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ALEKS Math Formula Sheet (PDF)
The ultimate one-page formula sheet covering every essential rule from Pre-Algebra through Pre-Calculus. Click below to save or print as a clean PDF study guide.
ALEKSMath.com Reference Guide
ALEKS Math Placement Comprehensive Formula Sheet
1. Arithmetic & Real Numbers
Order of Operations:P E M D A S (Parentheses, Exponents, Mult/Div, Add/Sub)
Fraction Division:(a/b) ÷ (c/d) = (a/b) · (d/c) = ad / bc
Percent Proportion:Part / Whole = Percent / 100
Percent Change:Change (%) = [(New - Old) / Old] × 100%
2. Algebra 1 & Coordinate Geometry
Slope Formula:m = (y₂ - y₁) / (x₂ - x₁)
Slope-Intercept Form:y = mx + b
Point-Slope Form:y - y₁ = m(x - x₁)
Distance Formula:d = √((x₂ - x₁)² + (y₂ - y₁)²)
Midpoint Formula:M = ((x₁+x₂)/2, (y₁+y₂)/2)
Standard Circle:(x - h)² + (y - k)² = r²
3. Exponent Laws & Factoring Special Forms
Exponent Rules:xᵃ · xᵇ = xᵃ⁺ᵇ | xᵃ / xᵇ = xᵃ⁻ᵇ
(xᵃ)ᵇ = xᵃᵇ | x⁻ᵃ = 1 / xᵃ | x⁰ = 1
(xᵃ)ᵇ = xᵃᵇ | x⁻ᵃ = 1 / xᵃ | x⁰ = 1
Special Products:a² - b² = (a - b)(a + b)
(a ± b)² = a² ± 2ab + b²
(a ± b)² = a² ± 2ab + b²
4. Geometry Area & Volume Formulas
Circle Area & Circumference:Area = πr²
Circumference = 2πr
Circumference = 2πr
Pythagorean Theorem:a² + b² = c²
(3-4-5, 5-12-13 Triples)
(3-4-5, 5-12-13 Triples)
Cylinder Volume:V = πr²h
Surface = 2πrh + 2πr²
Surface = 2πrh + 2πr²
Cone Volume:V = (1/3)πr²h
Sphere Volume:V = (4/3)πr³
Triangle Area:A = (1/2) · b · h
5. Algebra 2, Quadratics & Logarithms
Quadratic Formula:x = (-b ± √(b² - 4ac)) / (2a)
Discriminant: Δ = b² - 4ac
Discriminant: Δ = b² - 4ac
Logarithmic Properties:log_b(xy) = log_b(x) + log_b(y)
log_b(x/y) = log_b(x) - log_b(y)
log_b(xⁿ) = n · log_b(x)
log_b(x/y) = log_b(x) - log_b(y)
log_b(xⁿ) = n · log_b(x)
Complex Numbers:i = √(-1), i² = -1, i³ = -i, i⁴ = 1
|a + bi| = √(a² + b²)
|a + bi| = √(a² + b²)
Rational Exponent Rule:x^(m/n) = n√(xᵐ) = (n√x)ᵐ
6. Pre-Calculus & Trigonometric Identities
Pythagorean Identities:sin²(θ) + cos²(θ) = 1
1 + tan²(θ) = sec²(θ)
1 + cot²(θ) = csc²(θ)
1 + tan²(θ) = sec²(θ)
1 + cot²(θ) = csc²(θ)
Radian Conversion & Arc Length:Degrees = Radians × (180 / π)
Radians = Degrees × (π / 180)
Arc Length: s = r · θ (θ in rad)
Radians = Degrees × (π / 180)
Arc Length: s = r · θ (θ in rad)
Common Unit Circle Exact Values:• 0 rad (0°): (cos=1, sin=0, tan=0)
• π/6 rad (30°): (cos=√3/2, sin=1/2, tan=√3/3)
• π/4 rad (45°): (cos=√2/2, sin=√2/2, tan=1)
• π/3 rad (60°): (cos=1/2, sin=√3/2, tan=√3)
• π/2 rad (90°): (cos=0, sin=1, tan=undefined)
• π/6 rad (30°): (cos=√3/2, sin=1/2, tan=√3/3)
• π/4 rad (45°): (cos=√2/2, sin=√2/2, tan=1)
• π/3 rad (60°): (cos=1/2, sin=√3/2, tan=√3)
• π/2 rad (90°): (cos=0, sin=1, tan=undefined)