Core Mathematics — 2021

Correct 0.007985 to three significant figures.

Simplify: (11two)2.

Solve: 2√2x+1 = 32.

If log10 2 = m and log10 3 = n, find log10 24 in terms of m and n.

Find the 5th term of the sequence 2, 5, 10, 17, . . .

If P = {−3 < x < 1} and Q = {−1 < x < 3}, where x is an integer, find P ∩ Q.

Factorize 6pq − 3rs − 3ps + 6qr.

Mensah is 5 years old and joyce is thrice as old as mensah. In how many years will joyce be twice as old as Mensah?

If 16 ∗ 2(x+1) = 4x ∗ 8(1−x), find the value of x.

The circumference of a circular track is 9 km. A cyclist rides round it a number of times and stops after covering a distance of 302 km. How far is the cyclist from the starting point?

Simplify 2√7 − 14 √7 + 7 √21 .

If 4x + 2y = 16 and 6x − 2y = 4, find the value of (y − x).

In the diagram below, ∠ABC and ∠BCD are right angles, ∠BAD = t and ∠EDF = 70◦. Find the value of t.

The sum of the interior angles of a regular polygon with k sides is (3k − 10) right angles. Find the size of the exterior angle?

Make u the subject in x = 2u−3 3u+2 .

A trader paid import duty of 38 kobo in the naira on the cost of an engine. If a total of #22, 800.00 was paid as import duty, calculate the cost of the engine.

The height of an equilateral triangle of side is 10√3 cm. Calculate its perimeter.

In 4LM N, |LM | = 6cm, ∠LN M = x, angle L is right and sin x = 3 5 . Find the area of 4LM N

Consider the statements: {P = All students offering Literature(L) also offer History(H)}, {Q = Students offering History(H) do not offer Geography(G)}. Which of the Venn diagram correctly illustrate the two statements?

Find the quadratic equation whose roots are −2q and 5q.

If tan θ = 3 4 , 180◦ < θ < 270◦, find the value of cos θ.

If 2 x−3 − 3 x−2 = p (x−3)(x−2) , find p.

The diagonals of a rhombus are 12 cm and 5 cm. Calculate its perimeter.

In the diagram, 4XY Z is produced to T . if |XY | = |ZY | and ∠XY T = 40◦, find ∠XZT

A solid brass cube is melted and recast as a solid cone of height h and base radius r. If the height of the cube is h, find r in terms of h.

Which of the following is not an exterior angle of a regular polygon?

From a point T , a man moves 12 km due west and then moves 12 km due south to another point Q. Calculate the bearing of T from Q.

In the diagram below, O is the centre of the circle, ∠P QR = 72◦ and OR is parallel to P S. Find ∠OP S.

A trapezium of parellel sides 10cm and 21cm and height 8cm is inscribed in a circle of radius 7cm. Calculate the area of the region not covered by the trapezium. [Take π = 22 7 ]

Find, correct to two decimal places, the mean of 1 1 2 , 2 2 3 , 3 3 4 , 4 4 5 , and 5 5 6 .

A cyclist moved at a speed of X km/h for 2 hours. He then increased his speed by 2 km/h for the next 3 hours. If the total distance covered is 36 km, calculate his initials speed.

Find the first quartile of 7, 8, 7, 9, 11, 8, 7, 9, 6 and 8.

In the diagram below, find the value of x.

A cone has a base radius of 8 cm and height 11 cm. Calculate, correct to two decimal places, the curved surface area.

Given that sin x = 3 5 , 0 ≤ x ≤ 90, evaluate (tan x + 2 cos x).

In the diagram, line EC is a diameter of the circle. If ∠ABC equals 158◦, find ∠ADE.

Height(cm) 160 161 162 163 164 165 No. of players 4 6 3 7 8 9 The table shows the height of 37 players of a basketball team. Calculate, correct to one decimal place, the mean height of the players.

Let XY be a line segments with the coordinates X(−8, −12) and Y(p, q). If the midpoint of XY is (−4, −2), find the coordinates of Y .

It’s known that 500 tickets for a concert for adults and children were sold at $4.50 and $3.00 respectively. If the total receipts for the concert was $1987.50, how many tickets for adults were sold?

The distance d between two villages is more than 18 km but not more than 23 km. Which one of these inequalities represents the statements?

The pie chart represents the distribution of fruits on display in the shop. If there are 60 apples on display, how many oranges are there?

A box contains 40 identical balls of which 10 are red and 12 are blue. A ball is selected at random from the box, what is the probability that it is neither red nor blue?

A fair die is tossed twice, what is the probability to get a sum of at least 10.

A man will be x + 10 years old in 8 years time. If 2 years ago he was 63 years, find the value of x.

The equation of a line is given as 3x − 5y = 7. Find its gradient (slope).

For what value of x is 4−2x x+1 undefined?