. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear equations in one variable. The answer is worked out from the numbers in the question.
Which expression is a factor of 2x² − 7x − 15?Answer: 2x + 3. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, equivalent expressions. The answer is worked out from the numbers in the question.
Which expression is equivalent to (2x³y)² · x⁻⁴, for x ≠ 0?Answer: 4x²y². Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, equivalent expressions. The answer is worked out from the numbers in the question.
Which expression is equivalent to (3x − 2)(x + 5)?Answer: 3x² + 13x − 10. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, equivalent expressions. The answer is worked out from the numbers in the question.
Which expression is equivalent to (x² − 16)/(x² − x − 12), for x ≠ 4 and x ≠ −3?Answer: (x + 4)/(x + 3). Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, equivalent expressions. The answer is worked out from the numbers in the question.
Which expression is equivalent to 1/(x − 2) + 3/(x + 1), for x ≠ 2 and x ≠ −1?Answer: (4x − 5)/((x − 2)(x + 1)). Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, equivalent expressions. The answer is worked out from the numbers in the question.
Which of the following is a zero of the function p(x) = x³ − 2x² − 5x + 6?Answer: 3. Source: College Board, SAT Math section, Types of Math Tested: Advanced Math, nonlinear functions. The answer is worked out from the numbers in the question.
Problem-Solving and Data Analysis 9
A car travels at 54 kilometers per hour. How many meters does it travel each second?Answer: 15. Source: College Board, SAT Math section, Types of Math Tested: Problem-Solving and Data Analysis, ratios, rates, proportional relationships, and units. The answer is worked out from the numbers in the question.
A paint color mixes blue and white paint in the ratio 3 to 8 by volume. How much white paint goes with 12 liters of blue?Answer: 32 liters. Source: College Board, SAT Math section, Types of Math Tested: Problem-Solving and Data Analysis, ratios, rates, proportional relationships, and units. The answer is worked out from the numbers in the question.
A scatterplot shows the heights of bean plants, y, in centimeters, x weeks after planting. A line of best fit has the equation y = 2.4x + 6. What height does the line predict at 5 weeks?Answer: 18 centimeters. Source: College Board, SAT Math section, Types of Math Tested: Problem-Solving and Data Analysis, two-variable data: models and scatterplots. The answer is worked out from the numbers in the question.
A shop sold 150 coats in a month: 90 wool and 60 synthetic. Buyers returned 27 of the wool coats and 33 of the synthetic ones. If one returned coat is picked at random, what is the probability that it is wool?Answer: 9/20. Source: College Board, SAT Math section, Types of Math Tested: Problem-Solving and Data Analysis, probability and conditional probability. The answer is worked out from the numbers in the question.
After a 20% discount, a bicycle costs $336. What was its price before the discount?Answer: $420. Source: College Board, SAT Math section, Types of Math Tested: Problem-Solving and Data Analysis, percentages. The answer is worked out from the numbers in the question.
The data set 4, 9, 9, 12, 16 has a mean of 10. If the value 16 is replaced by 46, which statement is true?Answer: The mean rises and the median stays the same. Source: College Board, SAT Math section, Types of Math Tested: Problem-Solving and Data Analysis, one-variable data: distributions and measures of center and spread. The answer is worked out from the numbers in the question.
In a random sample of 400 voters in a town, 58% favor a new park. The poll's margin of error is 5 percentage points. Which conclusion does the poll best support?Answer: It is plausible that 53% to 63% of the town's voters favor the park. Source: College Board, Assessment Framework for the Digital SAT Suite, Table A37: Problem-Solving and Data Analysis, inference from sample statistics and margin of error (interpret margin of error).
The price of a jacket rose from $80 to $92. By what percent did the price increase?Answer: 15%. Source: College Board, SAT Math section, Types of Math Tested: Problem-Solving and Data Analysis, percentages. The answer is worked out from the numbers in the question.
Sixty volunteers were randomly assigned to drink tea or water before a memory test, and the tea group scored higher on average. The volunteers were not a random sample of any larger group. What do the results support?Answer: Tea likely raised scores for these volunteers. Source: College Board, Assessment Framework for the Digital SAT Suite, Table A37: Problem-Solving and Data Analysis, evaluating statistical claims (random assignment and evidence of cause; a result extends only to the population sampled).
