One hundred official-style questions spanning all four digital SAT Math domains, arranged from foundational to advanced within each domain — so you build fluency before you meet the hardest problems.
100Questions
4Domains
~150Min (self-paced)
MCFormat
1–5Difficulty
01
Algebra
Linear equations, inequalities, systems, and functions — the digital SAT's single largest content area.
Q1–Q35 · 35 items35% of test of real testEasy → Hard
Q1
Algebra
If 3x + 5 = 14, what is the value of x?
Isolate x: subtract 5 from both sides, then divide by 3.
Linear equations: undo operations in reverse order (PEMDAS backward).
3x + 5 = 14 → 3x = 9 → x = 9/3 = 3.
Q2
Algebra
If 4x − 3 = 21, what is the value of x?
Isolate x: subtract -3 from both sides, then divide by 4.
Linear equations: undo operations in reverse order (PEMDAS backward).
4x + -3 = 21 → 4x = 24 → x = 24/4 = 6.
Q3
Algebra
If 2x + 7 = 19, what is the value of x?
Isolate x: subtract 7 from both sides, then divide by 2.
Linear equations: undo operations in reverse order (PEMDAS backward).
2x + 7 = 19 → 2x = 12 → x = 12/2 = 6.
Q4
Algebra
If 5x − 2 = 23, what is the value of x?
Isolate x: subtract -2 from both sides, then divide by 5.
Linear equations: undo operations in reverse order (PEMDAS backward).
5x + -2 = 23 → 5x = 25 → x = 25/5 = 5.
Q5
Algebra
If 6x + 4 = 34, what is the value of x?
Isolate x: subtract 4 from both sides, then divide by 6.
Linear equations: undo operations in reverse order (PEMDAS backward).
6x + 4 = 34 → 6x = 30 → x = 30/6 = 5.
Q6
Algebra
If 7x − 1 = 27, what is the value of x?
Isolate x: subtract -1 from both sides, then divide by 7.
Linear equations: undo operations in reverse order (PEMDAS backward).
7x + -1 = 27 → 7x = 28 → x = 28/7 = 4.
Q7
Algebra
If 8x + 3 = 35, what is the value of x?
Isolate x: subtract 3 from both sides, then divide by 8.
Linear equations: undo operations in reverse order (PEMDAS backward).
8x + 3 = 35 → 8x = 32 → x = 32/8 = 4.
Q8
Algebra
If 9x − 6 = 21, what is the value of x?
Isolate x: subtract -6 from both sides, then divide by 9.
Linear equations: undo operations in reverse order (PEMDAS backward).
9x + -6 = 21 → 9x = 27 → x = 27/9 = 3.
Q9
Algebra
If 2x + 11 = 27, what is the value of x?
Isolate x: subtract 11 from both sides, then divide by 2.
Linear equations: undo operations in reverse order (PEMDAS backward).
2x + 11 = 27 → 2x = 16 → x = 16/2 = 8.
Q10
Algebra
If 5x + 9 = 44, what is the value of x?
Isolate x: subtract 9 from both sides, then divide by 5.
Linear equations: undo operations in reverse order (PEMDAS backward).
5x + 9 = 44 → 5x = 35 → x = 35/5 = 7.
Q11
Algebra
What is the solution to 2(x − 3) = 10?
Distribute the 2 first, then isolate x.
Distributive property: a(b − c) = ab − ac.
2(x−3)=10 → 2x−6=10 → 2x=16 → x=8.
Q12
Algebra
If 5x − 7 = 2x + 8, what is x?
Get all x-terms on one side, constants on the other.
Solving equations with variables on both sides.
5x−7=2x+8 → 3x=15 → x=5.
Q13
Algebra
What value of x satisfies (x/3) + 4 = 9?
Subtract 4, then multiply both sides by 3.
Fractional coefficients: multiply to clear denominators.
x/3 = 5 → x = 15.
Q14
Algebra
If 3x + 2y = 12 and y = 3, what is the value of x?
Substitute y = 3 into the first equation.
Substitution: replace a known variable, then solve for the other.
