# Expo: WAEC GCE Mathematics Questions and Answers 2022/2023 – theory / Objective

WAEC GCE Mathematics questions and answers for the year Jan/Feb, scheduled to hold on 5th February, 2022. Welcome to the WAEC Maths questions and answers for the year 2022. WAEC GCE Mathematics Objective Answers, WAEC Mathematics Essay 2022, WAEC GCE 2022 Mathematics, and the strategies you need to pass your WAEC GCE Mathematics exam with ease are all available here.

## Today’s WAEC GCE maths Objective Questions and answers

• 1-10: BDBBBDCDCC
• 41-50: CCBDAABACD

## WAEC GCE Mathematics 2022 theory Questions and Answers

Question 1.

In the diagram, L.PTQ = L.PSR = 900, /PQ/ = 10 ern, /PS/ = 14.4 cm and /TQ/ = 6 cm.

Calculate the area of quadrilateral QRST.

(b) Two opposite sides of a square are each decreased by 10% while the other two are each increased by 15% to form a rectangle. Find the ratio of the area of the rectangle to that of the square.

Math gce Observation.

We advise that student’s should always remember to apply the concept of similar triangles correctly.

Furthermore student should try and recognize the quadrilateral as a trapezium, this will help in finding its area.

Part (b) Candidates were expected to show that:

/PT/ = …./102 – 62 = 8 cm. m: =!J2L i.e ~ = 14.4.Hence, /SR/ = 10.8 cm.

/TO/ /SR/ 6 /SR/

Area of quadrilateral QRST = Yz (6 + 10.8) x 6.4 = 53.76 cm2. Don’t subtract the area of triangle PQT from triangle PRS.

This was also in order. In part (b) if the side of the square was y, then new breadth = 90 x y = 0.9y.

100

New length = 115 x Y = 1.15y. New area = 1.15y x 0.9y = 1.035/.

100

Hence, ratio = 1.035y² : y² = 1.035 : 1 or 207:200 .

In a class of 40 students, 18 passed Mathematics, 19 passed Accounts, 16 passed Economics, 5 passed Mathematics and Accounts only, 6 passed Mathematics only, 9 passed Accounts only, 2 Accounts and Economics only. If each student offered at least one of the subjects,
(a) How many students failed in all the subjects?
(b) Find the percentage number who failed in at least one of Economics and Mathematics.
(c) Calculate the probability that a student selected at random failed in Accounts.

Question 2.

(a) Copy and complete the table of values for the relation V = -X² + X + 2 for -3 ≤ x ≥ 3.

(b) Using scales of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the v-axis, draw a graph of the relation

y = -X² + X + 2.

(c) From the graph, find the:

(i)Minimum value of y;

(ii)Roots of the equation X² – x -2 = 0;

(iii)Gradient of the curve at x = -0.5.

3. (a) P varies directly as Q and inversely as the square of R.  If P = 1 when Q = 8 and R = 2, find the value of Q when P = 3 and R = 5.
(b) An aeroplane flies from town A(20oN, 60oE) to town B(20oN, 20oE).
(i) If the journey takes 6 hours, calculate, correct to 3 significant figures, the average speed of the aeroplane.
(ii) If it then flies due north from town B to town C, 420 km away, calculate, correct to the nearest degree, the latitude of town C.
[Take radius of the earth = 6400 km and  π = 3.142]

4. Using ruler and a pair of compasses only,
(a) construct a rhombus PQRS of side 7 cm and ÐPQR = 60o;
(b) locate point X such that X lies on the locus of points equidistant from PQ and QR and also equidistant from Q and R;
(c) measure /XR/.

5. (a) In a class of 50 students, 30 offered History, 15 offered History and Geography while 3 did not offer any of the two subjects.
(i) Represent the information on a Venn diagram.
(ii) Find the number of candidates that offered: History only; Geography only.
(b) A trader sold an article at a discount of 8% for N 828.00. If the article was initially marked to gain 25%, find the
(i) cost price of the article;
(ii) discount allowed.

