Mathematics JAMB, WAEC, NECO AND NABTEB Official Past Questions

If the volume of a hemisphere is increasing at a steady rate of 18π m\(^{3}\) s\(^{-1}\), at what rate is its radius changing when its is 6m?

A bowl is designed by revolving completely the area enclosed by y = x2 – 1, y = 3 and x ≥ 0 around the y-axis. What is the volume of this bowl?

If y = 2xcos2x – sin2x, find dy/dx when x = π/4

Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)

A predator moves in a circle of radius √2 centre (0,0), while a prey moves along the line y = x. If 0 \(\leq\) x \(\leq\) 2, at which point(s) will they meet?

In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.

if P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X is

3y = 4x – 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.

An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle.

P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and angle VUS = 50°, find angle UST.

A frustrum of pyramid with square base has its upper and lower sections as squares of sizes 2m and 5m respectively and the distance between them 6m. Find the height of the pyramid from which the frustrum was obtained.

If α and β are the roots of the equation 3x\(^2\) + 5x – 2 = 0, find the value of 1/α + 1/β

Solve the inequality 2 – x > x\(^2\).

A trader realizes 10x – x\(^2\) naira profit from the sale of x bags on corn. How many bags will give him the desired profit?

if (x – 1), (x + 1) and (x – 2) are factors of the polynomial ax\(^3\) + bx\(^2\) + cx – 1, find a, b, c in that order.

Evaluate (\(\frac{1}{2} – \frac{1}{4} + \frac{1}{8} – \frac{1}{16} + …) -1\)

Find the inverse of p under the binary operation * defined by p*q = p + q – pq, where p and q are real numbers and zero is the identity

The 3rd term of an A.P is 4x – 2y and the 9th term is 10x – 8y. Find the common difference.

A binary operation * is defined by a * b = a\(^b\). If a * 2 = 2 – a, find the possible values of a.

If \(P344_{6} – 23P2_{6} = 2PP2_{6}\), find the value of the digit P.

Simplify \(\frac{3(2^{n+1}) – 4(2^{n-1})}{2^{n+1} – 2^n}\)