WAEC GCE Mathematics Questions and Answers
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
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.
30. What type of quadrilateral is the shaded region?
(a)Trapezium
(b) Prism
(c) Rectangle
(d) Rhombus
31. Calculate 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. Find 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 2x2 – 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. Find 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)
WAEC GCE Mathematics Essay 2020
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