Unit 1
Real Numbers & Radicals
√(a·b) = √a · √b
Simplify by factoring out perfect squares. $\sqrt{48}=\sqrt{16\cdot3}=4\sqrt{3}$
Unit 2
Algebraic Expressions
Distribute, then combine like terms
$3(2x-4)+5x = 6x-12+5x = 11x-12$
Unit 3
Linear Equations
ax + b = c → x = (c−b)/a
Isolate the variable using inverse operations.
Unit 4
Proportions & Ratios
a/b = c/d → ad = bc
Cross-multiply to solve for the unknown.
Unit 5
Inequalities
−ax > b → x < −b/a (flip sign!)
Multiply or divide by a negative → reverse the inequality symbol.
Unit 6
Functions
f(x): substitute x and evaluate
$f(x)=2x^2-3,\;f(-2)=2(4)-3=5$
Unit 7
Slope & Linear Equations
m = (y₂−y₁)/(x₂−x₁)
Slope-intercept: $y=mx+b$. Point-slope: $y-y_1=m(x-x_1)$
Unit 8
Systems of Equations
Substitution or Elimination
Add/subtract equations to eliminate one variable, then solve.
Unit 9
Factoring & Quadratics
x²+bx+c = (x+p)(x+q) where p+q=b, pq=c
Discriminant: $b^2-4ac$. If $<0$: no real roots.
Unit 10
Exponent Laws
xᵃ · xᵇ = xᵃ⁺ᵇ | (xᵃ)ᵇ = xᵃᵇ
$(2x^2y)^3 = 2^3 x^6 y^3 = 8x^6y^3$