2001 - WAEC Mathematics Past Questions & Answers - page 1

1

Which of the following correctly expresses 48 as a product of prime factors?

A
3 x 4 x 4
B
2 x 3 x 8
C
2 x 2 x 2 x 3 x 4
D
2 x 2 x 2 x 2 x 3
CORRECT OPTION: d

48 = 2 x 2 x 2 x 2 x 3

2

Evaluate \((20_{three})^2 - (11_{three})^2\) in base three

A
101
B
121
C
202
D
2020
CORRECT OPTION: c

\((20_{three})^2 - (11_{three})^2\)

= \((20_{3} - 11_{3})(20_{3} + 11_{3})\)

= \((2_{3})(101_{3})\)

= \(202_{3}\) 

3
Evaluate \(log_{10}5 + log_{10}20\)
A
2
B
3
C
4
D
5
CORRECT OPTION: a
\(log_{10}5 + log_{10}20\
log_{10}[5\times 20]\
log_{10}100\
log_{10}10^2\
2log_{10}10=2\)
4

In a class of 80 students, every students studies Economics or Geography or both. If 65 students study Economics and 50 study Geography, how many study both subjects?

A
15
B
30
C
35
D
45
CORRECT OPTION: c

Let c = no of students that offered both subjects

\(\therefore\) No of students offering Economics = 65 - c

No of students offering Geography = 50 - c

65 - c + c + 50 - c = 80

115 - c = 80

c = 35

35 students offer both Economics and Geography.

5
If N varies directly as M and N = 8 when M = 20 find M when N = 7
A
13
B
15
C
\(17\frac{1}{2}\)
D
\(18\frac{1}{2}\)
CORRECT OPTION: c
N ∝ M
∴N = kM where k is a constant
N = 8 when M = 20
∴ 8 = k x 20
\(k = \frac{8}{20} = \frac{2}{5}\
∴ N = \frac{2}{5}M\
If N = 7\
∴ 7 = \frac{2}{5}M\
M = \frac{35}{2} = 17\frac{1}{2}\)
6
Express 0.0462 in standard form
A
0.460 x 10-1
B
0.462 x 10-2
C
4.62 x 10-1
D
4.62 x 10-2
CORRECT OPTION: d
7

In a bag of oranges, the ratio of the good ones to the bad ones is 5:4. If the number of bad oranges in the bag is 36, how many oranges are there in the altogether?

A
81
B
72
C
54
D
45
CORRECT OPTION: a

Ratio of good ones to bad ones is 5:4; If 36 is bad;

∴ the good ones = \(\frac{5\times 36}{4}=45\) oranges. 

The total number of oranges is 36 + 45 = 81.

8
A boy estimated his transport fare for a journey as N190 instead of N200. Find the percentage error in his estimate
A
95%
B
47.5%
C
5.26%
D
5%
CORRECT OPTION: d
The percentage error is \(\frac{error}{actual}\times \frac{100}{1}\%\
=\frac{200-190}{200}\times \frac{100}{1}\
=\frac{10}{200}\times \frac{100}{1}\% = 5\%\)
9
Evaluate \(5\frac{2}{5}\times \left(\frac{2}{3}\right)^2\div\left(1\frac{1}{2}\right)^{-1}\)
A
\(\frac{8}{25}\)
B
\(\frac{12}{25}\)
C
\(3\frac{3}{5}\)
D
\(4\frac{1}{8}\)
CORRECT OPTION: c
\(5\frac{2}{5}\times \left(\frac{2}{3}\right)^2 \left(1\frac{1}{2}\right)^{-1}\
\frac{27}{5}\times \frac{4}{9} \times \frac{3}{2}=3\frac{3}{5}
\)
10

The nth term of a sequence is \(2^{2n-1}\). Which term of the sequence is \(2^9?\)

A
3rd
B
4th
C
5th
D
6th
CORRECT OPTION: c

\(T_{n} = 2^{2n - 1}\)

\(2^{2n - 1} = 2^9\)

\(2n - 1 = 9 \implies 2n = 9 + 1\)

\(2n = 10 \implies n = 5\)

The 5th term = 2\(^9\)

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