SAT Math Practice Questions with Explanations
9 min read · Updated
Digital SAT Math rewards two things above raw knowledge: reading exactly what the question asks, and knowing when to graph instead of solve. The questions below cover all four domains. Try each one before reading the explanation.
Algebra
If 3x + 7 = 2x − 5, what is the value of x?
- A−12
- B−2
- C2
- D12
Explanation
Subtract 2x from both sides to get x + 7 = −5, then subtract 7: x = −12. The trap is 12 — a sign slip when moving the 7. Check by substituting: 3(−12) + 7 = −29 and 2(−12) − 5 = −29.
The graphs of y = 2x + 1 and y = −x + 7 intersect at the point (a, b). What is the value of a?
- A2
- B3
- C5
- D6
Explanation
At the intersection the y-values are equal: 2x + 1 = −x + 7, so 3x = 6 and x = 2. The trap is 5, which is b, the y-coordinate. On the real test you can also graph both lines on the calculator and read the intersection directly.
Advanced Math
The function f is defined by f(x) = x² − 6x + 5. For what value of x does f(x) reach its minimum?
- A1
- B3
- C5
- D−4
Explanation
For a parabola y = ax² + bx + c, the vertex is at x = −b / (2a) = 6 / 2 = 3. The minimum value itself is f(3) = −4, which is offered as a trap. 1 and 5 are the zeros of the function, not the vertex.
Problem-Solving and Data Analysis
After a 20% discount, a jacket costs $40. What was the price before the discount?
- A$32
- B$48
- C$50
- D$60
Explanation
A 20% discount leaves 80% of the original price, so 0.8p = 40 and p = 50. The trap is $48, which adds 20% of $40 back on — but the discount was 20% of the original price, not of the sale price.
Geometry and Trigonometry
A right triangle has legs of length 5 and 12. What is the length of its hypotenuse?
- A13
- B17
- C√119
- D60
Explanation
By the Pythagorean theorem, c² = 5² + 12² = 25 + 144 = 169, so c = 13. 17 adds the legs, and √119 subtracts their squares. 5-12-13 is one of the Pythagorean triples worth recognizing on sight, along with 3-4-5 and 8-15-17.
In right triangle ABC, angle C is the right angle and sin A = 3/5. What is the value of cos A?
- A3/4
- B4/5
- C5/3
- D5/4
Explanation
sin A = opposite / hypotenuse = 3/5, so the sides are 3, 4 and 5 and the side adjacent to A is 4. cos A = adjacent / hypotenuse = 4/5. 3/4 is tan A.
Student-produced responses
About a quarter of Math questions have no options: you type the answer. The entry rules are strict, and knowing them saves points:
- Up to 5 characters for a positive answer, 6 for a negative one (the minus sign counts).
- Fractions are fine — 7/2 — but never a mixed number like 3 1/2, which would be read as 31/2.
- If a decimal is too long, cut it off or round it at the fourth digit: 2/3 can go in as 2/3, .6666 or .6667, but not .66.
- No units, commas, dollar signs or percent signs.
- If more than one answer is correct, enter just one.
Three habits that save the most points
- Circle what the question asks for — x, 2x, the y-coordinate, the minimum value — before you start. Most wrong options are built from correct intermediate steps.
- Graph when the algebra is long. Systems, quadratics and questions about the number of solutions are often faster on the calculator.
- Plug in the options. For a multiple-choice question with an equation, testing the answer choices is legitimate and often quickest.