3x + 2(3) = 12 → 3x + 6 = 12 → 3x = 6 → x = 2.
Q15
Algebra
Which inequality represents "5 less than twice a number x is at least 9"?
"At least" means ≥. "5 less than twice x" is 2x − 5.
Translating words into algebraic inequalities.
"Twice a number" = 2x; "5 less than" that = 2x−5; "at least 9" = ≥ 9.
Q16
Algebra
What is the solution set of 4x + 3 < 15?
Subtract 3 then divide by 4 (positive, so inequality sign stays the same).
Linear inequalities: dividing by a positive number keeps the direction.
4x+3<15 → 4x<12 → x<3.
Q17
Algebra
If 2x + y = 10 and x − y = 2, what is the value of x?
Add the two equations to eliminate y.
Elimination method for systems of linear equations.
Adding: (2x+y)+(x−y)=10+2 → 3x=12 → x=4.
Q18
Algebra
A line has slope 3 and passes through (2, 5). What is its y-intercept?
Plug the point into y = mx + b and solve for b.
Slope-intercept form: y = mx + b.
5 = 3(2) + b → 5 = 6 + b → b = −1.
Q19
Algebra
What is the slope of the line that passes through (−1, 4) and (3, −12)?
Slope = (change in y)/(change in x).
Slope formula: m = (y₂−y₁)/(x₂−x₁).
m = (−12−4)/(3−(−1)) = −16/4 = −4.
Q20
Algebra
If f(x) = 2x − 5, what is f(4)?
Substitute x = 4 directly into the function.
Function evaluation: replace every x with the given input.
f(4) = 2(4) − 5 = 8 − 5 = 3.
Q21
Algebra
The sum of two numbers is 24 and their difference is 8. What is the larger number?
Let the numbers be x and y with x+y=24 and x−y=8. Add the equations.
Setting up a system from a word problem.
Adding: 2x = 32 → x = 16 (larger number); y = 8.
Q22
Algebra
A gym charges a $40 sign-up fee plus $15 per month. Which equation gives the total cost C after m months?
The fixed fee is added once; the monthly rate is multiplied by m.
Modeling linear cost with a fixed fee and variable rate.
Total = rate × months + fixed fee = 15m + 40.
Q23
Algebra
Solve the system: y = 2x − 1 and y = −x + 8. What is the value of x?
Set the two expressions for y equal to each other.
Substitution method: when both equations are solved for y, set them equal.
2x−1 = −x+8 → 3x = 9 → x = 3.
Q24
Algebra
If 3x − 4y = 10 and x = 2y, what is the value of y?
Substitute x = 2y into the first equation.
Substitution with an already-isolated variable.
3(2y) − 4y = 10 → 6y − 4y = 10 → 2y = 10 → y = 5.
Q25
Algebra
Tickets to a concert cost $8 for students and $12 for adults. If 50 tickets were sold for a total of $496, how many student tickets were sold?
Let s = student tickets, a = adult tickets. Set up s+a=50 and 8s+12a=496.
Systems from real-world mixture problems.
a = 50−s → 8s+12(50−s)=496 → 8s+600−12s=496 → −4s=−104 → s=26.
Q26
Algebra
For what value of k does the system 2x + y = 7 and 4x + 2y = k have infinitely many solutions?
The second equation must be a multiple of the first for infinite solutions.
Systems with infinitely many solutions are scalar multiples of each other.
Multiplying the first equation by 2: 4x+2y=14, so k=14.
Q27
Algebra
A line is parallel to y = −2x + 5 and passes through (1, 3). What is its equation?
Parallel lines share the same slope. Use point-slope form.
Parallel lines have equal slopes.
y−3=−2(x−1) → y=−2x+2+3=−2x+5.
Q28
Algebra
If |2x − 3| = 7, what is the sum of all possible values of x?
Absolute value equations split into two cases: positive and negative.
Absolute value equations: |A| = B means A = B or A = −B.
2x−3=7 → x=5; 2x−3=−7 → x=−2. Sum = 5+(−2)=3.
Q29
Algebra
A system 3x − 2y = 6 is paired with 6x − 4y = k. For which value of k does this system have infinitely many solutions (rather than none)?
