# 2007 - WAEC Mathematics Past Questions and Answers - page 1

1
Evaluate $$(111_{two})^2$$ and leave your answer in base 2
A
$$111001_{two}$$
B
$$110001_{two}$$
C
$$101001_{two}$$
D
$$10010_{two}$$
correct option: b
$$(111_{two})^{2}=(111_{two})(111_{two})\ =1 \times 2^{2}+1\times2^{1}+1\times 2^{0}=4+2+1=7_{_{ten}}\ (111_{two})^{2}=7\times 7=49\ \begin{matrix} 2 & 49\ 2 & 24\hspace{1mm}R\hspace{1mm}1\ 2 & 12\hspace{1mm}R\hspace{1mm}0\ 2 & 6\hspace{1mm}R\hspace{1mm}0\ 2 & 3\hspace{1mm}R\hspace{1mm}0\ 2 & 1\hspace{1mm}R\hspace{1mm}1\ & 0\hspace{1mm}R\hspace{1mm}1\hspace{1mm}\uparrow \end{matrix} \ =110001_{2}$$
2
Find the LCM of $$2^{3}\times 3\times 5^{2}, 2\times 3^{2}\times 5 \hspace{1mm}and \hspace{1mm}2^{2}\times 3^{2}\times 5$$
A
$$2^{2}\times 3^{3}\times 5^{2}$$
B
$$2^{3}\times 3^{23}\times 5$$
C
$$2^{2}\times 3^{2}\times 5^{2}$$
D
$$2^{3}\times 3^{3}\times 5^{2}$$
correct option: d
3
Simplify $$(0.3\times 10^{5})\div (0.4\times 10^{7})$$leaving your answer in standard form
A
$$7.5\times 10^{-4}$$
B
$$7.5\times 10^{-3}$$
C
$$7.5\times 10^{-2}$$
D
$$7.5\times 10^{-1}$$
correct option: b
$$(0.3\times 10^{5})\div (0.4\times 10^{7})\ \frac{3}{10}\times 10^{5}\div \frac{4}{10}\times 10^{7}=3\times 10^{4}\div 4\times 10^{6}\ \frac{3\times 10^{4}}{4\times 10^{7}}=\frac{3}{4}\times 10^{-2}=0.75\times 10^{-2}\ 7.5\times 10^{-3}$$
4
If $$p\propto \frac{1}{q}$$, which of the following is true?
A
$$\propto p^{2}$$
B
$$p\propto \frac{1}{q^{2}}$$
C
$$q\propto \sqrt{p}$$
D
$$q\propto \frac{1}{p}$$
correct option: d
$$p\propto \frac{1}{q} = q \propto \frac{1}{p}$$
5
Simplify $$3\sqrt{45}-12\sqrt{5}+16\sqrt{20}$$leaving your answer in surd form
A
$$29\sqrt{5}$$
B
$$14\sqrt{15}$$
C
$$12\sqrt{15}$$
D
$$11\sqrt{5}$$
correct option: a
$$3\sqrt{45}-12\sqrt{5}+16\sqrt{20}\ 3\sqrt{5\times 9}-12\sqrt{5}+16\sqrt{4\times 5}\ 3\times 3\sqrt{5}-12\sqrt{5}+16\times 2\sqrt{5}\ 9\sqrt{5}-12\sqrt{5}+32\sqrt{5}\ 29\sqrt{5}$$
6
Which of the following is true for the set $$P = \{-3.2\leq x< 5\}$$ where x is an integer
A
least value of x is -3.2
B
least value of x is -3
C
greatest value of x is 4.9
D
greatest value of x is 5
correct option: a
7
Simplify$$\frac{3x^{3}}{(3x)^{3}}$$
A
1
B
$$\frac{1}{3}$$
C
$$\frac{1}{9}$$
D
$$\frac{1}{27}$$
correct option: c
$$\frac{3x^{3}}{(3x)^{3}}\ \frac{3x^{3}}{3x\times 3x\times 3x}=\frac{3\times x\times x\times x}{3\times 3\times 3\times x\times x\times x}=\frac{1}{9}$$
8
N140,000 is shared between ABU, Kayode and Uche. Abu has twice as much as Kayode, and Kayode has twice as much as Uche. What is Kayode's share?
A
N80,000
B
N40,000
C
N20,000
D
N10,000
correct option: b
$$Abu = 2x\ Kayode = x\ Uche = \frac{x}{2}\ 2x+x+\frac{x}{2}=140,000\ \frac{7x}{2}=140,000\ 7x = 280,000\ x=\frac{280,000}{7}\ x=40,000$$Kayode receives N40,000
9
I am x years old and my brother is 3 years older how old was my brother last year
A
(x - 4) years
B
(x + 2) years
C
(3x - 1) years
D
(3x + 1) years
correct option: c
10
For what value of x is the expression $$\frac{2x-1}{x+3}$$not defined?
A
3
B
2
C
1/2
D
-3
correct option: d
x + 3 = 0 => x = -3