Core Mathematics — 2019

Express, correct to three significant figures, 0.003597.

Evaluate: (0.064)− 1 3 .

Solve: y+1 2 − 2y−1 3 = 4.

Simplify, correct to three significant figures, (27.63)2 − (12.37)2.

If 7 + y = 4(mod8), find the least value of y, 10 ≤ y ≤ 30.

If T = { prime numbers } and M = { odd numbers } are subsets of μ = {x : 0 < x ≤ 10} and x is an integer, find ( T′ ∩ M′ ).

Evaluate: log3 9−log2 8 log3 9 .

If 23y = 1111two , find the value of y.

If 6, P, and 14 are consecutive terms in an arithmetic progression, find the value of P.

Evaluate: 2√28 − 3√50 + √72.

If m : n = 2 : 1, evaluate 3m2−2n2 m2+mn .

H varies directly as p and inversely as the square of y. If H = 1, p = 8 and y = 2, find H in terms of p and y.

Solve 4x2 − 16x + 15 = 0.

Simplify: log10 6 − 3 log10 3 + 2 3 log10 27.

Bala sold an article for N6,900.00 and made a profit of 15%. Calculate his percentage profit if he had sold it for N6,600.00.

If 3p = 4q and 9p = 8q − 12, find the value of pq.

If (0.25)y = 32, find the value of y.

There are 8 boys and 4 girls in a lift. What is the probability that the first person who steps out of the lift will be a boy?

Simplify: x2−5x−14 x2−9x+14 .

Which of these values would make 3p−1 p2−p undefined?

The total surface area of a solid cylinder 165 cm2. Of the base diameter is 7 cm , calculate its height. [Take π = 22 7 ]

If 2a = √64 and b a = 3, evaluate a2 + b2.

In 4XY Z, |Y Z| = 32 cm, ∠Y XZ = 52◦ and ∠XZY = 90◦. Find, correct to the nearest cen- timetre, |XZ|.

If logx 2 = 0.3, evaluate logx 8.

An arc subtends an angle of 72◦ at the centre of a circle. Find the length of the arc if the radius of the circle is 3.5 cm . [Take π = 22 7 ]

Make b the subject of the relation lb = 1 2 (a + b)h.

Eric sold his house through an agent who charged 8% commission on the selling price. If Eric received $117, 760.00 after the sale, what was the selling price of the house?

Find the angle at which an arc of length 22 cm subtends at the centre of a circle of radius 15 cm . [Take π = 22 7 ]

A rectangular board has a length of 15 cm and width x cm . If its sides are doubled, find its new area.

In the diagram below, POS and ROT are straight lines. OPQR is a parallelogram, |OS| = |OT | and ∠OST = 50◦. Calculate the value of ∠OP Q.

Factorize completely: (2x + 2y)(x − y) + (2x − 2y)(x + y).

The interior angles of a polygon are 3xo, 2xo, 4xo, 3xo and 6xo. Find the size of the smallest angle of the polygon.

A box contains 2 white and 3 blue identical balls. If two balls are picked at random from the box, one after the other with replacement, what is the probability that they are of different colours?

Find the equation of a straight line passing through the point (1, −5) and having gradient of 3 4 .

The foot of a ladder is 6 m from the base of an electric pole. The top of the ladder rest against the pole at a point 8 m above the ground. How long is the ladder?

If tan x = 3 4 , 0 < x < 90◦, evaluate cos x 2 sin x .

From the top of a vertical cliff 20 m high, a boat at sea can be sighted 75 m away and on the same horizontal position as the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.

In the diagram, O is the centre of the circle of radius 18 cm . If ∠ZXY = 70◦, calculate the length of arc ZY . [Take π = 22 7 ]

In the diagram, RT is a tangent to the circle at R, ∠PQR = 70◦, ∠QRT = 52◦, ∠QSR = y and ∠PRQ = x. Find the value of y.

In the diagram, RT is a tangent to the circle at R, ∠PQR = 70◦, ∠QRT = 52◦, ∠QSR = y and ∠PRQ = x. Find the value of x.

Calculate the variance of 2, 4, 7, 8 and 9.

The fourth term of an arithmetic progression is 37 and the first term is -20. Find the common difference.

In the diagram, PQ is parallel to RS, ∠QFG = 105◦ and ∠FEG = 50◦. Find the value of m.

In the diagram, PQ is parallel to RS, ∠QFG = 105◦ and ∠FEG = 50◦. Find the value of n.

A box contains 5 red, 6 green and 7 yellow pencils of the same size. What is the probability of picking a green pencil at random?