# 2022–2023 WAEC GCE Mathematics Exam Questions and Solutions (Theory and Objectives)

###### 2022–2023 WAEC GCE Mathematics Exam Questions and Solutions (Theory and Objectives) 2022 WAEC GCE Mathematics exam questions and solutions. Thanks for visiting the 2022 WAEC Mathematics questions and Answers page. The WAEC GCE Mathematics Objective Answers, WAEC Mathematics Essay 2022, WAEC GCE 2022 Mathematics, and the advice you need to ace your WAEC GCE Mathematics test are all available here.2022–2023 WAEC GCE Physics Exam Questions and Solutions (Essay and Objectives)
Questions and Answers for the WAEC GCE Mathematics Essay and Objectives (Expo)
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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 = 900×2 ​​​​
4. What is 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, calculate 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, ​​ what is 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
26. The mean of 1,3,5,7 and​​ x​​ is 4. Find the value of​​ .x.
(a) 2
(b) 4
(c) 6
(d) 8
27. Find the median of 2,1,0,3,1,14,0,1 and 2.
(a) 0.0
(b) 0.5
(c) 1.0
(d)1.5
Number of goals​​  1 2 3 4 5 6 7
Number of teams​​  3 1 6 6 4 2 3
The table shows the distributions of goals scored by​​ 25 teams in a football competition. Use it to answer questions 28 and 29.
28. Calculate the probability that a team​​ selected at random scored at most 3 goals.
(a) 3/25​​
(b)​​ 1/5​​
(c)​​ 6/25​​
(d)​​ 2/5
29. Find the probability that a team selected at random scored either 4 or 7 goals.
(a) 9/25 ​​
(b)​​ 11/25 ​​
(c)​​ 3/5 ​​
(d)​​ 18/25
In the diagram, WXYZ, is a rectangle with dimension 8cm by 6cm,​​ P,​​ Q,​​ R​​ and S are the midpoints of the sides of the rectangle as shown. Use this information to answer questions​​ 30​​ and​​ 31.
(a)Trapezium
(b)​​ Prism
(c) Rectangle
(d) Rhombus
31. Find the area of the part of the rectangle that is​​ not shaded.​​
(a) 25​​ cm^2​​
(b) 24 cm^2 ​​
(c) 16 cm^2 ​​
(d)​​ 12 cm^2
32. The​​ total surface area of a hemisphere is 75πcm^2. Find its radius
(a) 5.0 cm ​​
(b) 7.0​​ cm​​
(c) 8.5​​ cm​​
(d)​​ 12.0 cm
33. Calculate the values of​​ x​​ for which​​ x−5/x(x−1)​​ is​​
(a) 0 or 5
(b) -5 or 5
(c) -1 or 5
(d) 0 or 1
34. Solve the equation 2×2​​ – x-6=0.
(a) x=−3/2​​ or 2
(b)​​ x=−2 or 3/2​​
(c)​​ x=−3 or 2
(d)​​ x=3 or−2
35. Factorize completely the expression (x+2)2​​ – (2 x+1)2
(a) (3  x+2)(1- xx)​​
(b) (3  x+2)(1-  x)​​
(c) (3 x+2)2​​
(d) 3( x+1)(1- x)
36. Find the nth​​ term of the sequence 2 x 3, 4 x 6
(a) 2n​​ x 3(n + 1)
(b) 2n​​ x 3n
(c) 2n​​ x 3n ​​​​
(d) 2n​​ x 3n-1
37. If 3x​​ = 4 (mod 5), find the least value of​​ xx
(a)1
(b) 2
(c) 3
(d) 4
38. The solution of​​ x​​ + 2​​ ≥​​ 2 x ​​ + 1 is illustrated on the number line as
39. If​​ p​​ and​​ q​​ are two statements, under what condition would​​ p​​ –​​ q​​ be​​ false?
(a) If​​ p​​ is true and​​ q​​ is true
(b) If​​ p​​ is true and​​ q​​ is false
(c) If​​ p​​ is false and​​ q​​ is false
(d) If​​ p​​ is false and​​ q​​ is true​​
40.The diagram shows a trapezium inscribed in a​​ semi-circle. If O is mid-point of WZ and​​ |WX| =​​ |XY|​​ =​​ |YZ|, calculate the value of​​ m.m.
(a) 900​​ (b) 600​​ (c) 450​​ (d) 300​​
41. Find the interquartile range of 1,3,4,5,8,9,10,11,12,14,16
(a) 6
(b) 7
(c) 8
(d) 9​​
42. Donations during the launching of a church project were sent in sealed envelopes. The table shows​​ the distribution of the amount of money in the envelopes.
No. of envelopes 4 7 20 9 4 5 3 1 2
Number of teams​​  5000 2000 1000 700 500 100 50 2 10
How much was the total donation?
(a) N26,792.00
(b)​​ N26,972.00
(c)​​ N62,792.00
(d)​​ N62,972.00
43.In the diagram, PQ is a straight line, (m+n)=1100, (n+r) = 1300​​ and (m+r)= 1200, find the ratio of m:n:r.
(a) 2:3:4
(b) 3:4:5
(c) 4:5:6
(d) 5:6:7
44. If​​ x: y = 14 : 38 and​​ y: z = 13​​ : 49, find​​ x: z
(a) 2:3
(b) 3:4
(c) 3:8
(d) 1:2
45. Calculate the mean deviation of 20, 30, 25, 40, 35, 50, 45, 40, 20 and 45.
(a) 8
(b) 9
(c) 10
(d) 10
46. M and N are two subsets of the universal set (U). if n(U)=48, n(M)=20, n(N)=30 and n(MUN)=40, find n(MՈN)’.
(a) 18
(b) 20
(c) 30
(d)38
47. Express 0.612 in the form​​ x/y, where​​ x​​ and​​ y​​ are integers and​​ y≠0.
(a)153/250
​​ (b)​​ 68/111​​
(c)​​ 61/100​​
(d)​​ 21/33
​​ ​​ ​​ ​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​In the diagram, PQ//RS. Find​​ xx​​ in terms of​​ y​​ and​​ z.
(a)x=2400​​ +  y- z ​​
(b)​​ x=1800​​ + y- z ​​
(c)​​ x=3600​​ +  y- z​​
(d)​​ x=3600– y- z
49. The diagonals of a rhombus WXYZ intersect at M. if​​ |MW|= 5 cm​​ |MX|= 5cm, calculate its perimeter.
(a) 42 cm
(b)​​ 48cm​​
(c) 52​​ cm​​
(d)​​ 60​​ cm
50. The graphs of​​ y=  x2​​ and​​ y=  x​​ intersect at which of these points?
(a) (0,0), (1,1)
(b) 0,0), (0,1)
(c) (1,0)(0,0)
(d)​​ (0,0)(0,0)​​
Essay 2022 for WAEC GCE Mathematics
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