The Complete ACT Mathematics Practice Book
354 questions with full worked solutions, covering every topic the ACT Math section draws on — and every wrong answer explained.
No email address, no sign-up, no watermark.
Every wrong answer explained
Most books tell you the right answer. This one takes each of the three wrong options apart and shows you the specific mistake that produces it — so you recognise the trap before you fall into it.
Checked by computation
Every answer was solved independently by computer algebra before it was published, including the wrong options — so the explanation of a distractor is never hand-waved.
Built from the real thing
The structure comes from ACT’s published blueprint for the enhanced test, cross-checked against the official practice form and three legacy forms — because ACT’s own booklet and its own blueprint disagree about the proportions, and a third source was needed to settle it. Every question here is written from scratch.
Chapters
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00
ACT Mathematics — Complete Study Guide
What the enhanced test is, the four-choice change, no formula sheet, the calculator, a study plan guide -
01
Integrating Essential Skills
Rates, percentages, ratios and averages — a fifth of the whole test 47 Q -
02
Number and Quantity
Exponents and roots, complex numbers, matrices, vectors and sequences 24 Q -
03
Algebra
Linear equations, systems, polynomials, quadratics and exponentials 48 Q -
04
Functions
Notation, composites, graphs, transformations and logarithms 43 Q -
05
Geometry
Angles, polygons, circles, solids, coordinate geometry and conics 20 Q -
06
Trigonometry
Right triangles, the sine and cosine rules, radians and trig graphs 22 Q -
07
Statistics and Probability
Centre and spread, tables, probability, counting and study design 29 Q -
08
Every Formula You Have to Know
Every formula the ACT expects you to know by heart, because it gives you none 11 Q -
09
Two Full Practice Papers
Two full 45-question papers, scored with ACT's own conversion table 90 Q -
10
The Challenge Set
Twenty questions harder than the test will ask, every wrong option a mistake you can actually make 20 Q
What the ACT Math section actually is
45 questions in 50 minutes, in one undivided block, with four answer choices and a calculator permitted throughout. That is the enhanced ACT, which replaced the 60-question, five-choice paper in 2025 and is the only version now given.
The ACT gives you no formula sheet. The SAT prints one on every module; the ACT prints none. Area, volume, slope, the distance formula, the quadratic formula and the trigonometric ratios all have to come from memory — which is why Chapter 8 exists.
Answer letters alternate: odd-numbered questions are lettered A, B, C, D and even-numbered ones F, G, H, J, so that losing your place on the answer sheet is obvious. Every question in this book follows that rule.
This is an independent study resource. Confirm dates, fees and registration with ACT; this site cannot do that for you.