The Top 50 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 four 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:
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 50, instead of the Top 75 I’ve done for the current SAT and ACT, because there aren’t enough questions in the official tests they’ve released.
If a question does appear on this list, I use the same description I used for the current SAT1.
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.
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.
Percent – All variations: basic, increase/decrease, markup, discount.
Factoring – The basics, plus zero product property, difference of two squares, perfect square trinomials, factor by grouping, u-substitution.
ax + by = c – Be comfortable finding intercepts and the slope.
Combine like terms – Frequently included in other question types.
Algebra translation – Convert a word problem into an equation.
Plug in zero for intercept – If 3x + 4y = 24, what is the y-intercept? Equations and word problems.
Function shifts – 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?
Answer is not x – You might solve for x but then be asked, "What is 2x - 3?"
Average – Arithmetic mean. Mostly basic but a few advanced ones, like the average sum trick.
Rectangle area – Basic or part of an algebraic word problem, sometimes quadratic.
Find the rate (exponential growth) – When given an exponential growth equation, identify the rate (or vice versa).
Match constants – If 3x + 4y = ax + by, what is a + b?
Discriminant – Use b^2 - 4ac to solve for the number of solutions in a quadratic equation.
Angle chasing – 180 in a line, 180 in a triangle, corresponding angles, vertical angles.
Value/frequency charts – They’ll tell you the value and frequency and then ask about mean or median.
Exponential y-intercept – You could be given a graph or an equation. Remember that anything to the power of 0 is 1.
SOHCAHTOA – Set up the basic ratios. Know that similar triangles have the same trig ratios. Sometimes combined with the Pythagorean Theorem.
-b/2a – Use this to find the x-coordinate of the vertex.
Median – Can be presented lots of ways: word problem, table, box and whisker plot, value/frequency histogram.
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.
Factor out constant – As in converting 3x + 6 into 3(x+2). Usually part of the factoring process.
System of equations, no solution – Know that the lines have to have the same slope.
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 operations, fractional exponents.
Similar triangles – Set up a proportion based on similar triangles. They have proof-like questions as well.
Fractional exponent – Rewrite radicals as fractional exponents and vice versa.
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.
Linear inequalities – You might be asked to solve one inequality or deal with a system.
Radicals – Arithmetic operation, translate to fractional power, solve as part of an equation.
Line of best fit – These are usually just slope questions. Sometimes they ask about specific points.
Identify function – Usually linear or exponential.
Pythagorean Triple – As in 3:4:5 or 5:12:13. Usually combined with SOHCAHTOA.
Quadratic and linear system – In the past, you’d generally need to substitute, factor, and solve. Now, you can probably use Desmos for a lot of these.
Rectangular prism – Volume and surface area.
Fractions – Usually a part of something else. You would not be directly tested on something like 3/4 + 5/7.
Radians – Be comfortable switching between degrees and radians.
Pythagorean Theorem – Usually part of something else, like SOHCAHTOA.
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.
Circle equation – Know horizontal and vertical shifts, how to find the radius. You sometimes need to complete the square.
Just for reference, here’s the graphic from my previous post that illustrates the differences between the math on the current SAT and the math on the digital SAT:
I think it’s good to err on the side of covering anything that appears on the old SAT if a question from the same family appears in the digital adaptive SAT. For example, if there are value/frequency tables and charts on the digital test, but they only ask about the mean, I would still cover the median with students.
I've been looking forward to your analysis. Brilliant work as always!