# 2001 - WAEC Mathematics Past Questions and Answers - page 1

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

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

**correct option:**c

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

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

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

= \(202_{3}\)

**correct option:**a

log_{10}[5\times 20]\

log_{10}100\

log_{10}10^2\

2log_{10}10=2\)

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?

**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.

**correct option:**c

∴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}\)

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**correct option:**d

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?

**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.

**correct option:**d

=\frac{200-190}{200}\times \frac{100}{1}\

=\frac{10}{200}\times \frac{100}{1}\% = 5\%\)

**correct option:**c

\frac{27}{5}\times \frac{4}{9} \times \frac{3}{2}=3\frac{3}{5}

\)

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

**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\(^9\)