SAT Math Practice — Hard-Difficulty Module

A Bluebook-style digital mock test, built for focused self-study in English.

Questions

35:00

Suggested Time

100%

Hard Difficulty

How this practice set was built

Every problem is an original question, written to target the exact traps and calculation patterns that most frequently cost Korean students points: compound percent change, complementary-angle trig identities, extraneous roots, weighted averages, conditional probability, and more.
All 20 correct answers were derived and cross-checked with three independent methods each (symbolic algebra, direct substitution, and an alternate computation path) using Python/SymPy before being placed in this test — so you can trust every answer key entry.
A built-in graphing calculator (Desmos) and reference sheet are available during the test, exactly as on the real Bluebook digital SAT.
Select an answer and press Check Answer to see immediate feedback and a full explanation — ideal for solo review.

The questions in this module ask you to solve problems in a range of math topics. You may use a calculator for all questions. Some questions will ask you to enter your own answer; on this practice version, all questions are multiple choice. Unless otherwise indicated, assume all variables and expressions represent real numbers.

Question 1 of 20

Reference Sheet

Circle area
A = πr²

Circle circumference
C = 2πr

Rectangle area
A = ℓw

Triangle area
A = ½bh

Pythagorean theorem
a² + b² = c²

Sphere volume
V = 4/3·πr³

Cylinder volume
V = πr²h

Cone volume
V = 1/3·πr²h

The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2π. The sum of the measures in degrees of the angles of a triangle is 180.

SAT Math Practice — Hard-Difficulty Module

Reference Sheet

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