Essential CSCA Formula Sheet (Math, Physics, Chemistry)

One of the biggest shocks for international students is that formula booklets are NOT provided during the CSCA exam. You are expected to have these memorized.

To save you from flipping through three different textbooks, we compiled the Essential CSCA Formula List covering core concepts from Conic Sections to Electromagnetism.

Pro Tip: Bookmark this page. Review it 30 minutes before your exam.

1. Mathematics Formulas

The Math section is calculation-heavy. Prioritize Conic Sections and Trig Identities.

Algebra & Functions

Concept	Formula
Quadratic Formula	x = (-b ± √(b² - 4ac)) / 2a
Vieta's Formulas	x₁ + x₂ = -b/a x₁x₂ = c/a
Logarithms	log(xy) = log(x) + log(y) logₐ(b) = logₓ(b) / logₓ(a)
Arithmetic Series	Sn = n(a₁ + an) / 2
Geometric Series	Sn = a₁(1 - rⁿ) / (1 - r)
Infinite Geometric	S = a₁ / (1 - r) (where \|r\| < 1)

Trigonometry

Concept	Formula
Pythagorean Identity	sin²θ + cos²θ = 1
Double Angle (Sin)	sin(2θ) = 2sinθcosθ
Double Angle (Cos)	cos(2θ) = cos²θ - sin²θ
Sine Rule	a/sinA = b/sinB = c/sinC = 2R
Cosine Rule	c² = a² + b² - 2ab·cosC

Analytic Geometry (Crucial)

Concept	Formula
Distance Formula	d = √((x₂ - x₁)² + (y₂ - y₁)²)
Circle Equation	(x - a)² + (y - b)² = r²
Ellipse	x²/a² + y²/b² = 1
Hyperbola	x²/a² - y²/b² = 1
Point-Line Dist.	d = \|Ax₀ + By₀ + C\| / √(A² + B²)

2. Physics Formulas

Exam Note: Pay close attention to Electromagnetism. Combine these formulas with the Right Hand Rule.

Mechanics

Concept	Formula
Kinematics (Velocity)	v = v₀ + at
Kinematics (Dist)	x = v₀t + ½at²
Kinematics (V²)	v² = v₀² + 2ax
Centripetal Force	F = mv² / r
Momentum	p = mv
Work & Power	W = Fs·cosθ P = Fv

Electromagnetism

Concept	Formula
Coulomb’s Law	F = k(q₁q₂) / r²
Electric Field	E = F/q = kQ/r²
Ohm’s Law	V = IR
Lorentz Force	F = qvB (Moving Charge)
Ampere’s Force	F = BIL (Current Wire)
Capacitance	C = Q/U

3. Chemistry Formulas

Focus on Stoichiometry and Reaction Rates. You must be able to calculate pH without a calculator.

Stoichiometry & Gas

Concept	Formula
Moles	n = m / M
Concentration	C = n / V (mol/L)
Gas Volume (STP)	V = n × 22.4 L/mol
Ideal Gas Law	pV = nRT

Equilibrium & Electrochemistry

Concept	Formula
Equilibrium Constant	Kc = ([C]ᶜ[D]ᵈ) / ([A]ᵃ[B]ᵇ)
pH Calculation	pH = -log[H⁺]
Nernst Equation	E = E° - (RT/nF)lnQ
Faraday’s Law	m = (M·I·t) / (n·F)