The Top 60 DSAT Math Questions
The most common question types on the digital adaptive SATs in the Bluebook app.
This is an analysis of the most common math questions on the six official digital adaptive tests that have been released by the College Board. If you would like to practice these questions, please visit Mathchops! We have a version that’s specifically for the digital SAT.
A few notes:
They are leaning really heavily on quadratic equations and geometry for their hardest questions. It’s very rare to see a truly difficult question in any other category. I’ll probably release another analysis that just focuses on the hard modules.
The linear versions of the new SAT were not included in the analysis, but I did analyze them separately (as a way to check my work). They are quite similar (more info in this post).
I’m only doing a top 60, instead of the Top 75 I’ve done for the ACT, because there aren’t enough questions in the official tests they’ve released.
Y-intercept – Usually either asking you to plug in 0 for x or figure it out based on the wordy description.
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.
System of equations – Substitution, elimination, multiply then eliminate.
Plug in – You have a value or a point that needs to be plugged into an equation or function.
Exponential growth – Be comfortable with this: Final = Initial(1+/- rate)^time. Sometimes there are fractional exponents.
Algebra translation – Convert a word problem into an equation.
Percent – All variations: basic, increase/decrease, markup, discount.
ax + by = c – Be comfortable finding intercepts and the slope.
Plug in zero for intercept – If 3x + 4y = 24, what is the y-intercept? Equations and word problems.
Factoring – The basics, plus zero product property, difference of two squares, perfect square trinomials, factor by grouping, u-substitution.
Combine like terms – Frequently included in other question types.
Translations – Mostly parabolas, sometimes cubic functions and circle equations.
Substitution (systems) – If y = 3x + 2 and 3x + 4y = 10, what is the value of x?
Meaning of a constant – Usually a slope or y-intercept in a word problem.
Plug in point – If (4, 6) is a point on the line 3x + 5y = k, what is the value of k?
Find the rate (exponential growth) – When given an exponential growth equation, identify the rate (or vice versa).
Answer is not x – You might solve for x but then be asked, "What is 2x - 3?"
Pythagorean Theorem – Usually part of something else, like SOHCAHTOA.
Similar triangles – Set up a proportion based on similar triangles. They have proof-like questions as well.
Rectangle area – Basic or part of an algebraic word problem, sometimes quadratic.
-b/2a – Use this to find the x-coordinate of the vertex.
Discriminant – Use b^2 - 4ac to solve for the number of solutions in a quadratic equation.
Average – Arithmetic mean. Mostly basic but a few advanced ones, like the average sum trick.
Given output, find input – If f(x) = 3x + 20 and f(m) = 41, what is the value of m?
Exponential y-intercept – You could be given a graph or an equation. Remember that anything to the power of 0 is 1.
Pythagorean Triple – As in 3:4:5 or 5:12:13. Usually combined with SOHCAHTOA.
Distribute negative – A common trap in equations.
Isolate variable – These usually require several algebraic moves (+/- from both sides, factor something out).
Ratio – Part:part, part:whole.
Quadratic and linear system – In the past, you’d generally need to substitute, factor, and solve. Now, you can use Desmos for a lot of these.
Factor out constant – As in converting 3x + 6 into 3(x+2). Usually part of the factoring process.
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.
Solution is intersection – Know that the point where two lines intersect is the solution to a system of their equations.
Match constants – If 3x + 4y = ax + by, what is a + b?
System of equations, no solution – Know that the lines have to have the same slope.
Angle chasing – 180 in a line, 180 in a triangle, corresponding angles, vertical angles.
Rectangular prism – Volume and surface area.
Conversion – Watch out for ones that involve powers. For example, they might give you the conversion for yards to miles, but then ask about square miles.
Linear inequalities – You might be asked to solve one inequality or deal with a system.
Range – Highest minus lowest in a group of numbers.
Fractions – Usually a part of something else. You would not be directly tested on something like 3/4 + 5/7.
SOHCAHTOA – Set up the basic ratios. Know that similar triangles have the same trig ratios. Sometimes combined with the Pythagorean Theorem.
Probability – Usually a basic part/whole question. But sometimes you have to know that probabilities add to 1, or be careful to note exactly what the numerator and denominator should be: “Given that the student was a junior, what is the probability…”
Identify function – Usually linear or exponential, but sometimes 1/x or sqrt(x).
Value/frequency charts – They’ll tell you the value and frequency and then ask about mean or median.
Median – Can be presented lots of ways: word problem, table, box and whisker plot, value/frequency histogram.
Circle equation – Know horizontal and vertical shifts, how to find the radius. You sometimes need to complete the square.
Factor by grouping – Used in equations like these: 3x^3 + 3x^2 +7x + 7.
Cubic equations – To be safe, know the general characteristics of the graph and be able to apply common equation-solving techniques.
Exponents – All basic operations.
Fractional exponent – Rewrite radicals as fractional exponents and vice versa.
Radicals – Arithmetic operation, translate to fractional power, solve as part of an equation.
Elimination (systems) – If 2x + y = 10 and 2x - 3y = 2, what is the value of y?
Line of best fit – These are usually just slope questions. Sometimes they ask about specific points.
Complete the square – Useful for circle equations, as an alternative to the quadratic formula, and for putting quadratic equations in vertex form.
Margin of error – They might ask for a “plausible value” based on the sample size, total population, and margin of error.
Multiply, then eliminate – In a system, multiply one equation by something so that you can add or subtract to eliminate a variable.
Area of a triangle – Sometimes just the basic formula, sometimes part of a harder question.
Radians – Be comfortable switching between degrees and radians.
Special right triangles – Know 30:60:90 and 45:45:90 triangles. Usually employed in harder questions.
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.
Thanks for this breakdown!