Geometry and Trigonometry 9
A circle has a radius of 10. One of its arcs is cut off by a central angle of 3π/5 radians. How long is the arc?Answer: 6π. Source: College Board, SAT Math section, Types of Math Tested: Geometry and Trigonometry, circles. The answer is worked out from the numbers in the question.
A right circular cone has a base radius of 6 centimeters and a height of 7 centimeters. What is its volume, in cubic centimeters?Answer: 84π. Source: College Board, SAT Math section, Types of Math Tested: Geometry and Trigonometry, area and volume. The answer is worked out from the numbers in the question.
Every side of a rectangle is made 3 times as long. By what factor does its area grow?Answer: 9. Source: College Board, SAT Math section, Types of Math Tested: Geometry and Trigonometry, area and volume. The answer is worked out from the numbers in the question.
If sin 28° = cos x° and 0 < x < 90, what is the value of x?Answer: 62. Source: College Board, SAT Math section, Types of Math Tested: Geometry and Trigonometry, right triangles and trigonometry. The answer is worked out from the numbers in the question.
In a right triangle, angle A is acute and sin A = 5/13. What is cos A?Answer: 12/13. Source: College Board, SAT Math section, Types of Math Tested: Geometry and Trigonometry, right triangles and trigonometry. The answer is worked out from the numbers in the question.
In the xy-plane, a circle has the equation (x − 4)² + (y + 1)² = 36. What are its center and radius?Answer: Center (4, −1), radius 6. Source: College Board, SAT Math section, Types of Math Tested: Geometry and Trigonometry, circles. The answer is worked out from the numbers in the question.
The legs of a right triangle measure 9 and 40. How long is its hypotenuse?Answer: 41. Source: College Board, SAT Math section, Types of Math Tested: Geometry and Trigonometry, right triangles and trigonometry. The answer is worked out from the numbers in the question.
Triangle JKL is similar to triangle MNP, with side JK matching MN and side KL matching NP. If JK = 8, KL = 14 and MN = 20, what is NP?Answer: 35. Source: College Board, SAT Math section, Types of Math Tested: Geometry and Trigonometry, lines, angles, and triangles. The answer is worked out from the numbers in the question.
Two lines cross. One of the four angles formed measures (2x + 14)°, and the angle vertical to it measures 76°. What is the value of x?Answer: 31. Source: College Board, SAT Math section, Types of Math Tested: Geometry and Trigonometry, lines, angles, and triangles. The answer is worked out from the numbers in the question.
This free SAT math practice test has 60 questions of our own in the test's four math areas, each worked out. It is unofficial and not affiliated with, endorsed by or sponsored by the College Board, which owns the SAT.
Read the full guide
Four areas, in the test's shares
The College Board's outline, read October 12, 2026, gives Algebra and Advanced Math 13 to 15 questions each, and Problem-Solving and Data Analysis and Geometry and Trigonometry 5 to 7 each. This bank holds 21, 21, 9 and 9.
The section, timed
Exam mode is a timed SAT practice test of the math section: 44 questions in 70 minutes, the real count and time. On test day they come as two 35-minute modules, and the second is harder or easier depending on the first.
Reading the notation
Powers are written x² or x⁻⁴, and a caret marks any other exponent, as in 2^(w/5). √ is a square root. About a quarter of the real answers are typed in; here each question has four choices.
Questions and answers
Is there an SAT math practice test PDF with answers?
Yes. Print the question sheet opens 44 questions split like the real section: 15, 15, 7 and 7 across the four areas. Tick With answer key to add every answer and its working, then choose Save as PDF in the print window.
What math is on the SAT?
Four areas, by the College Board: Algebra (linear equations, functions, systems and inequalities), Advanced Math (quadratic, exponential, polynomial, rational and radical equations), Problem-Solving and Data Analysis (ratios, percentages, data and probability), and Geometry and Trigonometry (area, volume, angles, triangles and circles).
Can you use a calculator on the SAT math section?
Yes, on every Math question. The College Board's framework says the Bluebook testing app has a Desmos graphing calculator built in, and students may bring an approved handheld calculator of their own.
Is this SAT math practice test the real exam?
No. Every question was written for this site from the College Board's published description of the section. None repeats or rewords a real, released or sample question, and a result here does not forecast a score.
How is the SAT math section scored?
The College Board reports a Math score from 200 to 800, half of the total score. Its framework says scoring weighs which questions were answered correctly, not only how many. This page counts the number right in each area.