Digital SAT Math Practice Questions with Answers & Explanations (2026 Free Practice Test)
Preparing for the Digital SAT Math? You’re in the right place. This free practice test features 30 original Digital SAT Math questions designed to help you master the concepts tested on the latest SAT.
These questions cover the same skill areas emphasized on the Digital SAT, including algebra, advanced math, problem-solving, data analysis, geometry, and trigonometry. Every question includes the correct answer and a detailed explanation to help you understand the reasoning behind the solution.
Disclaimer: These are original practice questions created for educational purposes. They are not official College Board questions.
Table of Contents
- Linear Equations
- Percentages
- Systems of Equations
- Functions
- Exponents
- Quadratic Equations
- Geometry
- Probability
- Statistics
- Word Problems
- Answer Key
- Frequently Asked Questions
What Topics Are Covered in the Digital SAT Math Section?
The Digital SAT Math section measures your ability to apply mathematical concepts to real-world situations. Questions generally fall into four broad domains:
- Algebra
- Advanced Math
- Problem Solving and Data Analysis
- Geometry and Trigonometry
The practice questions below are designed to reflect these categories while gradually increasing in difficulty.
Digital SAT Math Practice Questions with Answers
Questions 1–10 (Easy)
These questions focus on foundational algebra, percentages, functions, geometry, and exponents.
Topics include:
- Linear equations
- Percent increase and decrease
- Function notation
- Exponent rules
- Rectangle area
- Basic probability
Question 1: Linear Equations
A gym charges a one-time membership fee of $40 plus $25 per month. If a member paid $190 in total, for how many months did they pay?
A. 5
B. 6
C. 7
D. 8
Answer: B. 6
Explanation
Let m represent the number of months.
The total cost consists of:
- One-time membership fee = $40
- Monthly fee = $25 × m
For this problem, the total paid is $190, so: 40+25m=190
Step 1: Subtract the membership fee
Subtract 40 from both sides:
25m=150
Step 2: Divide by 25
m=15025m = \frac{150}{25}m=6
Therefore, the member paid for 6 months.
Question 2: Percent
A jacket originally costs $120. It is discounted by 15%.
What is the sale price?
A. $96
B. $100
C. $102
D. $108
Answer: C. $102
Explanation
15% of 120:
[
120\times0.15=18
]
Sale price:
[
120-18=102
]
Question 3: Systems of Equations
Solve:
[
x+y=18
]
[
2x-y=9
]
A. (7,11)
B. (9,9)
C. (8,10)
D. (6,12)
Answer: B. (9,9)
Explanation
Add the equations:
[
3x=27
]
[
x=9
]
Then,
[
y=18-9=9
]
Question 4: Functions
If
[
f(x)=4x-7,
]
find (f(6)).
A. 17
B. 19
C. 24
D. 31
Answer: A. 17
Explanation
Step-by-Step Explanation
Substitute x=6x = 6x=6 into the function:f(6)=4(6)−7f(6) = 4(6) – 7
Multiply:4×6=244 \times 6 = 24
Subtract 7:24−7=1724 – 7 = 17
Therefore,f(6)=17f(6) = 17
Question 5: Exponents
Simplify
[
\frac{5^6}{5^2}
]
A. (5^2)
B. (5^3)
C. (5^4)
D. (5^8)
Answer: C. (5^4)
Explanation
Subtract exponents:
[
5^{6-2}=5^4
]
Question 6: Quadratic Equations
Solve
[
x^2-13x+40=0
]
A. 4 and 10
B. 5 and 8
C. 6 and 7
D. 2 and 20
Answer: B. 5 and 8
Explanation
Factor:
[
(x-5)(x-8)=0
]
Question 7: Geometry
A rectangle has a length of 18 cm and a width of 11 cm.
What is its area?
A. 198 cm²
B. 176 cm²
C. 58 cm²
D. 396 cm²
Answer: A. 198 cm²
Explanation
Area:
[
18\times11=198
]
Question 8: Probability
A box contains 6 blue, 5 black, and 4 red pens.
