Mathematics 2005 Jamb Examination
Question 1
Find the value of m if $13_m + 24_m = 41_m$
If 13m + 24m = 41m
1 * m1 + 3 0 + 2 * m1 + 4 * m0 = 4 * m1 + 1 * m0
1 * m + 3 * 1 + 2 * m + 4 * 1 = 4 * m + 1 * 1
m + 3 + 2m + 4 = 4m + 1
3m + 7 = 4m + 1
4m -3m = 7 - 1
m = 6
Not clear enough?
Question 2
If 3214 is divided by 234 and leaves a remainder r, what is the value of r?
Convert to decimal:
$$ \begin{align*} 321_4 &= 3 \cdot 4^2 + 2 \cdot 4 + 1 = 48 + 8 + 1 = 57 \\ 23_4 &= 2 \cdot 4 + 3 = 11 \\ 57 \div 11 &= 5 \text{ remainder } 2 \\ r &= 2 \end{align*} $$
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Question 3
Simplify
\[3\dfrac{1}{2} - \left(2\dfrac{1}{3} \times 1\dfrac{1}{4} \right) + \dfrac{3}{5} \]
First convert to improper fractions:
\[3\dfrac{1}{2} = \dfrac{7}{2}, \quad 2\dfrac{1}{3} = \dfrac{7}{3}, \quad 1\dfrac{1}{4} = \dfrac{5}{4}\]
Multiply: \[\dfrac{7}{3} \times \dfrac{5}{4} = \dfrac{35}{12}\]
Subtract and add: \[\dfrac{7}{2} - \dfrac{35}{12} + \dfrac{3}{5} = \dfrac{42}{12}-\dfrac{35}{12}+\dfrac{36}{60}\]\[ = \dfrac{7}{12}+\dfrac{36}{60} = 1\dfrac{11}{60}\]
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Question 4
If the interest on N150.00 for \(2\dfrac{1}{2}\) years is N4.50, find the interest on N250.00 for 6 months at the same rate
Simple interest: \[SI = P \cdot r \cdot t\]
\[4.50 = 150 \cdot r \cdot 2.5 \implies r = \dfrac{4.5}{150 \cdot 2.5} = 0.012 = 1.2\%\]
Then for N250 for 0.5 years: \[SI = 250 \cdot 0.012 \cdot 0.5 = 1.5\]
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Question 5
Three boys shared some oranges. The first received 1/3 of the oranges and the second received 2/3 of the remaining. If the third boy received the remaining 12 oranges, how many oranges did they share
Let x = the number of oranges
The 1st received 1/3 of x = 1/3x
∴Remainder = x - 1/3x = 2x/3
The 2nd received 2/3 of 2x/3 = 2/3 * 2x/3 = 4x/3
The 3rd received 12 oranges
∴1/3x + 4x/9 + 12 = x
(3x + 4x + 108)/9 = x
3x + 4x + 108 = 9x
7x + 108 = 9x
9x - 7x = 108
2x = 108
x = 54 oranges
Not clear enough?
Question 6
Compute step by step:
\[81^{3/4} = (3^4)^{3/4} = 3^3 = 27\]
\[27^{1/3} = 3\]
Numerator: \(27 - 3 = 24\)
Denominator: \(3 \times 2^3 = 24\)
Therefore: \[\dfrac{24}{24} = 1\]
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Question 7
Use logarithm properties:
\[\log 4.5 = \log \dfrac{9}{2} = \log 9 - \log 2 = \log 3^2 - \log 2 = 2 \log 3 - \log 2\]
\[2 \cdot 0.4771 - 0.3010 = 0.9542 - 0.3010 = 0.6532\]
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Question 8
Simplify $$\dfrac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}}$$
Rationalize the denominator:
$$\dfrac{\sqrt{12} - \sqrt{3}}{\sqrt{12} + \sqrt{3}} \cdot \dfrac{\sqrt{12} - \sqrt{3}}{\sqrt{12} - \sqrt{3}}$$ $$= \dfrac{(\sqrt{12} - \sqrt{3})^2}{12 - 3}$$ $$= \dfrac{12 - 2\sqrt{36} + 3}{9} $$ $$= \dfrac{3}{9} $$ $$= \dfrac{1}{3}$$Not clear enough?
Question 9
The Venn diagram above shows a class of 40 students with the games they play. How many of the students play two games only?
From the diagram, the numbers in the intersections (students playing exactly two games) sum to 15.
Two games played only = 5 + 7 + 3 = 15
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Question 10
Compute step by step:
\[m(p+q+r) = 3(-3 + 7 + \dfrac{5}{2}) \]\[= 3(4 + \dfrac{5}{2}) \]\[= 3 \cdot \dfrac{13}{2} \]\[= \dfrac{39}{2} = 19.5\]
Not clear enough?
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This question is based on Literary Appreciation
'My brother you flash your teeth in response to every hypocrisy.
My brother with gold-rimmed glasses You give your master a blue-eyed faithful look.
My poor brother in immaculate evening dress Screaming and whispering and pleading in the parlours of condescension'.
Diop: The Renegade
The poet's attitude here is
Choose the word or phrase which is most nearly opposite in meaning to the word in capitals.
VACUITY :
For this question, choose the most appropriate stress pattern from the options. The stressed syllable is written in capital letters.
obligation