Summary
This post provides a comprehensive reference list of 103 ACT Math concepts organized into seven categories: Pre-Algebra, Elementary Algebra, Intermediate Algebra, Coordinate Geometry, Plane Geometry, Trigonometry, and Statistics & Probability. Each concept is tagged by test frequency (High, Medium, or Low) and difficulty level (Foundational, Intermediate, or Advanced), and every concept that has a corresponding formula links directly to the relevant section of the WCT ACT Math Formula Sheet. The post also includes a recommended three-phase study sequence tied to score targets, a section explaining the connection between this list and the formula sheet, a five-question FAQ about the enhanced ACT, and an author bio.
Every ACT Math concept,
organized for you.
This reference covers all 103+ topics that appear on the ACT Math test, sorted by category, frequency, and difficulty. Every concept that has a formula links directly to the corresponding section of the WCT formula sheet.
Pre-Algebra
| # | Concept | Frequency | Difficulty | Formula Sheet |
|---|---|---|---|---|
| 1 | Fractions, decimals, and percents | High | Foundational | § Fractions, Decimals & Percentages |
| 2 | Percent change & percent of a number | High | Foundational | § Fractions, Decimals & Percentages |
| 3 | Ratios and proportions | High | Foundational | § Rates, Ratios & Proportions |
| 4 | Unit conversion & rate problems | High | Intermediate | § Rates, Ratios & Proportions |
| 5 | Concentration (mixture) problems | Low | Intermediate | § Rates, Ratios & Proportions |
| 6 | Absolute value | Medium | Foundational | — |
| 7 | Order of operations (PEMDAS) | High | Foundational | — |
| 8 | Factors, multiples, GCF & LCM | Medium | Foundational | — |
| 9 | Prime numbers & factorization | Medium | Foundational | — |
| 10 | Integers: positive, negative, even, odd | High | Foundational | § Number Definitions |
| 11 | Averages: mean, median, and mode | High | Foundational | § Data, Probability & Combinatorics |
| 12 | Simple and compound interest | Medium | Intermediate | § Fractions, Decimals & Percentages |
| 13 | Number line & comparing values | Medium | Foundational | — |
| 14 | Remainders & repeating patterns | Medium | Intermediate | — |
| 15 | Basic probability | High | Foundational | § Data, Probability & Combinatorics |
| 16 | Basic counting principles | Medium | Intermediate | § Data, Probability & Combinatorics |
Elementary Algebra
| # | Concept | Frequency | Difficulty | Formula Sheet |
|---|---|---|---|---|
| 17 | Solving linear equations | High | Foundational | — |
| 18 | Solving linear inequalities | High | Foundational | — |
| 19 | Word problems → equations | High | Intermediate | — |
| 20 | Substitution & evaluating expressions | High | Foundational | — |
| 21 | Combining like terms & distributive property | High | Foundational | — |
| 22 | Exponent rules | High | Intermediate | § Exponents, Roots & Polynomials |
| 23 | Square roots & radicals (basic) | High | Intermediate | § Exponents, Roots & Polynomials |
| 24 | Systems of equations (substitution & elimination) | High | Intermediate | — |
| 25 | Factoring: GCF and trinomials | High | Intermediate | § Exponents, Roots & Polynomials |
| 26 | Difference of squares | Medium | Intermediate | § Exponents, Roots & Polynomials |
| 27 | FOIL / polynomial multiplication | High | Intermediate | — |
| 28 | Multi-step equations with fractions | Medium | Intermediate | — |
Intermediate Algebra
| # | Concept | Frequency | Difficulty | Formula Sheet |
|---|---|---|---|---|
| 29 | Quadratic equations: factoring | High | Intermediate | § Parabolas |
| 30 | Quadratic formula (incl. discriminant & sum/product of roots) | Low | Intermediate | § Parabolas |
| 31 | Parabolas: vertex, axis of symmetry | High | Intermediate | § Parabolas |
| 32 | Vertex form of a quadratic | Medium | Intermediate | § Parabolas |
| 33 | Functions: domain, range, notation | High | Intermediate | — |
| 34 | Function composition & evaluation | High | Intermediate | — |
| 35 | Parent graphs & transformations | High | Intermediate | § Parent Graphs & Transformations |
| 36 | Radical expressions | Medium | Intermediate | § Exponents, Roots & Polynomials |
| 37 | Exponential and radical equations | Medium | Advanced | — |
| 38 | Rational expressions (simplify, multiply, divide) | Medium | Advanced | — |
