Year : 
2007
Title : 
Mathematics (Core)
Exam : 
WASSCE/WAEC MAY/JUNE

Paper 1 | Objectives

1 - 10 of 67 Questions

# Question Ans
1.

Evaluate \((111_{two})^2\) and leave your answer in base 2

A. \(111001_{two}\)

B. \(110001_{two}\)

C. \(101001_{two}\)

D. \(10010_{two}\)

Detailed Solution

\((111_{two})^{2}=(111_{two})(111_{two})\\
=1 \times 2^{2}+1\times2^{1}+1\times 2^{0}=4+2+1=7_{_{ten}}\\
(111_{two})^{2}=7\times 7=49\\
\begin{matrix}
2 & 49\\
2 & 24\hspace{1mm}R\hspace{1mm}1\\
2 & 12\hspace{1mm}R\hspace{1mm}0\\
2 & 6\hspace{1mm}R\hspace{1mm}0\\
2 & 3\hspace{1mm}R\hspace{1mm}0\\
2 & 1\hspace{1mm}R\hspace{1mm}1\\
& 0\hspace{1mm}R\hspace{1mm}1\hspace{1mm}\uparrow
\end{matrix} \\
=110001_{2}\)
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. \(2^{3}\times 3^{3}\times 5^{2}\)

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. \(7.5\times 10^{-1}\)

Detailed Solution

\((0.3\times 10^{5})\div (0.4\times 10^{7})\\
\frac{3}{10}\times 10^{5}\div \frac{4}{10}\times 10^{7}=3\times 10^{4}\div 4\times 10^{6}\\
\frac{3\times 10^{4}}{4\times 10^{7}}=\frac{3}{4}\times 10^{-2}=0.75\times 10^{-2}\\
7.5\times 10^{-3}\)
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. \(q\propto \frac{1}{p}\)

Detailed Solution

\(p\propto \frac{1}{q} = q \propto \frac{1}{p}\)
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. \(11\sqrt{5}\)

Detailed Solution

\(3\sqrt{45}-12\sqrt{5}+16\sqrt{20}\\
3\sqrt{5\times 9}-12\sqrt{5}+16\sqrt{4\times 5}\\
3\times 3\sqrt{5}-12\sqrt{5}+16\times 2\sqrt{5}\\
9\sqrt{5}-12\sqrt{5}+32\sqrt{5}\\
29\sqrt{5}\)
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

A

7.

Simplify\(\frac{3x^{3}}{(3x)^{3}}\)

A. 1

B. \(\frac{1}{3}\)

C. \(\frac{1}{9}\)

D. \(\frac{1}{27}\)

Detailed Solution

\(\frac{3x^{3}}{(3x)^{3}}\\
\frac{3x^{3}}{3x\times 3x\times 3x}=\frac{3\times x\times x\times x}{3\times 3\times 3\times x\times x\times x}=\frac{1}{9}\)
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

Detailed Solution

\(Abu = 2x\\
Kayode = x\\
Uche = \frac{x}{2}\\
2x+x+\frac{x}{2}=140,000\\
\frac{7x}{2}=140,000\\
7x = 280,000\\
x=\frac{280,000}{7}\\
x=40,000\)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

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

Detailed Solution

x + 3 = 0 => x = -3
1.

Evaluate \((111_{two})^2\) and leave your answer in base 2

A. \(111001_{two}\)

B. \(110001_{two}\)

C. \(101001_{two}\)

D. \(10010_{two}\)

Detailed Solution

\((111_{two})^{2}=(111_{two})(111_{two})\\
=1 \times 2^{2}+1\times2^{1}+1\times 2^{0}=4+2+1=7_{_{ten}}\\
(111_{two})^{2}=7\times 7=49\\
\begin{matrix}
2 & 49\\
2 & 24\hspace{1mm}R\hspace{1mm}1\\
2 & 12\hspace{1mm}R\hspace{1mm}0\\
2 & 6\hspace{1mm}R\hspace{1mm}0\\
2 & 3\hspace{1mm}R\hspace{1mm}0\\
2 & 1\hspace{1mm}R\hspace{1mm}1\\
& 0\hspace{1mm}R\hspace{1mm}1\hspace{1mm}\uparrow
\end{matrix} \\
=110001_{2}\)
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. \(2^{3}\times 3^{3}\times 5^{2}\)

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. \(7.5\times 10^{-1}\)

Detailed Solution

\((0.3\times 10^{5})\div (0.4\times 10^{7})\\
\frac{3}{10}\times 10^{5}\div \frac{4}{10}\times 10^{7}=3\times 10^{4}\div 4\times 10^{6}\\
\frac{3\times 10^{4}}{4\times 10^{7}}=\frac{3}{4}\times 10^{-2}=0.75\times 10^{-2}\\
7.5\times 10^{-3}\)
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. \(q\propto \frac{1}{p}\)

Detailed Solution

\(p\propto \frac{1}{q} = q \propto \frac{1}{p}\)
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. \(11\sqrt{5}\)

Detailed Solution

\(3\sqrt{45}-12\sqrt{5}+16\sqrt{20}\\
3\sqrt{5\times 9}-12\sqrt{5}+16\sqrt{4\times 5}\\
3\times 3\sqrt{5}-12\sqrt{5}+16\times 2\sqrt{5}\\
9\sqrt{5}-12\sqrt{5}+32\sqrt{5}\\
29\sqrt{5}\)
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

A

7.

Simplify\(\frac{3x^{3}}{(3x)^{3}}\)

A. 1

B. \(\frac{1}{3}\)

C. \(\frac{1}{9}\)

D. \(\frac{1}{27}\)

Detailed Solution

\(\frac{3x^{3}}{(3x)^{3}}\\
\frac{3x^{3}}{3x\times 3x\times 3x}=\frac{3\times x\times x\times x}{3\times 3\times 3\times x\times x\times x}=\frac{1}{9}\)
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

Detailed Solution

\(Abu = 2x\\
Kayode = x\\
Uche = \frac{x}{2}\\
2x+x+\frac{x}{2}=140,000\\
\frac{7x}{2}=140,000\\
7x = 280,000\\
x=\frac{280,000}{7}\\
x=40,000\)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

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

Detailed Solution

x + 3 = 0 => x = -3