6. The area of a rectangular football field is 7200m2 while its perimeter is 360m.  calculate the:
(a) dimensions of the field;
(b) cost of clearing the field at N6.50 per square meter, leaving a margin of 2m wide along the longer sides;
(c) percentage of the part not cleared.

7. Two fair dice are thrown.
M is the event described by “the sum of the scores is 10” and
N is the event described by “the difference between the scores is 3”.
(a) Write out the elements of M and N.
(b) Find the probability of M or N.
(c) Are M and N mutually exclusive? Give reasons.

8. (a) The total surface area of two spheres are in the ratio 9 : 49. If the radius of the smaller sphere is 12 cm, find, correct to the nearest cm3, the volume of the bigger sphere.
(b) A cyclist starts from a point X and rides 3 km due West to a point Y.  At Y, he changes direction and rides 5 km North-West to a point Z.
(i) How far is he from the starting point, correct to the nearest km?
(ii) Find the bearing of Z from X, to the nearest degree.

## 2022 WAEC GCE Mathematics likely questions and answers

These questions below are for practice.

1. Simplify:​​ √108 108 ​​ +√125125​​ ­-​​ √75.75.

(a) √33​​ +​​ 5√555​​ ​​

(b).​​ 6√36√3​​ -​​ 5√555​​

(c)​​ 6√36√3​​ +​​ √22​​

(d).​​ 6√36√3​​ -​​ √22​​

2. Evaluate:​​ (64^1/2+ 125^1/3)64^1/2+ 125^1/3

(a). 121

(b). 144

(c) 169

(d). 196

3. Given that​​ y​​ varies inversely as the square of​​ x.​​ if​​ x=3 when​​ y=100, find the equation connecting ​​ x​​ and​​ y

(a) yx2=300

(b).​​ yx2=900

(c)​​ yx2=100x9100x9​​

(d) y = 900x2 ​​​​

4. Find the value of​​ x for which 32four​​ = 22 base x

(a). three

(b) five

(c) Six

(d) seven

5. Simplify:​​ 2 whole number1/4 x 3 whole number1/2 ÷4 whole number3/8

(a).​​ 5/9

​​ (b)​​ 1 whole number1/5​​

(c)​​ 1 whole number 1/4​​

(d)​​ 1 whole number 4/5

6. There are 250 boys and 150 girls in a school. If 60% of the boys and 40% of the girls play football. What percentage of the school play football?

(a). 40.0%

(b) 42.2%

(c) 50.0%

(d) 52.5%

7. If log10​​ (6 x−4) x-4)​​ – log10​​ 2=1, solve for​​ xx

(a). 2

(b) 3

(c) 4

(d) 5

8. If F =​​ 9C/5+ 32, find C when F = 98.6

(a) 30

(b) 37

(c) 39

(d) 41

9. If​​ y ÷​​ 2 x ​​ = 4 and​​ y−3x=−1, ​​ find the value of (x+y)

(a) 3

(b) 2

(c) 1

(d) -1

10. If​​ x:y:z=2:3:4,​​ Evaluate​​ 9x+3y/6z−2y

(a)1 whole number1/2​​

(b)​​ 2

(c)​​ ​​ 2 whole number1/2​​

(d)​​ 3

11. Simplify:​​ 2−18m^2/1+3m

(a) 2(1+3m)

(b) 2(2+3m2)

(c) 2(1-3m)

(d) 2(1-3m2)

12. A curve is such that when​​  y = 0,​​ x​​ = -2 or​​ x=3. Find the equation for the curve.

(a).​​ y=  x^2-5 x -6

(b).​​ y= x^2+5x−6

(c)​​ y= x2+x−6

(d)​​ y=x^2-  x-6

13. The volume of a cylindrical tank, 10m high is 385m3. Find the diameter of the tank. Take​​ π=22/7

(a). 14 m

(b). 10 m

(c). 7 m

​​ (d). 5 m

14. The surface of a sphere is​​ 7927cm27927cm2. Find correct to the nearest whole number, its volume. Take​​ ​​ [π=22/7]

(a)113 cm^3

​​ (b)​​ 131cm^3

(c)​​ 311cm^3

(d)​​ 414cm^3

15. A piece of thread of length 21.4cm is used to form a sector of a circle of radius 4.2cm on a piece of cloth. Calculate, correct to the nearest degree, the angle of the sector.​​ Take​​ π=22/7

(a) 1700​​

(b) 1770​​

(c) 1820​​

(d) 1920​​

16.