What is the probability of selecting a black pen?
A. (\frac13)
B. (\frac15)
C. (\frac{5}{15})
D. (\frac{5}{14})
Answer: A. (\frac13)
Explanation
Total pens = 15
Probability:
[
\frac5{15}=\frac13
]
Question 9: Linear Functions
A line passes through (3,8) and (7,20).
Find its slope.
A. 2
B. 3
C. 4
D. 5
Answer: B. 3
Explanation
[
\frac{20-8}{7-3}=\frac{12}{4}=3
]
Question 10: Word Problem
A school bookstore sells notebooks for $4 and calculators for $18. The store sold 30 items for $330.
How many calculators were sold?
A. 10
B. 12
C. 15
D. 18
Answer: C. 15
Explanation
Let (c) represent calculators.
[
4(30-c)+18c=330
]
[
120-4c+18c=330
]
[
14c=210
]
[
c=15
]
Questions 11–20 (Medium)
The next set introduces multi-step equations and more advanced applications.
Topics include:
- Systems of equations
- Ratios and proportions
- Circle geometry
- Quadratic equations
- Function evaluation
- Data analysis
- Coordinate geometry
Question 11: Algebra
Solve:
[
7x-9=40
]
A. 5
B. 6
C. 7
D. 8
Answer: C. 7
Explanation
[
7x=49
]
[
x=7
]
Question 12: Percent Increase
A phone costs $800 and increases by 10%.
New price?
A. $840
B. $860
C. $880
D. $900
Answer: C. $880
Explanation
10% of 800 is 80.
[
800+80=880
]
Question 13: Ratio
The ratio of boys to girls is 4:5.
There are 36 students.
How many are girls?
A. 16
B. 18
C. 20
D. 24
Answer: C. 20
Question 14: Quadratics
Solve:
[
x^2-11x+30=0
]
A. 5 and 6
B. 4 and 7
C. 3 and 10
D. 2 and 15
Answer: A. 5 and 6
Question 15: Exponents
Simplify
[
3^2\times3^5
]
A. (3^6)
B. (3^7)
C. (3^{10})
D. (9^7)
Answer: B. (3^7)
Question 16: Functions
If
[
g(x)=2x^2-3
]
find (g(4)).
A. 25
B. 29
C. 32
D. 35
Answer: B. 29
Question 17: Circle
The circumference of a circle is
[
10\pi
]
Find its radius.
A. 2
B. 5
C. 10
D. 20
Answer: B. 5
Question 18: Data Analysis
The average of five numbers is 18.
Four numbers are 12, 16, 20, and 22.
Find the fifth number.
A. 18
B. 20
C. 22
D. 30
Answer: B. 20
Explanation
Total:
[
18\times5=90
]
Known sum:
[
12+16+20+22=70
]
Fifth number:
[
90-70=20
]
Question 19: Linear Equations
A line has slope 4 and passes through (2,3).
Find the equation.
A. (y=4x-5)
B. (y=4x+5)
C. (y=3x-2)
D. (y=2x+4)
Answer: A
Question 20: Word Problem
A bakery sells muffins for $3 and cookies for $2.
It sold 80 items for $200.
How many muffins were sold?
A. 30
B. 40
C. 50
D. 60
Answer: B. 40
Questions 21–30 (Hard)
These questions are comparable to the more challenging problems found on the Digital SAT.
Topics include:
- Advanced algebra
- Word problems
- Statistics
- Linear functions
- Quadratic equations
- Probability
- Multi-step reasoning
Question 21: Linear Equations
Solve:
[
5x+12=47
]
A. 5
B. 6
C. 7
D. 8
Answer: C. 7
Question 22: Percent
A bicycle costs $450.
It is discounted by 20%.
Sale price?
