2016 - WAEC Mathematics Past Questions and Answers - page 4
31
The marks of eight students in a test are: 3, 10, 4, 5, 14, 13, 16 and 7. Find the range
A
16
B
14
C
13
D
11
correct option: c
First, arrange the marks in order of magnitude; 3, 4, 5, 7, 10, 13, 14, 16
Hence range = 16 - 3 = 13
Users' Answers & CommentsHence range = 16 - 3 = 13
32
If log2(3x - 1) = 5, find x.
A
2.00
B
3.67
C
8.67
D
11
correct option: d
Log2(3x - 1) = 5
Log2(3x - 1) = Log225
Log2(3x - 1) = Log232
3x - 1 = 32
3x = 32 + 1 = 33
x = \(\frac{33}{3}\)
= 11
Users' Answers & CommentsLog2(3x - 1) = Log225
Log2(3x - 1) = Log232
3x - 1 = 32
3x = 32 + 1 = 33
x = \(\frac{33}{3}\)
= 11
33
A sphere of radius rcm has the same volume as cylinder of radius 3cm and height 4cm. Find the value of r
A
\(\frac{2}{3}\)
B
2
C
3
D
6
correct option: c
Volume of sphere = Volume of cylinder
i.e. \(\frac{4}{3} \pi r^3 = \pi r^2 h\)
\(\frac{4}{3} \pi r^3 = \pi \times 3^2 \times 4\)
r3 = \(\frac{\pi \times 9 \times 4 \times 3}{4 \pi}\)
r = 3\(\sqrt{27}\)
= 3
Users' Answers & Commentsi.e. \(\frac{4}{3} \pi r^3 = \pi r^2 h\)
\(\frac{4}{3} \pi r^3 = \pi \times 3^2 \times 4\)
r3 = \(\frac{\pi \times 9 \times 4 \times 3}{4 \pi}\)
r = 3\(\sqrt{27}\)
= 3
34
Express 1975 correct to 2 significant figures
A
20
B
1,900
C
1,980
D
2,000
correct option: d
Users' Answers & Comments35
The diagram, MOPQ is a trapezium with QP||MO, MQ||NP, NQ||OP, |QP| = 9cm and the height of \(\Delta\) QNP = 6cm, calculate the area of the trapezium.
A
96cm2
B
90cm2
C
81cm2
D
27cm2
correct option: c
Area of \(\Delta\) QNP = \(\frac{1}{2} \times 9 \times 6 \) = 27cm2
Area of \(\Delta\) QMN = Area of \(\Delta\) QNP
= Area of \(\Delta\) PNO (triangles between the same parallels)
Hence, area of the trapezium
3 x area of \(\Delta\) QNP
= 3 x 27
= 81cm2
Users' Answers & CommentsArea of \(\Delta\) QMN = Area of \(\Delta\) QNP
= Area of \(\Delta\) PNO (triangles between the same parallels)
Hence, area of the trapezium
3 x area of \(\Delta\) QNP
= 3 x 27
= 81cm2
36
The perimeter of a sector of a circle of radius 21cm is 64cm. Find the angle of the sector [Take \(\pi = \frac{22}{7}\)]
A
70o
B
60o
C
55o
D
42o
correct option: b
Perimeter of a sector
= 2r + \(\frac{\theta}{360^o}\) x 2 x \(\frac{22}{7}\) x 21
64 = 2 x 21 + \(\frac{\theta}{360^o}\) x 2 x \(\frac{22}{7}\) x 21
64 = 42 + \(\frac{\theta}{360^o}\) x 44 x 3
64 - 42 = \(\frac{\theta}{360^o}\) x 11 x 3
22 = \(\frac{33\theta}{90}\)
\(\theta = \frac{22 \times 30}{11}\)
= 60o
Users' Answers & Comments= 2r + \(\frac{\theta}{360^o}\) x 2 x \(\frac{22}{7}\) x 21
64 = 2 x 21 + \(\frac{\theta}{360^o}\) x 2 x \(\frac{22}{7}\) x 21
64 = 42 + \(\frac{\theta}{360^o}\) x 44 x 3
64 - 42 = \(\frac{\theta}{360^o}\) x 11 x 3
22 = \(\frac{33\theta}{90}\)
\(\theta = \frac{22 \times 30}{11}\)
= 60o
37
Examine M' \(\cap\) N from the venn diagram
A
{f, g}
B
{e}
C
{e, f, g}
D
{e, f, g}
correct option: a
From the venn diagram given,
M = (a, b, c), N = (c, f, g)
U = (a, b, c, d, e, f, g)
Thus M' \(\cap\) N = (e, f, g) \(\cap\) (c, f, g)
= (f, g)
Users' Answers & CommentsM = (a, b, c), N = (c, f, g)
U = (a, b, c, d, e, f, g)
Thus M' \(\cap\) N = (e, f, g) \(\cap\) (c, f, g)
= (f, g)
38
If 20(mod 9) is equivalent to y(mod 6), find y.
A
1
B
2
C
3
D
4
correct option: b
First, reduce 20(mod 9) to its simplest form in mod 9; 9 x 2 + 2 = 2(mod 9)
If 2(mod 9) y(mod 6), then y = 2 by comparism
Users' Answers & CommentsIf 2(mod 9) y(mod 6), then y = 2 by comparism
39
Simplify \(\frac{(p - r)^2 - r^2}{2p^2 - 4pr}\)
A
\(\frac{1}{2}\)
B
p - 2r
C
\(\frac{1}{p - 2r}\)
D
\(\frac{2p}{p - 2r}\)
correct option: a
\(\frac{(p - r)^2 - r^2}{2p^2 - 4pr}\)
= \(\frac{(p - r)(p - r) - r^2}{2p^2 - 4pr}\)\
= \(\frac{p^2 - 2pr + r^2 - r^2}{2p(p - 2r}\)
= \(\frac{p^2 - 2pr}{2p(p - 2r)}\)
= \(\frac{p(p - 2r)}{2p(p - 2r)}\)
= \(\frac{1}{2}\)
Users' Answers & Comments= \(\frac{(p - r)(p - r) - r^2}{2p^2 - 4pr}\)\
= \(\frac{p^2 - 2pr + r^2 - r^2}{2p(p - 2r}\)
= \(\frac{p^2 - 2pr}{2p(p - 2r)}\)
= \(\frac{p(p - 2r)}{2p(p - 2r)}\)
= \(\frac{1}{2}\)
40
In the diagram, O is the centre of the circle, < QPS = 100o, < PSQ = 60o and < QSR. Calculate < SQR
A
20o
B
40o
C
60o
D
80o
correct option: a
In the diagram, < RPQ = 80o(angles in same segment)
< SPR = 100o - < RPQ
= 100 - 80
= 20o
< SQR = < SPR = 20o (same reason as above)
< SQR = 20o
Users' Answers & Comments< SPR = 100o - < RPQ
= 100 - 80
= 20o
< SQR = < SPR = 20o (same reason as above)
< SQR = 20o