About a quarter of digital SAT Math questions have no answer choices: you type the answer. The entry rules are strict and easy to learn. This guide gives the rules in plain words, the tools the Math section provides and the reference-sheet formulas. The site's practice tests check your typed answers with the same rules (81 such questions in the book).
Note: The Math directions say that, unless a question tells you otherwise, all variables and expressions stand for real numbers, figures are drawn to scale, figures lie in a plane, and the domain of a function f is every real x for which f(x) is a real number. "Drawn to scale" means you may use a figure to check whether an answer is reasonable.
An SPR question gives you no answer choices: you type your own answer into a small box. Here are the College Board's entry rules in plain words:
A "character" is any digit, decimal point, fraction bar or minus sign. So 7/2 uses 3 characters, 0.125 uses 5, and −3.5 uses 4.
Note: The repeating-decimal examples in this chapter show how this book applies the College Board's rules. Follow the College Board's directions on test day if they differ in any detail.
Three habits keep your SPR entries safe:
If your work ends with a radical or π, stop and reread. A question that involves a circle or a special right triangle usually asks for a number you can type, such as the value of k when an area is written as k√3 or a volume as kπ.
Example 1: An answer that does not fit as a fraction
Problem: 12x − 7 = 118. What value of x is the solution to the given equation?
Thinking: Add 7 to both sides to get 12x = 125, so x = 125/12. That fraction is already reduced, but it has 6 characters, one more than the 5 allowed for a positive answer. Switch to the decimal: 125 ÷ 12 = 10.41666…
Entry: Five characters are allowed, so enter 10.41 (cut off) or 10.42 (rounded). Either fills the space.
Traps: 10.4 does not fill the space, 10.42% contains a symbol, and 10 5/12 is a mixed number.
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The reference sheet is not a full formula list. Here is what it contains:
Just as useful is knowing what the sheet does not give you. You must know these from memory: slope and the forms of a line, distance and midpoint, the circle equation, the quadratic formula and discriminant, the vertex formula, SOH-CAH-TOA and sin x° = cos(90° − x°), similar-triangle proportions, arc length and sector area, degree-radian conversion, exponent rules, percent change, exponential models, mean and median, and probability. Appendix D collects them.
Know the sheet well enough that you rarely need to open it. It pays off most on volume questions, where the cone, sphere and pyramid formulas are easy to mix up, and on special right triangles.
Example 5: Working backward from a volume
Problem: A sphere has a volume of 36π cubic centimeters. What is the radius, in centimeters, of the sphere?
Thinking: The sheet gives V = (4/3)πr^3. Set (4/3)πr^3 = 36π. Divide both sides by π to get (4/3)r^3 = 36, then multiply by 3/4 to get r^3 = 27. So r = 3.
Traps: Using the cone or cylinder formula by mistake gives a different value, so match the formula to the shape named in the question. Stopping at r^3 = 27 and answering 27 solves for the wrong quantity.
Adapted from Chapter 15 of the book.
Every exam fact on this page was checked against the official College Board pages below on 29 October 2026. Policies and tools change, so confirm details on the College Board website before test day.
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