2007 - WAEC Mathematics Past Questions & 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
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