| 39 | Absolute value equations & inequalities | Medium | Intermediate | — |
| 40 | Sequences: arithmetic, geometric & repeating patterns | High | Intermediate | § Sequences & Series |
| 41 | Complete the square | Low | Advanced | § Exponents, Roots & Polynomials |
| 42 | Binomial expansion | Low | Advanced | — |
| 43 | Exponential equations (common base method) | Medium | Advanced | — |
| 44 | Logarithms (basic) | Medium | Advanced | § Logarithms |
| 45 | Inverse functions | Medium | Advanced | — |
| 46 | Matrices: basic operations | Medium | Advanced | § Matrices |
| 47 | Complex numbers | High | Advanced | § Exponents, Roots & Polynomials |
Coordinate Geometry
| # | Concept | Frequency | Difficulty | Formula Sheet |
|---|---|---|---|---|
| 48 | Slope formula | High | Foundational | § Graphing Lines |
| 49 | Slope-intercept form (y = mx + b) | High | Foundational | § Graphing Lines |
| 50 | Point-slope form | Medium | Foundational | § Graphing Lines |
| 51 | Parallel & perpendicular lines | High | Intermediate | § Graphing Lines |
| 52 | Distance formula | High | Intermediate | § Graphing Lines |
| 53 | Midpoint formula | High | Foundational | § Graphing Lines |
| 54 | Graphing linear inequalities | Medium | Intermediate | — |
| 55 | Graphing parabolas | High | Intermediate | § Parabolas |
| 56 | Circles: equation and graphing | Medium | Advanced | § Circles / § Conic Sections |
| 57 | Reflections, translations, transformations | Medium | Intermediate | § Parent Graphs & Transformations |
| 58 | x-intercepts and y-intercepts | High | Foundational | — |
| 59 | Ellipses (equation & key features) | Medium | Advanced | § Conic Sections |
| 60 | Vectors (basic) | Low | Advanced | § Vectors |
Plane Geometry
| # | Concept | Frequency | Difficulty | Formula Sheet |
|---|---|---|---|---|
| 61 | Angles: complementary, supplementary, vertical | High | Foundational | § Angles |
| 62 | Parallel lines & transversals | High | Foundational | § Angles |
| 63 | Triangle angle sum = 180° | High | Foundational | § Triangles |
| 64 | Pythagorean theorem | High | Foundational | § Triangles |
| 65 | Special right triangles (30-60-90 & 45-45-90) | High | Intermediate | § Triangles |
| 66 | Triangle similarity & congruence | High | Intermediate | § Triangles |
| 67 | Area of triangles, rectangles, parallelograms | High | Foundational | § Polygons |
| 68 | Area of trapezoids | Medium | Intermediate | § Polygons |
| 69 | Circumference & area of circles | High | Foundational | § Circles |
| 70 | Arc length & sector area | Medium | Intermediate | § Circles |
| 71 | Volume: prisms & cylinders | High | Intermediate | § Solids |
| 72 | Volume: pyramids, cones, spheres | Medium | Advanced | § Solids |
| 73 | Surface area | Medium | Intermediate | § Solids |
| 74 | Properties of quadrilaterals | Medium | Intermediate | § Polygons |
| 75 | Perimeter of polygons | High | Foundational | § Polygons |
| 76 | Interior angles of polygons | Medium | Intermediate | § Polygons |
| 77 | Coordinate proofs & geometric reasoning | Low | Advanced | — |
| 78 | Inscribed angles & central angles | Low | Advanced | § Circles |
Trigonometry
| # | Concept | Frequency | Difficulty | Formula Sheet |
|---|---|---|---|---|
| 79 | SOHCAHTOA (right triangle trig) | High | Intermediate | § Trigonometry |
| 80 | Reciprocal trig ratios (csc, sec, cot) | Medium | Intermediate | § Trigonometry |
| 81 | Special angle values (0°, 30°, 45°, 60°, 90°) | High | Intermediate | § Trigonometry |
| 82 | Inverse trig functions | Medium | Advanced | § Trigonometry |
| 83 | Pythagorean identities | Medium | Advanced | § Trigonometry |
| 84 | Radian measure | Medium | Advanced | § Trigonometry |
| 85 | Unit circle (key angles) | Low | Advanced | § Trigonometry |
| 86 | ASTC rule (signs of trig functions by quadrant) | Low | Advanced | — |
| 87 | Graphs of sin, cos, tan | Medium | Advanced | — |
| 88 | Amplitude, period, phase shift | Medium | Advanced | — |
| 89 | Law of Sines | Medium | Advanced | § Trigonometry |
| 90 | Law of Cosines | Medium | Advanced | § Trigonometry |
Statistics & Probability
| # | Concept | Frequency | Difficulty | Formula Sheet |
|---|---|---|---|---|
| 91 | Mean, median, and mode | High | Foundational | § Data, Probability & Combinatorics |
| 92 | Measures of spread: range and standard deviation | Medium | Intermediate | § Data, Probability & Combinatorics |