For infinitely many solutions, the second equation must be an exact multiple of the first.
Systems with infinitely many solutions: identical lines (proportional coefficients AND constants).
Multiplying the first equation by 2 gives 6x − 4y = 12, so only k = 12 makes the lines identical.
Q30
Algebra
If 2x + 3y = 16 and 5x − 3y = 5, what is the value of x + y?
Add the equations to eliminate y and solve for x, then find y.
Elimination then back-substitution.
Adding: 7x = 21 → x = 3. Substituting: 2(3)+3y=16 → y=10/3. So x+y = 19/3.
Q31
Algebra
A boat travels 60 miles downstream in 3 hours and returns upstream in 5 hours. What is the speed of the boat in still water, in mph?
Let b = boat speed, c = current speed. Downstream: b+c=20; upstream: b−c=12.
Rate problems: distance = rate × time, with current adding/subtracting.
b+c=60/3=20; b−c=60/5=12. Adding: 2b=32 → b=16.
Q32
Algebra
If 3(2x − 1) − 4 = 5(x + 2), what is the value of x?
Distribute both sides fully before combining like terms.
Multi-step equations with distribution on both sides.
6x−3−4=5x+10 → 6x−7=5x+10 → x=17.
Q33
Algebra
For what value of x is the equation (x+2)/4 − (x−1)/3 = 1 true?
Multiply every term by the LCD, 12, to clear fractions first.
Clearing denominators in rational linear equations.
3(x+2) − 4(x−1) = 12 → 3x+6−4x+4=12 → −x+10=12 → x=-2.
Q34
Algebra
If |3x + 1| − 5 = 2, what is the positive solution for x?
Isolate the absolute value first, then split into two cases.
Multi-step absolute value equations.
|3x+1|=7 → 3x+1=7 → x=2, or 3x+1=−7 → x=−8/3. The positive solution is x=2.
Q35
Algebra
A system consists of 4x − 6y = 10 and kx − 9y = 15. For what value of k does the system have infinitely many solutions?
For infinitely many solutions, the second equation must be a scalar multiple of the first.
Ratio test for dependent systems: coefficients and constants scale together.
Scale factor from −6y to −9y is 1.5; check constants: 10×1.5=15 ✓. So k = 4×1.5 = 6.
02
Advanced Math
Quadratics, exponents, polynomials, and nonlinear functions — equally weighted with Algebra.
Q36–Q70 · 35 items35% of test of real testEasy → Hard
Q36
Advanced Math
What is the value of 2³ × 2⁴?
When multiplying powers with the same base, add the exponents.
If x² + y² = 25 and y = x + 1, what is one possible value of x?
Substitute y = x+1 into the circle equation and solve the resulting quadratic.
Nonlinear systems: substitution turns two equations into one quadratic.
x²+(x+1)²=25 → 2x²+2x+1=25 → 2x²+2x−24=0 → x²+x−12=0 → (x+4)(x−3)=0 → x=3 or x=−4.
Q68
Advanced Math
The expression (x² − 4)/(x² − 5x + 6) simplifies to which of the following (x ≠ 2, 3)?
Factor both the numerator and denominator, then cancel common factors.
Simplifying rational expressions by factoring.
(x²−4)=(x−2)(x+2); (x²−5x+6)=(x−2)(x−3). Canceling (x−2): (x+2)/(x−3).
Q69
Advanced Math
If f(x) = 2x² − 3x + 1 and g(x) = f(x + 1), what is g(0)?
First find f(1), since g(0) = f(0+1).
Composite/shifted functions: evaluate the inner expression first.
g(0)=f(1)=2(1)²−3(1)+1=2−3+1=0.
Q70
Advanced Math
If 3^(2x) = 27^(x−1), what is the value of x?
Rewrite 27 as 3³ so both sides share a base of 3.
Solving exponential equations by matching bases, then equating exponents.
3^(2x) = (3³)^(x−1) = 3^(3x−3). So 2x = 3x−3 → x = 3.
03
Problem-Solving & Data Analysis
Ratios, percentages, statistics, and data interpretation from tables and scatterplots.
Q71–Q85 · 15 items15% of test of real testEasy → Hard
Q71
Problem-Solving & Data Analysis
A recipe calls for 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed for 8 cups of sugar?
Set up a proportion: 3/2 = x/8.
Ratios and proportional reasoning.
3/2 = x/8 → x = 3×8/2 = 12.
Q72
Problem-Solving & Data Analysis
A shirt originally priced at $40 is on sale for 25% off. What is the sale price?
Find 25% of $40, then subtract from the original price.
Percent decrease: new price = original × (1 − discount rate).
40 × 0.75 = $30.
Q73
Problem-Solving & Data Analysis
A car travels 210 miles using 7 gallons of gas. What is the car's fuel efficiency in miles per gallon?
Divide total miles by total gallons.
Unit rate: rate = quantity ÷ unit.
210 ÷ 7 = 30 miles per gallon.
Q74
Problem-Solving & Data Analysis
In a class of 30 students, 18 are girls. What percent of the class is boys?
Find the number of boys first, then convert to a percent of the total.
Percent of a whole.
Boys = 30−18 = 12. 12/30 = 40%.
Q75
Problem-Solving & Data Analysis
A survey of 400 people found that 25% prefer tea over coffee. How many people prefer tea?
Multiply the total by the percentage (as a decimal).
Percent of a total quantity.
400 × 0.25 = 100.
Q76
Problem-Solving & Data Analysis
The data set {4, 7, 7, 9, 13} has what mean?
Add all values and divide by the number of values.
Mean (average) = sum of values ÷ count of values.
(4+7+7+9+13)/5 = 40/5 = 8.
Q77
Problem-Solving & Data Analysis
The data set {2, 5, 6, 6, 9, 20} has a mean of 8 but a median of 6. This large gap between mean and median suggests the data set has:
Compare how sensitive the mean is to extreme values versus the median.
Mean vs. median: the mean is pulled toward outliers; the median resists them.
The value 20 is far from the rest of the data, pulling the mean above the median — a classic sign of an outlier.
Q78
Problem-Solving & Data Analysis
Two data sets have the same mean, but Set A has a standard deviation of 2 and Set B has a standard deviation of 8. Which statement is true?
Standard deviation measures spread, not central tendency.
Standard deviation: a larger value indicates more variability/spread in the data.
A standard deviation of 8 (Set B) indicates values are, on average, farther from the mean than Set A's deviation of 2.
Q79
Problem-Solving & Data Analysis
In a scatterplot, a line of best fit has equation y = 2.5x + 10. According to this model, what is the predicted value of y when x = 6?
Substitute x = 6 into the line of best fit equation.
Using a line of best fit to make predictions.
y = 2.5(6) + 10 = 15 + 10 = 25.
Q80
Problem-Solving & Data Analysis
A jar contains 5 red, 3 blue, and 2 green marbles. What is the probability of randomly picking a blue marble?
Probability = favorable outcomes ÷ total outcomes.
Basic probability.
Total marbles = 5+3+2=10. P(blue)=3/10.
Q81
Problem-Solving & Data Analysis
A two-way table shows that of 200 students, 120 take Spanish and 90 take French, with 40 taking both. How many students take neither language?
Use the inclusion-exclusion principle to find students taking at least one language.
Two-way tables and the inclusion-exclusion principle: |A∪B| = |A|+|B|−|A∩B|.
Students taking at least one = 120+90−40=170. Neither = 200−170=30.
Q82
Problem-Solving & Data Analysis
A company's revenue R (in thousands) after t years is modeled by R = 50(1.08)^t. According to this model, what is the approximate annual percent growth rate?
In the model A(1+r)^t, r is the growth rate.
Exponential growth models: (1+r) is the growth factor.
1.08 = 1 + 0.08, so the growth rate r = 8% per year.
Q83
Problem-Solving & Data Analysis
A researcher wants to estimate the average height of adults in a city. Which sampling method would most likely produce the LEAST biased result?
Unbiased sampling requires every member of the population to have an equal chance of selection.
Random sampling minimizes bias; convenience samples from specific groups introduce bias.
Only a random sample from the entire population avoids systematic bias toward any subgroup (e.g., athletes, gym-goers).
Q84
Problem-Solving & Data Analysis
A data set of 50 test scores has a mean of 78. If one score of 98 is removed, what is the new mean of the remaining 49 scores?
Find the original total, subtract the removed score, then divide by the new count.
Effect of removing a value on the mean: recompute the total sum.
Original sum = 78×50=3900. New sum=3900−98=3802. New mean=3802/49≈77.59.
Q85
Problem-Solving & Data Analysis
In a bag of 40 marbles, the ratio of red to blue to green marbles is 2:3:5. If 8 more green marbles are added, what is the new probability of drawing a green marble?
Find the original count of each color from the ratio, then update the total after adding marbles.
Ratios combined with probability after a change in the sample space.
Parts: 2+3+5=10 → each part=4. Green=20. After adding 8: green=28, total=48. P=28/48.
04
Geometry & Trigonometry
Area, volume, triangles, circles, and right-triangle trigonometry.
Q86–Q100 · 15 items15% of test of real testEasy → Hard
Q86
Geometry & Trigonometry
What is the area of a rectangle with length 9 and width 5?
Area of a rectangle = length × width.
Basic area formula for rectangles.
9 × 5 = 45.
Q87
Geometry & Trigonometry
What is the perimeter of a square with side length 7?
Perimeter of a square = 4 × side length.
Basic perimeter formula for squares.
4 × 7 = 28.
Q88
Geometry & Trigonometry
A right circular cylinder has radius 3 and height 10. What is its volume in terms of π?
Volume of a cylinder = πr²h.
Volume formula for a cylinder.
V = π(3)²(10) = π·9·10 = 90π.
Q89
Geometry & Trigonometry
In a right triangle, the two legs have lengths 6 and 8. What is the length of the hypotenuse?
Use the Pythagorean theorem: a² + b² = c².
Pythagorean theorem for right triangles.
6²+8²=36+64=100 → c=√100=10.
Q90
Geometry & Trigonometry
Two angles of a triangle measure 50° and 65°. What is the measure of the third angle?
The angles of a triangle sum to 180°.
Triangle angle sum theorem.
180 − 50 − 65 = 65°.
Q91
Geometry & Trigonometry
A circle has a circumference of 18π. What is its radius?
Circumference = 2πr, so solve for r.
Circumference formula for a circle.
18π = 2πr → r = 9.
Q92
Geometry & Trigonometry
In a right triangle, angle A measures 30° and the hypotenuse is 12. What is the length of the side opposite angle A?
A circle in the xy-plane is given by (x − 2)² + (y + 1)² = 16. What is the radius of the circle?
The standard circle equation is (x−h)²+(y−k)²=r².
Standard form of a circle equation.
r²=16 → r=4.
Q96
Geometry & Trigonometry
In a right triangle, cos(θ) = 5/13. What is the value of sin(θ)?
Use the Pythagorean identity: sin²θ + cos²θ = 1, or think of a 5-12-13 right triangle.
Pythagorean identity and special right-triangle ratios.
If adjacent=5, hypotenuse=13, then opposite=√(13²−5²)=√144=12. sinθ=12/13.
Q97
Geometry & Trigonometry
If sin(x°) = cos(50°) for 0 < x < 90, what is the value of x?
Complementary angles: sin(x) = cos(90 − x).
Co-function identity: sin(θ) = cos(90° − θ).
sin(x)=cos(50) means x + 50 = 90 → x = 40.
Q98
Geometry & Trigonometry
A cone has a radius of 3 and a slant height of 5. What is the volume of the cone (in terms of π)?
First find the height using the Pythagorean theorem, then use V = (1/3)πr²h.
Cone volume formula combined with the Pythagorean theorem (radius, height, slant height form a right triangle).
h=√(5²−3²)=√16=4. V=(1/3)π(3)²(4)=(1/3)π(36)=12π.
Q99
Geometry & Trigonometry
An angle measures 5π/6 radians. What is its measure in degrees?