Digital SAT Algebra Clinic Cheatsheet

Digital SAT Algebra Cheatsheet

Published

Pocket card for forms and flips — not a substitute for timed Bluebook Math.

Quick reference for linear, quadratic, systems, exponents, and inequalities on Digital SAT Math. Calculator (including Desmos) is allowed on every item; still write the model first. For traps, tool choice, and a tonight drill, use the full Algebra Clinic.

Digital Math Reminders

Modules

Two adaptive Math modules. Protect Module 1 accuracy — it routes Module 2 difficulty.

Tool Check

Clean one-equation algebra → pencil. Intersections / messy systems / graphs → Desmos. Desmos does not carry across modules.

SPR Entry

Negatives allowed. Positive ≤5 characters; negative ≤6 including minus. No %, commas, or $.

Linear Equations

Standard form

Ax + By = C

Slope-intercept

y = mx + b

Point-slope

y − y₁ = m(x − x₁)

Slope

m = (y₂ − y₁)/(x₂ − x₁)

Quadratic Equations

Standard

ax² + bx + c = 0

Factored

a(x − r₁)(x − r₂) = 0

Vertex form

a(x − h)² + k

Quadratic formula

x = [−b ± √(b² − 4ac)] / (2a)

Vertex x

x = −b / (2a)

Systems

Substitution

Solve one variable → substitute → back-substitute.

Elimination

Align opposites → add → solve → substitute.

Graph / Desmos

Intersection = solution. Strong when algebra is messy.

Solution types

One · none (parallel) · infinitely many (same line).

Exponents & Radicals

aᵐ · aⁿ = aᵐ⁺ⁿ · aᵐ/aⁿ = aᵐ⁻ⁿ · (aᵐ)ⁿ = aᵐⁿ
a⁰ = 1 (a ≠ 0) · a⁻ⁿ = 1/aⁿ
√(ab) = √a · √b · √(a/b) = √a/√b · (√a)² = a (a ≥ 0)
a¹ᐟ² = √a · aᵐᐟⁿ = (ⁿ√a)ᵐ

Functions

Notation

f(x) = expression

Linear

f(x) = mx + b

Quadratic

f(x) = ax² + bx + c

Domain = allowed x · Range = resulting y. Watch division by zero and even roots of negatives when the stem requires real values.

Inequalities

Same steps as equations — flip the inequality when multiplying or dividing by a negative.
|x| = a → x = a or x = −a (a ≥ 0)
|x| < a → −a < x < a
|x| > a → x < −a or x > a
Compound: “and” = intersection · “or” = union. Test a point.

Quick Reference

Distance

d = √[(x₂−x₁)² + (y₂−y₁)²]

Midpoint

((x₁+x₂)/2, (y₁+y₂)/2)

Discriminant

b² − 4ac

Exponential growth (simple model)

A = P(1 + r)ᵗ

Word-problem check

Define the variable as what the stem asks. Percent of what? Discount order? Units before submit.

Next Steps

Formulas do not score by themselves. Run the clinic drill, then a timed Bluebook Math module.