Core Mathematics 2021 - WASSCE

Mathematics

Question 1

Correct 0.00798516 to three significant figures.

Question 2

Simplify: \((11)_2\)^2

Question 3

Solve: \(2^{\sqrt{2x + 1}} = 32\)

Question 4

If \(\log_{10} 2 = m\) and \(\log_{10} 3 = n\), find \(\log_{10} 24\) in terms of m and n.

Question 5

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

Question 6

If \(P = \{-3 < x < 1\}\) and \(Q = \{-1 < x < 3\}\), where x is a real number, find \(P \cap Q\).

Question 7

Factorize \(6pq - 3rs - 3ps + 6qr\).

Question 8

What number should be subtracted from the sum of \(2\frac{1}{6}\) and \(2\frac{7}{12}\) to give \(3\frac{1}{4}\)?

Question 9

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?

Question 10

If \(16 \times 2^{(x + 1)} = 4^{x} \times 8^{(1 − x)}\), find the value of x.

Question 11

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?

Question 12

Simplify \(2\sqrt{7} - \frac{14}{\sqrt{7}} + \frac{7}{\sqrt{21}}\)

Question 13

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

Question 14

Given that R is directly proportional to L and inversely proportional to P, R = 3 when L = 9 and P = 0.8, find R when L = 15 and P = 1.8.

Question 15

**DIAGRAM WILL BE PROVIDED.** In the diagram, \(\angle ABC\) and \(\angle BCD\) are right angles, \(\angle BAD = t\) and \(\angle EDF = 70^\circ\). Find the value of t.

Question 16

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.

Question 17

Make U the subject of the relation: \(x = \frac{2U - 3}{3U + 2}\).

Question 18

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.

Question 19

The height of an equilateral triangle is \(10\sqrt{3}\) cm. Calculate its perimeter.

Question 20

In a \(\triangle LMN\), \(|LM| = 6\) cm, \(\angle LMN = 90^\circ\), \(\angle LNM = x\) and \(\sin x = \frac{3}{5}\). Find the area of \(\triangle LMN\).

Question 21

**DIAGRAM WILL BE PROVIDED.** 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?

Question 22

Find The quadratic Equation whose roots are \(-2q\) And \(5q\).

Question 23

If \(\tan \theta = \frac{3}{4}\), \(180^\circ < \theta < 270^\circ\), find the value of \(\cos \theta\).

Question 24

If \(\frac{2}{(x - 3)} - \frac{3}{(x - 2)} = \frac{p}{(x - 3)(x - 2)}\), find p.

Question 25

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

Question 26

**DIAGRAM WILL BE PROVIDED.** In the diagram, \(\triangle XYZ\) is produced to T. If \(|XY| = |ZY|\) and \(\angle XYT = 40^\circ\), find \(\angle XZT\).

Question 27

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.

Question 28

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

Question 29

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.

Question 30

**DIAGRAM WILL BE PROVIDED.** In the diagram, O is the centre of the circle PQRS, \(\angle PQR = 72^\circ\) and \(OR\parallel PS\). Find \(\angle OPS\).

Question 31

A trapezium of parallel sides 10 cm and 21 cm and height 8 cm is inscribed in a circle of radius 7 cm. Calculate the area of the region not covered by the trapezium. [Take \(\pi = \frac{22}{7}\)]

Question 32

Find correct to two decimal places the mean of \(1\frac{1}{2},\;2\frac{2}{3},\;3\frac{3}{4},\;4\frac{4}{5}\) and \(5\frac{5}{6}\).

Question 33

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.

Question 34

**DIAGRAM WILL BE PROVIDED.** Find the value of \((x + y)\) in the diagram.

Question 35

**DIAGRAM WILL BE PROVIDED.** In the diagram, MP is a tangent to the circle NQR, \(\angle PNQ = 64^\circ\) and \(|RQ| = |RN|\). Find the angle marked t.

Question 36

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

Question 37

**DIAGRAM WILL BE PROVIDED.** In the diagram, PQRS is a circle. find the value of x.

Question 38

A cone has a base radius of 8 cm and height 11 cm. Calculate, correct to two decimal places, the curved surface area. [Take \(\pi = \frac{22}{7}\)]

Question 39

Given that \(\sin x = \frac{3}{5}\), \(0^\circ \le x \le 90^\circ\), evaluate \((\tan x + 2\cos x)\).

Question 40

**DIAGRAM WILL BE PROVIDED.** In the diagram \(EC\) is a diameter of circle ABCDE. If \(\angle ABC = 158^\circ\), find \(\angle ADE\).

Question 41

**TABLE WILL BE PROVIDED.** The table shows the heights of thirty-seven players of a basketball team. Calculate, correct to one decimal place, the mean height of the players.

Question 42

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

Question 43

Five hundred tickets were sold for a concert. Tickets for adults and children were sold at USD 4.50 and USD 3.00, respectively. If the total receipts for the concerts was USD 1987.50, how many tickets for adults were sold?

Question 44

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

Question 45

**DIAGRAM WILL BE PROVIDED.** The pie chart represents the distribution of fruits on display in a shop. If there are 60 apples on display, how many oranges are there?

Question 46

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

Question 47

A fair die is tossed twice. What is the probability of getting a sum of at least 10?

Question 48

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

Question 49

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

Question 50

For what value of x is \(4 - \frac{2x}{x + 1}\) undefined?