In the diagram which of the following ratios is​​ equal to​​ ∣PN∣ / ∣PQ∣

(a) ∣PN∣/ ∣PR∣​​

(b).​​ ∣PM∣/∣PQ∣

​​ (c)​​∣PM∣/∣PR∣

​​ (d)​​ ∣PR/ ∣PQ∣

​​17.

In the diagram​​ PS​​ and​​ RS​​ are tangents to the circle centre O,​​ <PSR​​ = 700,​​ <POR​​ = m and​​ <PQR​​ = n. Find (m+n).

(a) 1100​​

(b) 1350​​

(c) 1650​​

(d) 2250

​​ 18.

Find the value of t in the diagram

(a) 630​​

(b) 1170​​

(c) 1260​​

(d) 2340​​

​​ 19.

In the diagram,​​ PR​​ is a tangent to the circle at Q, QT//RS,​​ <SQR = 350​​ and​​ <RSQ = 500. Find the value of​​ <QST.

(a) 400​​

(b) 650​​

(c) 85​​

(d) 950​​

20. The angles of a polygon are​​ x, 2 x , 2 x,  (x-300), (x-200) and (x-100). Find the value of​​ x.

(a) 450​​

(b) 840​​

(c) 850​​

(d) 950

21. If​​ M​​ ​​ and​​ N​​ are the points (-3, 8) and (5, -7) respectively, find​​ |MN|.

(a) 8 units

(b) 11 units

(c) 15 units

(d) 17 units​​

22. The equation of the line through the points (4, 2) and (-8, -2) is​​ 3y​​ = p  x​​ +​​ q, where​​ pp​ and​​ q​​ are constants. Find the value of​​ p.

(a) 1

(b) 2

(c) 3

(d) 9

23. The angle of elevation of the top of a tree from a point 27 m​​ away and on the same horizontal ground as the foot of the tree is 300. Find the height of the tree.

(a) 27 m ​​

(b) 13.5√3 m​​

(c)​​ 13.5√2 m

(d)​​ 9√3 m

24. If tan​​ x=4/3, 00​​ < x<900, find the value of sin​​ x​​ – cos x .

(a) 1/10​​

(b)​​ 1/5​​

(c)​​ 5/12​​

(d)​​ 1 whole number 2 /5

25. Given that​​ Y​​ is 20​​ m​​ on a bearing of 3000​​ from​​ X, how far south of​​ Y​​ is​​ X?

(a) 10 m ​​

(b) 15 m

​​ (c) 25 m ​​

(d) 30 m

DISCLAIMER: The WAEC GCE questions and answers above are not the ones meant for this year’s GCE examination instead there are for you to practice.

## How Do I pass GCE WAEC Mathematics Examination 2022

Mathematics takes a different shape when it comes to examination. For that reason, I will give you different tricks to use and ensure that you pass your examination.

### 1. Solve mathematical problems everyday

There is this informal saying that ‘when you leave mathematics, mathematics will also leave you‘. Ensure you solve at least one mathematical problem each day in order to get well acquainted with it.

However, you may not have all it takes to solve mathematics as frequent as that. Ensure you solve at least twice or thrice a week. Each time you want to solve, give it at least 1 hour 30 minutes and you will see yourself doing well.

Syllabus contains all the topics which you need to read in order to pass an examination. It shows you the areas of concentration such that you don’t have to read a whole textbook before you pass.

See Other Syllabus: