The Top 75 SAT Math Questions
The most common math question types from the last 10 QAS SATs.
This is an analysis of the most common math questions on the last 10 QAS SATs (through March 2023). I need to know this information in order to make the questions and question-selection algorithms for Mathchops. So I tagged every question from the most recent SATs a bunch of different ways. Then one of my partners helped me make a Python script and we did a ton of data analysis.
A few observations:
We continue to see more exponential graphs, absolute value equations, circle equations, and proofs. These are all getting emphasized on the released digital SATs also.
More questions incorporated fractions.
There were fewer ‘Algebra Moves’ questions – things like combining like terms, isolating variables, squaring both sides. Those questions still appear, but that general category went down from about 17% to 15%.
Slope – Use the slope formula. Go back and forth from equation to graph. Find the equation when given two points. Find the slope based on a word problem.
Y-intercept – Usually either asking you to plug in 0 for x or figure it out based on the wordy description.
System of equations – Substitution, elimination, multiply then eliminate.
Algebra translation – Convert a word problem into an equation.
Percent – All variations: basic, increase/decrease, markup, discount.
Exponential growth – Be comfortable with this: Final = Initial(1+/- rate)^time. Sometimes there are fractional exponents.
Plug in – You have a value or a point that needs to be plugged into an equation or function.
Ratio – Part:part, part:whole.
Line of best fit – These are usually just slope questions. Sometimes they ask about specific points.
Function shifts – Mostly parabolas, sometimes cubic functions and circle equations.
Fractions – Evenly split between calculator and non-calculator, but usually a part of something else. You would not be directly tested on something like 3/4 + 5/7.
Median – Presented lots of ways: word problem, table, box and whisker plot, value/frequency histogram.
Answer is not x – You might solve for x but then be asked, "What is 2x - 3?"
Meaning of a constant – Usually a slope or y-intercept in a word problem.
Combine like terms – Frequently included in other question types.
Probability – Almost all probability questions are in the form of table data. The key is to identify the numerator and the denominator: "What is the probability of selecting a female from the group of left-handed students?"
Decimals – Almost never appears in the non-calculator section.
Average – Arithmetic mean. Mostly basic but a few advanced ones, like the average sum trick.
Plug in zero for intercept – If 3x + 4y = 24, what is the x-intercept? Equations and word problems.
Fractional exponent – Rewrite radicals as fractional exponents and vice versa.
Set parenthesis equal to zero – Also known as the zero product property: (x + 3)(x - 4) = 0, so x must equal -3 and 4.
Distribute – As in 3(x + 2) = 3x + 6.
No solution – If ax + 4 = 5x + 8, what value of 'a' would result in zero solutions? Also appears in systems.
Factoring – The basics, plus zero product property, difference of two squares, perfect square trinomials, factor by grouping, u-substitution.
Similar triangles – Set up a proportion based on similar triangles.
Substitution (systems) – If y = 3x + 2 and 3x + 4y = 10, what is the value of x?
Radicals – Arithmetic operation, translate to fractional power, solve as part of an equation.
Given graph, find equation – Usually a linear equation, testing your knowledge of slope and y-intercept. There have been more exponential graphs recently.
Elimination (systems) – If 2x + y = 10 and 2x - 3y = 2, what is the value of y?
Conversion – They give you the conversion but you have to execute it correctly (oz/pounds, $5/pound, etc.)
Value/frequency – Bar graph or table. Usually part of median or arithmetic mean question.
FOIL – Usually just the basics, as in (x+3)(x-4).
Isolate variable – These usually require several algebraic moves (+/- from both sides, factor something out).
Pick numbers – This is never required but is often helpful.
Circle equation – Know horizontal and vertical shifts, how to find the radius. You sometimes need to complete the square.
Parallel – Know that parallel lines have the same slope.
Perfect square trinomial – Useful for completing the square. Sometimes required as part of a multistep solution.
Discriminant – Use b^2 - 4ac to solve for the number of solutions in a quadratic equation.
Perpendicular – Know that perpendicular lines have negative, reciprocal slopes.
Residual – Find the difference between the actual data point and the point that is predicted by the line of best fit.
Absolute value equations – Know that there are always two solutions to an absolute value equation. For example, if |2x - 3| = 7, then 2x - 3 could equal 7 or -7.
Rectangle area – Basic or part of an algebraic word problem, sometimes quadratic.
Scales don’t match – The origin won't be included, or the scales increase at different rates.
Angle chasing – 180 in a line, 180 in a triangle, corresponding angles, vertical angles.
c = product of roots, b = -sum – Use when in x^2 + bx + c form. Usually not required but often helpful.
Pythagorean theorem – Often combined with SOHCAHTOA or similar triangles.
Box and whisker plot – Usually asks for the median or range. The toughest one asks you to identify the correct plot based on the data.
Exponential graph – Know the basics of exponential graphs and shifts.
Plug in answers – Like picking numbers, it’s not required but it’s often helpful.
Basic exponents – All basic operations, fractional, negative.
Infinite solutions – If ax + 4 = 5x + 4, what value of 'a' would result in infinite solutions?
Percent increase – The price was $20. Now it's $28. What's the percent increase?
Questions about a study – Often something about margin of error or the setup of the study.
30:60:90 – Know the side/angle relationships for 30_60_90 triangles.
Match constants – If 3x + 4y = ax + by, what is a + b?
Negatives – Arithmetic, distributing the negative over a parenthesis. Like fractions, they aren't directly tested.
SOHCAHTOA – Set up the basic ratios. Know that similar triangles have the same trig ratios. Sometimes combined with the Pythagorean Theorem.
System of equations, no solution – Know that the lines have to have the same slope.
Range – Table, box and whisker plot, list of numbers.
Proof – Know what is required to make two triangles similar or congruent.
Vertex form – Be comfortable with y = a(x - h)^2 + k
Polynomial multiplication – Distribute with more than two terms in the parenthesis.
Scale factor – Find the area or volume when only given one dimension (or the reverse). For example, they might give you the conversion for feet to yards, but you need to know that there are 9 square feet in 1 square yard.
Given two points, find the y intercept – Find the slope, then plug one of the points back in to find the y intercept.
Distribute negative – A common trap in equations.
Standard deviation – Just know that S.D. is related to how spread out the data points are.
Square both sides – It's often better to plug in the answers but sometimes you have to square both sides to get rid of the radical.
MPH – Be comfortable with conversions that involve miles per hour.
Graphing Linear Inequalities – Know how to graph, shade, and find the solutions to linear inequalities.
Order matters – In similar shapes, know that the order of the letters is significant (first corresponds to the first, etc).
Complete the square – Useful for circle equations, as an alternative to the quadratic formula, and for putting quadratic equations in vertex form.
Multiply, then eliminate – In a system, multiply one equation by something so that you can add or subtract to eliminate a variable.
Percent decrease – The price was $80. Now it's $60. What's the percent decrease?
Factor out constant – As in converting 3x + 6 into 3(x+2). Usually part of the factoring process.
Quadratic formula – Sometimes the answers will be in a form that suggests they are expecting you to know/use the quadratic formula.
Analysis by Mike McGibbon and Jon Bedard. Visit mathchops.com to practice the most common SAT and ACT math problem types. To learn more about Mathchops, listen to our Tests and the Rests podcast profile.
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What do you mean by pick numbers?
What about 45-45-90 right triangles? No problems on these?