SAT Algebra Formula Sheet
Every formula and identity you need for the Algebra domain on the Digital SAT — slope, lines, systems, inequalities, and proportions.
Below are the 13 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 |
|---|---|---|
| Slope of a line | m = (y₂ − y₁) / (x₂ − x₁) | Two points on a line. |
| Slope-intercept form | y = mx + b | m = slope, b = y-intercept. |
| Point-slope form | y − y₁ = m(x − x₁) | Line through (x₁,y₁) with slope m. |
| Standard form | Ax + By = C | When you need integer coefficients or x/y intercepts quickly. |
| Distance formula | d = √((x₂−x₁)² + (y₂−y₁)²) | Length of segment between two points. |
| Midpoint formula | M = ((x₁+x₂)/2, (y₁+y₂)/2) | Centre of a segment. |
| Parallel lines | m₁ = m₂ | Two lines that never meet. |
| Perpendicular lines | m₁ · m₂ = −1 | Lines that meet at 90°. |
| Proportion | a/b = c/d ⇔ ad = bc | Cross-multiplication. |
| Percent change | (new − old) / old × 100% | Increase positive, decrease negative. |
| Distance, rate, time | d = r · t | Rate × time = distance. |
| Mixture (concentration) | C₁V₁ + C₂V₂ = Cₘ(V₁+V₂) | Combining two solutions. |
| Linear inequality flip | Multiply or divide by a negative ⇒ flip the inequality sign. | Single most common slip. |
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
- Linear Equations in One Variable6 Qs
- Linear Equations in Two Variables6 Qs
- Linear Functions6 Qs
- Systems of Linear Equations6 Qs
- Linear Inequalities6 Qs
- Absolute Value Equations6 Qs
- Slope and Rate of Change6 Qs
- Point-Slope and Standard Form6 Qs
- Parallel and Perpendicular Lines6 Qs
- Graphing Linear Equations6 Qs
- Linear Word Problems6 Qs
- Rates, Ratios and Proportions6 Qs
- Percentage Applications6 Qs
- Mixture Problems6 Qs
- Distance, Rate and Time6 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.