NECO SSCE Mathematics flashcards

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

Standard form

A number written as A × 10ⁿ where 1 ≤ A < 10 and n is an integer; used to express very large or very small quantities compactly.

Change of base formula

log_a b = log_c b ÷ log_c a, allowing logarithms in any base to be rewritten using common logarithms (base 10) or natural logarithms (base e).

Rationalising a surd denominator

Multiply numerator and denominator by the conjugate of the denominator, e.g. for 1/(√a + √b) multiply by (√a − √b)/(√a − √b), removing the surd from the denominator.

Simple interest formula

I = PRT/100, where P is principal, R is rate per cent per annum and T is time in years; the interest is not added to the principal for later periods.

HCF and LCM product rule

For two positive integers a and b, HCF(a,b) × LCM(a,b) = a × b, so LCM = ab ÷ HCF; this holds only for two numbers, not three.

Number of subsets formula

A set with n distinct elements has 2ⁿ subsets in total, including the empty set and the set itself; it has 2ⁿ − 1 proper subsets.

Converting base 10 to base b

Divide the decimal number repeatedly by b, recording each remainder; read the remainders from the last division upward to obtain the digits in base b.

Quadratic formula

For ax² + bx + c = 0 with a ≠ 0, the roots are x = [−b ± √(b² − 4ac)]/2a; the formula applies when the quadratic does not factorise easily.

Discriminant

The expression b² − 4ac in ax² + bx + c = 0: positive means two distinct real roots, zero means equal roots, negative means no real roots.

Sum and product of roots

If α and β are roots of ax² + bx + c = 0, then α + β = −b/a and αβ = c/a; these give the quadratic x² − (sum)x + (product) = 0.

Sum of a geometric series

Sₙ = a(1 − rⁿ)/(1 − r) for r ≠ 1, where a is the first term and r the common ratio; the sum to infinity is a/(1 − r) when |r| < 1.

Remainder theorem

When a polynomial f(x) is divided by (x − a), the remainder equals f(a); if f(a) = 0 then (x − a) is a factor of f(x).

Direct and inverse variation

Direct variation means y = kx so y/x is constant; inverse variation means y = k/x so xy is constant, where k is the constant of variation.

Interior angle sum of polygon

A polygon with n sides has interior angles summing to (n − 2) × 180°; for a regular polygon each interior angle is (n − 2)180°/n.

Angle at the centre theorem

The angle subtended by an arc at the centre of a circle is twice the angle the same arc subtends at any point on the remaining circumference.

Cyclic quadrilateral rule

A quadrilateral with all four vertices on a circle has opposite angles that sum to 180°; each exterior angle equals the interior opposite angle.

Volume of a cone

V = ⅓πr²h, one third of the volume of a cylinder with the same base radius r and perpendicular height h; slant height l = √(r² + h²).

Area of a triangle formula

Area = ½ab sin C, where a and b are two sides and C is the included angle; also Area = √[s(s−a)(s−b)(s−c)] with s = (a+b+c)/2.

Similar shapes ratio rule

If two similar figures have corresponding lengths in ratio k, their areas are in ratio k² and their volumes in ratio k³; angles remain equal.

Surface area of a sphere

The total surface area of a sphere of radius r is 4πr², equal to four times the area of its great circle; its volume is (4/3)πr³.

Probability of an event

P(E) = number of favourable outcomes ÷ total number of equally likely outcomes; P(E) lies between 0 and 1, and P(not E) = 1 − P(E).

Mutually exclusive events

Two events that cannot occur together, so P(A ∩ B) = 0; therefore P(A ∪ B) = P(A) + P(B) for such events.

Independent events rule

Events A and B are independent when the occurrence of one does not affect the other; then P(A ∩ B) = P(A) × P(B).

Mean of grouped data

For grouped data the mean is Σfx ÷ Σf, where x is the midpoint of each class interval and f is the corresponding class frequency.

Standard deviation

The square root of the variance: for n values, SD = √[Σ(x − x̄)²/n]; it measures the spread of data about the mean in the original units.

Ogive

A cumulative frequency curve plotted against the upper class boundaries; the median is read at cumulative frequency N/2, and quartiles at N/4 and 3N/4.

Sine rule

In any triangle, a/sin A = b/sin B = c/sin C, where a is opposite angle A; used with two angles and a side, or two sides and a non-included angle.

Cosine rule

a² = b² + c² − 2bc cos A; used to find a side when two sides and the included angle are known, or an angle when all three sides are known.

Three-figure bearing

An angle measured clockwise from the North direction, written with three digits, e.g. 045°; the back bearing is found by adding or subtracting 180°.

Trigonometric identity

sin²θ + cos²θ = 1 for all angles θ; dividing by cos²θ gives 1 + tan²θ = sec²θ, and dividing by sin²θ gives 1 + cot²θ = cosec²θ.

Angle of depression

The angle measured downwards from the horizontal line of sight to an object below the observer; it equals the angle of elevation from the object to the observer.

Length of an arc

For a circle of radius r, an arc subtending θ radians at the centre has length rθ; in degrees the length is (θ/360) × 2πr.