Grade 11 Maths Formula Sheet

Every Grade 11 maths formula: quadratic formula, discriminant, quadratic patterns, functions, depreciation, effective rates, probability, trig rules and…

This sheet collects every formula and identity in the CAPS Grade 11 syllabus, grouped by topic. The exam's information sheet gives the quadratic formula, finance formulas, analytical geometry formulas and the sine, cosine and area rules, but you must know the identities, reduction formulae and the discriminant conditions by heart.

Each row has a short note on when to use the formula and the most common slip to avoid.

Algebra and number patterns

Formula	Expression	Note
Quadratic formula	`x = [−b ± √(b² − 4ac)] / 2a`	Write down a, b and c first.
Discriminant	`Δ = b² − 4ac`	Δ > 0: two real roots; Δ = 0: equal roots; Δ < 0: no real roots.
Rational exponents	`a^(m/n) = ⁿ√(aᵐ)`	Find the root first to keep numbers small.
Quadratic pattern	`Tₙ = an² + bn + c`	2a = second difference; 3a + b = T₂ − T₁; a + b + c = T₁.

Functions

Formula	Expression	Note
Parabola (turning point form)	`y = a(x + p)² + q`	Turning point (−p; q).
Axis of symmetry	`x = −b/2a`	For y = ax² + bx + c.
Hyperbola	`y = a/(x + p) + q`	Asymptotes x = −p and y = q.
Exponential	`y = a·bˣ⁺ᵖ + q`	Asymptote y = q.
Average gradient	`[f(x₂) − f(x₁)] / (x₂ − x₁)`	Gradient of the line joining two points on the graph.

Finance and probability

Formula	Expression	Note
Straight-line depreciation	`A = P(1 − in)`	Same amount lost each year.
Reducing-balance depreciation	`A = P(1 − i)ⁿ`	Percentage of the current value lost each year.
Effective rate	`1 + i_eff = (1 + i_nom/m)ᵐ`	m = compounding periods per year.
Independent events	`P(A and B) = P(A) × P(B)`	Use to test for independence.
Addition rule	`P(A or B) = P(A) + P(B) − P(A and B)`	Works for any two events.

Trigonometry

Formula	Expression	Note
Identities	`tan θ = sin θ/cos θ; sin²θ + cos²θ = 1`	Change everything to sin and cos when proving.
Reduction (180° ± θ, 360° − θ)	`sin(180° − θ) = sin θ; cos(180° + θ) = −cos θ; tan(360° − θ) = −tan θ`	Use CAST to get the sign.
Co-functions	`sin(90° − θ) = cos θ; cos(90° − θ) = sin θ`	The function changes for 90° ± θ.
Sine rule	`a/sin A = b/sin B = c/sin C`	Side and opposite angle known.
Cosine rule	`a² = b² + c² − 2bc cos A`	Two sides and the included angle, or three sides.
Area rule	`Area = ½ab sin C`	Two sides and the angle between them.

Analytical geometry, statistics and measurement

Formula	Expression	Note
Equation of a line	`y − y₁ = m(x − x₁)`	Gradient and one point.
Angle of inclination	`tan θ = m`	If m < 0, θ = 180° − reference angle.
Variance	`σ² = Σ(x − x̄)² / n`	CAPS divides by n.
Standard deviation	`σ = √σ²`	Use σx on the calculator.
Cone surface area	`πr² + πrs`	s is the slant height: s² = r² + h².

How to use them

Learn the identities and reduction formulae by heart: they're not on the information sheet.
For the sine and cosine rules, sketch and label the triangle with a, b, c opposite A, B, C.
When interest is compounded monthly or quarterly, adjust both i and n.
Check every root of a surd equation in the original equation.

Frequently asked questions

Which Grade 11 formulas are on the information sheet?

The information sheet normally includes the quadratic formula, finance formulas, analytical geometry formulas, the sine, cosine and area rules, and the statistics formulas. Identities, reduction formulae and circle theorems are not given.

How do I remember when to use the sine or cosine rule?

If you know a side and the angle opposite it, use the sine rule. If you know two sides and the angle between them, or all three sides, use the cosine rule.

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