| 93 | Weighted averages | High | Intermediate | — |
| 94 | Basic probability | High | Foundational | § Data, Probability & Combinatorics |
| 95 | Compound probability (AND/OR rules) | Medium | Intermediate | § Data, Probability & Combinatorics |
| 96 | Venn diagrams & sets | High | Foundational | — |
| 97 | Permutations | Medium | Intermediate | § Data, Probability & Combinatorics |
| 98 | Combinations | Medium | Intermediate | § Data, Probability & Combinatorics |
| 99 | Interpreting graphs: scatter, bar, line | High | Foundational | — |
| 100 | Reading data tables | High | Foundational | — |
| 101 | Expected value | Medium | Advanced | § Data, Probability & Combinatorics |
| 102 | Normal distribution (basic) | Low | Advanced | — |
| 103 | Box & whisker and stem & leaf plots | Low | Foundational | — |
Recommended Study Sequence
Not all topics deserve equal time. Based on exam frequency and the way concepts build on each other, here is how we recommend students prioritize their ACT Math preparation.
Phase 1: Master First
- Fractions, decimals, percents
- Solving linear equations
- Pythagorean theorem
- Special right triangles
- Slope and graphing lines
- Exponent rules
- Factoring and FOIL
- Mean, median, and mode
- Angles and triangles
- Area and circumference
Phase 2: Build On It
- Quadratic equations and formula
- Parabolas and vertex form
- Functions (domain, range, notation)
- Sequences (arithmetic and geometric)
- Systems of equations
- SOHCAHTOA
- Distance and midpoint
- Volume formulas
- Probability and counting
- Data interpretation
Phase 3: Score Ceiling
- Logarithms
- Matrices
- Vectors
- Conic sections
- Law of Sines and Cosines
- Radian measure and unit circle
- Complex numbers
- Inverse functions
- Expected value
- Normal distribution
Score targeting tip: Students aiming for a score of 26 or below should spend 90% of their study time in Phases 1 and 2. Phase 3 topics typically appear in ten questions and require significant effort for modest point gains. If your goal is 27 or above, Phase 3 becomes essential.
How This List Connects to the Formula Sheet
The ACT gives students no formulas on test day. Unlike the SAT, there is no reference sheet — every formula must be memorized before you walk in. Students who have internalized the relevant formulas work faster, make fewer errors, and approach harder questions with more confidence.
The WCT ACT Math Formula Sheet covers all 19 topic areas referenced in the concept tables above, from number definitions through conic sections. We recommend using this concept list and the formula sheet together: as you study each concept, locate its corresponding formula, then practice applying it until it becomes automatic. The clickable links in the Formula Sheet column of each table take you directly to the right section.
Frequently Asked Questions
Does the ACT provide a formula sheet?
No. Unlike the SAT, the ACT provides no formula reference on test day. Every formula must be memorized in advance, which is exactly what our ACT Math Formula Sheet is designed to help with.
How many math questions are on the ACT?
The ACT Math section contains 45 questions to be completed in 50 minutes for students testing in standard time. Questions are generally arranged from easiest to hardest, though this ordering is not perfectly consistent across every test.
How do these phases relate to ACT score targets?
A student who has truly mastered Phase 1 and Phase 2 can realistically reach a score in the 26 to 28 range. Phase 3 concepts are needed for scores of 30 and above. Many students aiming for a 22 to 24 can get there with a solid command of Phase 1 alone.
How is ACT math different from SAT math?
The ACT covers a broader range of content, with notably more trigonometry and geometry, but the questions tend to be more straightforward. The SAT has fewer questions, more time per question, and a heavier emphasis on multi-step reasoning and data analysis. Which test suits a given student depends on their individual strengths.
Can I use a calculator on the ACT Math section?
Yes. The entire ACT Math section allows a calculator. The full list of approved calculators is available on the ACT calculator policy page. If you are taking the enhanced ACT digitally, the Desmos graphing calculator is built directly into your testing platform.
