Cameroon GCE O-Level Mathematics flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Quadratic formula

For ax² + bx + c = 0 with a ≠ 0, the solutions are x = (−b ± √(b² − 4ac)) ÷ 2a. Substitute coefficients carefully, keeping signs of negative b and c.

Discriminant meaning

The value b² − 4ac from a quadratic equation. Positive means two distinct real roots, zero means one repeated real root, negative means no real roots (the curve misses the x-axis).

Completing the square

Rewrite x² + bx + c as (x + b/2)² − (b/2)² + c. This locates the vertex of the parabola and solves quadratics without factorising.

Factor and remainder theorem

For polynomial f(x), (x − a) is a factor exactly when f(a) = 0. The remainder on dividing by (x − a) equals f(a), so substitution gives the remainder directly.

Laws of indices

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. These rules apply only when the bases are identical.

Rationalising a surd denominator

To remove √a from a denominator, multiply numerator and denominator by √a. For a denominator like a + √b, multiply by its conjugate a − √b instead.

Laws of logarithms

log(ab) = log a + log b; log(a/b) = log a − log b; log(a^n) = n log a. These convert multiplication into addition and allow solving equations with unknown exponents.

Arithmetic progression formulas

The nth term is a + (n − 1)d and the sum of n terms is (n/2)[2a + (n − 1)d], where a is the first term and d the common difference.

Geometric progression formulas

The nth term is ar^(n−1) and the sum of n terms is a(r^n − 1)/(r − 1) for r ≠ 1, where a is the first term and r the common ratio.

Direct and inverse variation

Direct variation means y = kx, so y/x stays constant. Inverse variation means y = k/x, so xy stays constant. Find k from one data pair, then substitute.

Simultaneous equations by elimination

Multiply each equation so one variable has equal coefficients, then add or subtract the equations to remove it. Solve for the remaining variable and back-substitute.

Inequality on a number line

Multiplying or dividing an inequality by a negative number reverses its sign. Open circles mark strict inequalities (<, >); filled circles mark ≤ and ≥.

Circle mensuration formulas

Area = πr² and circumference = 2πr. Arc length of a sector is (θ/360) × 2πr and sector area is (θ/360) × πr², with θ in degrees.

Cylinder and cone formulas

Cylinder: volume πr²h, curved surface 2πrh. Cone: volume (1/3)πr²h, curved surface πrl where l is the slant height, found by l² = r² + h².

Sphere formulas

Volume of a sphere is (4/3)πr³ and its surface area is 4πr². A hemisphere has half the volume and a total surface of 3πr² including the flat face.

Prism and pyramid volume

Volume of a prism or cylinder equals cross-sectional area times length. Volume of a pyramid or cone is one third of base area times perpendicular height.

Similar figures and scale factor

If lengths scale by k, areas scale by k² and volumes by k³. Use this to convert between model and real dimensions, surface areas, and capacities.

Sine rule

In any triangle, a/sin A = b/sin B = c/sin C, where each side is opposite its matching angle. Use it with a known side and its opposite angle.

Cosine rule

a² = b² + c² − 2bc cos A. Use it when two sides and the included angle are known, or when all three sides are known and an angle is required.

Area of a triangle

Area = ½ab sin C, using two sides and the angle between them. This works for any triangle, not only right-angled ones, and needs the included angle.

Exact trigonometric values

sin 30° = ½, cos 30° = √3/2, tan 30° = 1/√3; sin 45° = cos 45° = 1/√2; tan 45° = 1; sin 60° = √3/2, cos 60° = ½, tan 60° = √3.

Angles of elevation and depression

Both are measured from the horizontal. Elevation is measured upward to an object; depression is measured downward. They are alternate angles when taken between two parallel horizontal lines.

Bearing notation

A three-figure bearing is measured clockwise from due north, so it always has three digits, for example 045° or 210°. Back bearings differ by 180°.

Gradient and equation of line

Gradient m = (y₂ − y₁)/(x₂ − x₁). A line is y = mx + c, where c is the y-intercept. Parallel lines have equal gradients; perpendicular gradients multiply to −1.

Distance and midpoint formulas

Distance between two points = √[(x₂ − x₁)² + (y₂ − y₁)²]. Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2), the average of the two coordinate pairs.

Equation of a circle

A circle with centre (a, b) and radius r has equation (x − a)² + (y − b)² = r². With centre at the origin this reduces to x² + y² = r².

Angle properties of circles

The angle in a semicircle is 90°; the angle at the centre is twice the angle at the circumference; angles in the same segment are equal; opposite angles of a cyclic quadrilateral sum to 180°.

Tangent and radius property

A tangent meets a radius at right angles at the point of contact. Two tangents drawn from an external point to the same circle are equal in length.

Polygon angle sums

Interior angles of an n-sided polygon sum to (n − 2) × 180°. In a regular polygon each exterior angle is 360°/n and each interior angle is 180° − 360°/n.

Mean of grouped data

Mean = Σfx ÷ Σf, where x is each class midpoint and f its frequency. The midpoint is the average of the lower and upper class boundaries.

Median and mode

For n ordered values the median is the ((n+1)/2)th value, or the mean of the two middle values if n is even. The mode is the most frequently occurring value.

Probability rules

P(event) = favourable outcomes ÷ total equally likely outcomes, and P(not E) = 1 − P(E). For mutually exclusive events P(A or B) = P(A) + P(B).