Paper 1  Objectives  48 Questions
JAMB Exam
Year: 1998
Level: SHS
Time:
Type: Question Paper
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#  Question  Ans 

1. 
If 1011_{2} + x_{7} = 25_{10}, solve for X. A. 20_{7} B. 14 C. 20 D. 24
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Detailed Solution1011_{2} + x_{7} = 25_{10} = 1011_{2} = 1 x 2^{3} + 0 x 2^{2} + 1 x 2^{1} + 1 x 2^{o}= 8 + 0 + 2 + 1 = 11_{10} x_{7} = 25_{10}  11_{10} = 14_{10} \(\begin{array}{cc} 7 & 14 \\ 7 & 2 R 0 \\ & 0 R 2 \end{array}\) X = 20_{7} 

2. 
Evaluate [\(\frac{1}{0.03}\) \(\div\) \(\frac{1}{0.024}\)]^{1} correct to 2 decimal places A. 3.76 B. 1.25 C. 0.94 D. 0.75
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Detailed Solution[\(\frac{1}{0.03}\) + \(\frac{1}{0.024}\)]= [\(\frac{1}{0.03 \times 0.024}\)]^{1} = [\(\frac{0.024}{0.003}\)]^{1} = \(\frac{0.03}{0.024}\) = \(\frac{30}{24}\) = 1.25 

3. 
If b^{3} = a^{2} and c^{\(\frac{1}{3}\)} = a^{\(\frac{1}{2}\)}b, express c in terms of a A. a^{\(\frac{1}{2}\)} B. a^{\(\frac{1}{3}\)} C. a^{\(\frac{3}{2}\)} D. a^{\(\frac{2}{3}\)}
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Detailed Solutionc^{\(\frac{1}{3}\)} = a^{\(\frac{1}{2}\)}b= a^{\(\frac{1}{2}\)}b x a^{2} = a^{\(\frac{3}{2}\)} = (c^{\(\frac{1}{3}\)})^{3} = (a^{\(\frac{3}{2}\)})^{\(\frac{1}{3}\)} c = a^{\(\frac{1}{2}\)} 

4. 
Given that log_{4}(Y  1) + log_{4}(\(\frac{1}{2}\)x) = 1 and log_{2}(y + 1) + log_{2}x = 2, solve for x and y respectively A. 2, 3 B. 3, 2 C. 2, 3 D. 3, 2
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Detailed Solutionlog_{4}(y  1) + log_{4}(\(\frac{1}{2}\)x) = 1log_{4}(y  1)(\(\frac{1}{2}\)x) \(\to\) (y  1)(\(\frac{1}{2}\)x) = 4 ........(1) log_{2}(y + 1) + log_{2}x = 2 log_{2}(y + 1)x = 2 \(\to\) (y + 1)x = 2_{2} = 4.....(ii) From equation (ii) x = \(\frac{4}{y + 1}\)........(iii) put equation (iii) in (i) = y (y  1)[\(\frac{1}{2}(\frac{4}{y  1}\))] = 4 = 2y  2 = 4y + 4 2y = 6 y = 3 x = \(\frac{ 

5. 
Find the value of k if \(\frac{k}{\sqrt{3} + \sqrt{2}}\) = k\(\sqrt{3  2}\) A. 3 B. 2 C. \(\sqrt{3}\) D. \(\sqrt 2\)
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Detailed Solution\(\frac{k}{\sqrt{3} + \sqrt{2}}\) = k\(\sqrt{3  2}\)\(\frac{k}{\sqrt{3} + \sqrt{2}}\) x \(\frac{\sqrt{3}  \sqrt{2}}{\sqrt{3}  \sqrt{2}}\) = k\(\sqrt{3  2}\) = k(\(\sqrt{3}  \sqrt{2}\)) = k\(\sqrt{3  2}\) = k\(\sqrt{3}\)  k\(\sqrt{2}\) = k\(\sqrt{3  2}\) k2 = \(\sqrt{2}\) k = \(\frac{2}{\sqrt{2}}\) = \(\sqrt{2}\) 

6. 
A market woman sells oil in cylindrical tins 10cm deep and 6cm in diameter at N15.00 each. If she bought a full cylindrical jug 18cm deep and 10cm in diameter for N50.00, how much did she make by selling all the oil? A. N62.50 B. N35.00 C. N31.00 D. N25.00
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Detailed SolutionV\(\pi\)r^{2}h = \(\pi\)(3)^{2}(10) = 90\(\pi\)cm^{3}V = \(\pi\)(5)^{2} x 18 = 450\(\pi\)cm^{3} No of volume = \(\frac{450\pi}{90\pi}\) = 5 selling price = 5 x N15 = N75 profit = N75  N50 = N25.00 

7. 
A man is paid r naira per hour for normal work and double rate for overtime. if he does a 35hour week which includes q hours of overtime, what is his weekly earning in naira? A. r(35 + q) B. q(35r  q) C. q(35 + r) D. r(35 + 2q)
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Detailed SolutionThe cost of normal work = 35rThe cost of overtime = q x 2r = 2qr The man's total weekly earning = 35r + 2qr = r(35 + 2q) 

8. 
When the expression pm^{2} + qm + 1 is divided by (m  1), it has a remainder is 4, Find p and q respectively A. 2, 1 B. 1, 2 C. 3, 2 D. 2, 3
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Detailed Solutionpm^{2} + qm + 1 = (m  1) Q(x) + 2p(1)^{2} + q(1) + 1 = 2 p + q + 1 = 2 p + q = 1.....(i) pm^{2} + qm + 1 = (m  1)Q(x) + 4 p(1)^{2} + q(1) + 1 = 4 p  q + 1 = 4 p  q = 3....(ii) p + q = 1, p  q = 3 2p = 2, p = 1 1 + q = 1 q = 2 

9. 
Factorize r^{2}  r(2p + q) + 2pq A. (r  2q)(2r  p) B. (r  p)(r + p0 C. (r  q)(r  2p) D. (2r  q)(r + p)
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Detailed Solutionr^{2}  r(2p + q) + 2pq = r^{2}  2pr qr + 2pq= r(r  2p)  q(r  2p) = (r  q)(r  2p) 

10. 
Solve for the equation \(\sqrt{x}\)  \(\sqrt{(x  2)}\)  1 = 0 A. \(\frac{3}{2}\) B. \(\frac{2}{3}\) C. \(\frac{4}{9}\) D. \(\frac{9}{4}\)
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Detailed Solution\(\sqrt{x}\)  \(\sqrt{(x  2)}\)  1 = 0= \(\sqrt{x}\)  \(\sqrt{(x  2)}\) = 1 = (\(\sqrt{x}\)  \(\sqrt{(x  2)}\))^{2} = 1 = x  2 \(\sqrt{x(x  2)}\) + x 2 = 1 = (2x  3)^{2} = [2 \(\sqrt{x(x  4)}\)]^{2} = 4x^{2}  12x + 9 = 4(x^{2}  2x) = 4x^{2}  12x + 9 = 4x^{2}  8x 4x = 9 x = \(\frac{9}{4}\) 
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