Solve WASSCE Core Mathematics Questions & Answers

Question 1

A brother is seven years older than his sister. In five years he will be twice her age. How old is the sister now?

Question 2

A cyclist rides at \(20\text{ km h}^{-1}\). How long will he take to travel \(100\text{ m}\)?

Question 3

Which line intersects \(y=-x^2+6x-4\) at roots of \(x^2-6x+8=0\)?

Question 4

Evaluate \(\tan30^{\circ}-3\sin60^{\circ}\).

Question 5

If \(3\log(x-1)=\log27\), find \(x\).

Question 6

Evaluate \(\tan30^{\circ}-\sin45^{\circ}\).

Question 7

Preamble: \(C\!:\) “The code compiles.” \(D\!:\) “The program runs.” Given \(C\Rightarrow D\), which is **always true**?

Question 8

If \(\dfrac{2x+y}{3}=x-y\), find \(x:y\).

Question 9

A sum GH¢\(600\) shared 4:3 between A&B. B gives his share 2:1 to X and Y. How much does Y get?

Question 10

From \(4x+6y=8\) and \(2x+3y=4\), compute \(x+2y\).

Question 11

Preamble: Let \(P\!:\) “Kwame revises thoroughly.” \(Q\!:\) “Kwame passes the test.” Given \(P\Rightarrow Q\), which conclusion is logically valid?

Question 12

Simplify \(\frac{\sqrt{3} + \sqrt{48}}{\sqrt{6}}\).

Question 13

A gadget marked GH¢\(50\) is sold at GH¢\(45\). What percentage reduction is this?

Question 14

A farmer buys 10 bags of fertiliser at GH¢45 each and 6 bags at GH¢60 each. What is the average cost per bag?

Question 15

Find the line that intersects \(y=-x^2+2x-3\) to solve \(x^2+2x-5=0\).

Question 16

A building 10 m high casts a 5 m shadow. Calculate the elevation angle.

Question 17

GH¢\(720\) shared 3:2 by A and B. B splits 1:3 to C and D. How much to D?

Question 18

Simplify \(\frac{\sqrt{8} + \sqrt{18}}{\sqrt{2}}\).

Question 19

Find the **mean** (to the nearest whole number) of the masses 83, 47, 62, 49, 55, 72, 58, 62.

Question 20

What is the decimal value of \(7B_{16}\)?

Question 21

GH¢\(900\) split 5:4 to P and Q. Q gives share 3:2 to R and S. Find R’s amount.

Question 22

Least \(x\) if \(29\equiv7\pmod x\).

Question 23

The length of a rectangular lawn is \(3\text{ cm}\) longer than its width. If the perimeter is \(42\text{ cm}\), find the width.

Question 24

Find the 11\(^{\text{th}}\) term of the sequence \(\tfrac14,\ \tfrac58,\ 1,\ 1\tfrac38,\ldots\).

Question 25

In 150 students, 90 take Maths, 80 Biology, 70 Chemistry; 40 take both M & B, 30 M & C, 25 B & C and 15 all three. How many take at least one subject?

Question 26

An arithmetic sequence has \(a_{1}= -\tfrac12\) and \(d=\tfrac43\). Find \(T_{12}\).

Question 27

Simplify \(\dfrac{m^{2}-4m+4}{2-m}\).

Question 28

In a regular \(n\)-gon each exterior angle is \((2n+4)^{\circ}\). Find \(n\).

Question 29

A 150° sector has area 150 cm². Determine circle area.

Question 30

Find the range of 3.5, 7.2, 4.8, 6.1.

Question 31

For which \(x\) is \(\frac{1}{x^{2}-5x+6}\) undefined?

Question 32

Simplify \(\frac{5}{6} - 7\frac{3}{5} + 4\frac{1}{2}\).

Question 33

Simplify \(\frac{8}{9} - 12\frac{1}{5} + 3\frac{2}{3}\).

Question 34

Simplify \(\frac{\sqrt{12} + \sqrt{75}}{\sqrt{3}}\).

Question 35

A sector of a circle has area 40 cm\(^2\) and angle \(140^{\circ}\). Find the area of the circle.

Question 36

An article is reduced by 20% from GH¢\(25\). What is its new price?

Question 37

A container has 12 red, 18 blue and 30 black balls. What is the probability that a randomly chosen ball is **neither red nor blue**?

Question 38

How many odd integers lie strictly between 20 and 80?

Question 39

A rectangle’s length is \(4\text{ cm}\) longer than its width. If the perimeter is \(28\text{ cm}\), find the width.

Question 40

The sum of the interior angles of a regular polygon is \(1260^{\circ}\). How many sides does it have?

Question 41

Given that \(p = x - \frac{1}{x}\) and \(q = x^{2} + \frac{1}{x^{2}}\), express \(q\) in terms of \(p\).

Question 42

Find the **range** of the following masses (kg): 83, 47, 62, 49, 55, 72, 58, 62.

Question 43

If \(x + \frac{1}{x} = 5\), find the value of \(x^{3} + \frac{1}{x^{3}}\).

Question 44

Evaluate \(\tan15^{\circ}-2\sin75^{\circ}\).

Question 45

Dina and Rose share GH¢\(875.08\) in ratio \(3:2\). Rose gives her share to Efua and Ama in ratio \(1:2\). How much does Ama receive?

Question 46

A sector area 25 cm² subtends \(90^{\circ}\). Find area of the circle.

Question 47

Compute \(\frac{8{,}000{,}000\times0.003}{0.0005}\) in standard form.

Question 48

Find least \(x\) if \(23\equiv5\pmod x\).

Question 49

Find the least value of \(x\) if \(17\equiv3\pmod x\).

Question 50

In a circle of radius \(15\text{ cm}\), the length of an arc is \(18\text{ cm}\). Find the angle, in degrees (nearest whole number), that the arc subtends at the centre. \([\pi=\frac{22}{7}]\)

WASSCE Maths Mock