A. $340
B. $350
C. $360
D. $380
Answer: C. $360
Question 23: Systems of Equations
Solve:
[
x+y=15
]
[
x-y=3
]
A. (9,6)
B. (8,7)
C. (10,5)
D. (6,9)
Answer: A. (9,6)
Question 24: Functions
If
[
f(x)=2x+9
]
find
[
f(-4)
]
A. -1
B. 1
C. -8
D. 17
Answer: B. 1
Question 25: Exponents
Simplify
[
\frac{7^5}{7^2}
]
A. (7^2)
B. (7^3)
C. (7^5)
D. (7^7)
Answer: B. (7^3)
Question 26: Quadratic Equations
Solve
[
x^2-9x+14=0
]
A. 2 and 7
B. 3 and 6
C. 1 and 14
D. 4 and 5
Answer: A. 2 and 7
Question 27: Geometry
A rectangle has a length of 15 cm and a width of 8 cm.
Find its perimeter.
A. 46 cm
B. 60 cm
C. 120 cm
D. 23 cm
Answer: A. 46 cm
Question 28: Probability
A box contains 5 red, 7 blue, and 8 green marbles.
What is the probability of selecting a green marble?
A. (\frac25)
B. (\frac13)
C. (\frac{7}{20})
D. (\frac12)
Answer: A. (\frac25)
Explanation
Total marbles:
[
5+7+8=20
]
Probability:
[
\frac8{20}=\frac25
]
Question 29: Statistics
The quiz scores are:
72, 80, 84, 88, 90, 96
Find the median.
A. 84
B. 85
C. 86
D. 88
Answer: C. 86
Question 30: Word Problem
A movie theater charges $15 for an adult ticket and $9 for a child ticket.
A total of 60 tickets were sold for $708.
How many adult tickets were sold?
A. 24
B. 28
C. 32
D. 36
Answer: B. 28
Explanation
Let (a) represent adult tickets.
[
15a+9(60-a)=708
]
[
6a=168
]
[
a=28
]
Tips for Scoring Higher on SAT Math
1. Master Algebra
Nearly half of the SAT Math section tests algebraic reasoning. Become comfortable solving equations, inequalities, and systems of equations.
2. Learn Function Notation
Understand how to evaluate functions, identify patterns, and interpret graphs.
3. Memorize Essential Geometry Formulas
Know formulas for:
- Area
- Perimeter
- Circumference
- Volume
- Surface area
- Pythagorean Theorem
4. Practice Without a Calculator
Many Digital SAT questions can be solved mentally or with basic arithmetic.
5. Use the Built-In Desmos Calculator Wisely
The Digital SAT provides the Desmos graphing calculator for every math question. Learn when graphing is faster than solving algebraically.
6. Review Every Mistake
The fastest way to improve your SAT score is to understand why an answer is wrong—not just memorize the correct answer.
Frequently Asked Questions
Are these official SAT questions?
No. These are completely original practice questions created to mirror the style and difficulty of the Digital SAT.
Are these questions suitable for the Digital SAT?
Yes. They are designed around the current Digital SAT Math content domains, including Algebra, Advanced Math, Geometry, and Data Analysis.
Is a calculator allowed on the Digital SAT?
Yes. Students have access to the built-in Desmos graphing calculator throughout the entire Math section and may also bring an approved handheld calculator.
How many questions are on the Digital SAT Math section?
The Digital SAT Math section contains 44 questions split across 2 adaptive modules.
What is a good SAT Math score?
A score of 700–800 is considered excellent, while 650+ is competitive for many colleges. Highly selective universities often expect scores in the upper range.
Key of Success
Consistent practice is one of the most effective ways to improve your SAT Math score. Work through each problem carefully, review the explanations, and revisit topics where you struggle. Over time, you’ll build both speed and confidence for test day.
If you’re aiming for a top score, combine these practice questions with full-length timed practice tests and regular review sessions.
Related SAT Resources
- Digital SAT Algebra Practice Questions
- SAT Geometry Practice Test
- SAT Advanced Math Questions
- SAT Vocabulary Practice
- Digital SAT Reading & Writing Practice
- Full-Length Digital SAT Practice Test