Cameroon GCE O-Level Mathematics cheat sheet

Cameroon GCE O-Level Mathematics - Core Facts and Formulas

• Algebra: for ax² + bx + c = 0, x = (−b ± √(b² − 4ac)) / 2a; the discriminant b² − 4ac gives two real roots if positive, one repeated root if zero, and no real roots if negative.

• Indices and surds: a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(mn), a^0 = 1, a^(−n) = 1/a^n, and √(ab) = √a × √b; rationalise 1/√a by multiplying numerator and denominator by √a.

• Logarithms: log(ab) = log a + log b, log(a/b) = log a − log b, log(a^n) = n log a, log_a a = 1, log_a 1 = 0; change of base log_a x = log_b x ÷ log_b a.

• Sequences: arithmetic term a + (n−1)d with sum (n/2)[2a + (n−1)d]; geometric term ar^(n−1) with sum a(r^n − 1)/(r − 1) for r ≠ 1.

• Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h and curved surface 2πrh; cone volume (1/3)πr²h and curved surface πrl; sphere volume (4/3)πr³ and surface 4πr².

• Trigonometry: sine rule a/sin A = b/sin B = c/sin C; cosine rule a² = b² + c² − 2bc cos A; area of triangle = ½ab sin C; exact values sin 30° = ½, cos 60° = ½, tan 45° = 1.

• Coordinate geometry: gradient m = (y₂ − y₁)/(x₂ − x₁); line y = mx + c; parallel lines share m, perpendicular gradients multiply to −1; distance = √[(x₂ − x₁)² + (y₂ − y₁)²]; midpoint averages the coordinates.

• Statistics: mean = Σfx ÷ Σf for grouped data; median position (n+1)/2 for ordered raw data; mode is the most frequent value; probability of an event = favourable outcomes ÷ total equally likely outcomes, and P(not E) = 1 − P(E).

• Angles and polygons: interior angle sum of an n-sided polygon = (n − 2) × 180°; each exterior angle of a regular n-gon = 360°/n; angle in a semicircle is 90°; the angle between a tangent and a radius is 90°.