ACT Elementary Algebra Formula Sheet
Variables, equations, polynomials, and basic factoring formulas for the ACT Elementary Algebra reporting category.
Below are the 9 formulas tested in this category, with the situation each one applies to. Drill until you can write the whole sheet from memory in under two minutes — that's the standard top scorers reach by test day.
Each formula links back to the topic page where it's worked into example problems. If a formula doesn't yet feel automatic, click into the topic page and grind that topic's six practice questions.
Formulas
| Concept | Formula | When to use it |
|---|---|---|
| Distributive property | a(b + c) = ab + ac | Multiply across parentheses. |
| Combine like terms | 3x + 2x = 5x | Same variable & power only. |
| Solve linear equation | isolate x using inverse ops | Whatever you do to one side, do to the other. |
| Quadratic factoring | x² + (p+q)x + pq = (x+p)(x+q) | Find p, q whose product = c, sum = b. |
| Difference of squares | a² − b² = (a − b)(a + b) | Factor pattern. |
| Inequality flip rule | flip ≥ ↔ ≤ when × or ÷ by a negative | Easy to forget. |
| Slope from two points | (y₂ − y₁)/(x₂ − x₁) | Rise over run. |
| Slope-intercept line | y = mx + b | Direct read. |
| Point-slope line | y − y₁ = m(x − x₁) | When you have a point and a slope. |
How to memorise this sheet in a week
Day 1. Read every row out loud. Connect each formula to a worked example by clicking into the topic page on which it appears. Goal: understand why each formula is true, not just memorise it.
Day 2. Cover the right-hand columns and quiz yourself on each concept. Write the formula and the use case from memory. Mark the ones you missed.
Day 3. Re-quiz only the ones you missed yesterday. Keep cycling until your error count hits zero.
Day 4. Re-do the full quiz. You should know every row.
Day 5. Apply each formula in a problem context — pick a topic page from the list below and solve all six questions.
Day 6–7. Sit a real past paper. Note any formulas you blanked on under time pressure and add them back to your daily quiz.
Topics that use these formulas
- Algebraic Expressions6 Qs
- Solving Linear Equations6 Qs
- Multi-Step Equations6 Qs
- One-Variable Inequalities6 Qs
- Polynomials (Basic)6 Qs
- Basic Factoring6 Qs
- Substitution and Evaluation6 Qs
- Elementary Word Problems6 Qs
Common mistakes when applying these formulas
Three errors account for the majority of dropped points on formula-driven questions:
- Substituting before simplifying. Always simplify symbolically as far as you can before plugging numbers in. It cuts arithmetic errors in half.
- Mixing units. If a formula expects metres and you have centimetres, convert first, not at the end. The number you compute is meaningless until the units agree.
- Forgetting the ½ in area or volume formulas. Triangle, trapezoid, sector, cone, pyramid — all have a ½ or ⅓ that's easy to drop. Write the formula on the page before plugging in.