SAT Math

Two 35-minute modules of 22 questions each. Calculator is allowed on every question. About 75% are multiple choice (A–D) and 25% are student-produced response (you type the number). Four domains: Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry.

• Algebra (≈35%)

  Linear equations and inequalities in one and two variables, linear systems, and graph-equation translation. The bedrock of the section — master this first.

• Advanced Math (≈35%)

  Quadratics, polynomial and rational expressions, exponential equations, and nonlinear functions. Watch for equivalent forms — factored vs vertex vs standard.

• Problem-Solving & Data Analysis (≈15%)

  Ratios, percentages, unit conversion, two-way tables, statistics, and probability. Read tables and figures carefully before computing.

• Geometry & Trigonometry (≈15%)

  Triangles (including special right triangles), circles, area and volume, lines and angles, and basic right-triangle trig.

5 Sample Questions

Digital SAT scoring has no wrong-answer penalty. Always answer every question.

1. Sample 1

   If $3x + 7 = 22$, what is the value of $x$?

   • A.

     $3$

   • B.

     $5$

   • C.

     $7$

   • D.

     $15$

   Show answer & explanation

   Answer: B

   Subtract 7: $3x = 15$. Divide by 3: $x = 5$.

2. Sample 2

   The function $f(x) = (x-3)(x+2)$ has zeros at which values of $x$?

   • A.

     $-3$ and $2$

   • B.

     $3$ and $-2$

   • C.

     $0$ and $6$

   • D.

     $-6$ and $0$

   Show answer & explanation

   Answer: B

   Set each factor to zero: $x - 3 = 0 \to x = 3$; $x + 2 = 0 \to x = -2$.

3. Sample 3

   A store marks up wholesale price by 40% to get the retail price. If the retail price is $70, what was the wholesale price?

   • A.

     $28

   • B.

     $42

   • C.

     $50

   • D.

     $56

   Show answer & explanation

   Answer: C

   Retail = 1.4 × Wholesale → Wholesale = 70 / 1.4 = 50.

4. Sample 4

   A right triangle has legs of length 6 and 8. What is the length of its hypotenuse?

   • A.

     $10$

   • B.

     $12$

   • C.

     $14$

   • D.

     $\sqrt{48}$

   Show answer & explanation

   Answer: A

   $\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$. This is the classic 6-8-10 triple.

5. Sample 5

   The population of a town grows at 5% per year. If the current population is 20,000, what will it be after 3 years? (Round to the nearest whole number.)

   • A.

     $23{,}000$

   • B.

     $23{,}153$

   • C.

     $23{,}625$

   • D.

     $26{,}500$

   Show answer & explanation

   Answer: B

   $20000 \times 1.05^3 = 20000 \times 1.157625 \approx 23{,}153$.