Year :
1994
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
1 - 10 of 48 Questions
| # | Question | Ans |
|---|---|---|
| 1. |
Solve for x if \(25^{x} + 3(5^{x}) = 4\) A. 1 or -4 B. 0 C. 1 D. -4 or 0 Detailed Solution\(25^{x} + 3(5^{x}) = 4\)Let \(5^{x}\) = y. \((5^{2})^{x} + 3(5^{x}) - 4 = 0\) \(y^{2} + 3y - 4 = 0\) \(y^{2} - y + 4y - 4 = 0\) \(y(y - 1) + 4(y - 1) = 0\) \((y + 4)(y - 1) = 0\) \(y = -4 ; y = 1\) y = -4 is not possible. y = 1 \(\implies\) x = 0. |
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| 2. |
The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number A. 29 B. 26 C. 25 D. 24 Detailed SolutionLet the sum of the 12 numbers be x and the 13th number be y.\(\frac{x}{12} = 3 \implies x = 36\) \(\frac{36 + y}{13} = 5 \implies 36 + y = 65\) \(y = 65 - 36 = 29\) |
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| 3. |
Evaluate \(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\) A. \(\frac{28}{39}\) B. \(\frac{13}{39}\) C. \(\frac{39}{28}\) D. \(\frac{84}{13}\) Detailed Solution\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\)\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} - \frac{10}{10} + \frac{3}{4})]\) = \(\frac{1}{3} \div [\frac{5}{7}(\frac{-1}{10} + \frac{3}{4})]\) = \(\frac{1}{3} \div [\frac{5}{7}(\frac{-2 + 15}{20})]\) = \(\frac{1}{3} \div [\frac{5}{7} \times \frac{13}{20}]\) \(\frac{1}{3} + [\frac{13}{28}]\) = \(\frac{1}{3} \times \frac{28}{13}\) = \(\frac{28}{39}\) |
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| 4. |
Evaluate \(\frac{0.36 \times 5.4 \times 0.63}{4.2 \times 9.0 \times 2.4}\) A. 0.013 B. 0.014 C. 0.14 D. 0.13 Detailed Solution\(\frac{0.36 \times 5.4 \times 0.63}{4.2 \times 9.0 \times 2.4}\)= \(\frac{36}{420} \times \frac{54}{90} \times \frac{63}{240}\) = \(\frac{6}{70} \times \frac{18}{30} \times \frac{21}{80}\) = \(\frac{27}{2000}\) = 0.0135 \(\approx\) = 0.014 |
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| 5. |
Evaluate \(\frac{log_5 (0.04)}{log_3 18 - log_3 2}\) A. 1 B. -1 C. \(\frac{2}{3}\) D. -\(\frac{2}{3}\) Detailed Solution\(\frac{log_5 0.04}{log_3 18 - log_3 2}\)= \(\frac{log_5 0.04}{log_3(\frac{18}{2})}\) = \(\frac{log_5 0.04}{log_3 9}\) = \(\frac{-2}{2}\) = -1 Let log5 0.04 = x 5x = 0.04 x = \(\frac{4}{100}\) = 5-2 Let log3 9 = z 32 = 32 z = 3 |
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| 6. |
Without using table, solve the equation 8x-2 = \(\frac{2}{25}\) A. 4 B. 6 C. 8 D. 10 Detailed Solution8x-2 = \(\frac{2}{25}\)= 200x-2 = 2 = 100x-2 = 1 x-2 = \(\frac{1}{100}\) x-2 = 10-2 x = 10 |
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| 7. |
Simplify \(\sqrt{48}\) - \(\frac{9}{\sqrt{3}}\) + \(\sqrt{75}\) A. 5√3 B. 6√3 C. 8√3 D. 18√3 Detailed Solution\(\sqrt{48}\) - \(\frac{9}{\sqrt{3}}\) + \(\sqrt{75}\)Rearrange = \(\sqrt{48}\) + \(\sqrt{75}\) - \(\frac{9}{\sqrt{3}}\) = (√16 x √3) + (√25 x √3) - \(\frac{9}{\sqrt{3}}\) =4√3 + 5√3 - \(\frac{9}{\sqrt{3}}\) Rationalize \(\to\) 9√3 = \(\frac{9}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\) = \(\frac{9\sqrt{3}}{\sqrt{9}}\) - \(\frac{9\sqrt{3}}{\sqrt{3}}\) = 3√3 |
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| 8. |
Given that \(\sqrt{2} = 1.414\), find without using tables, the value of \(\frac{1}{\sqrt{2}}\) A. 0.141 B. 0.301 C. 0.667 D. 0.707 Detailed Solution\(\frac{1}{\sqrt{2}}\) = \(\frac{1}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)= \(\frac{\sqrt{2}}{2}\) = \(\frac{1.414}{2}\) = 0.707 |
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| 9. |
Given that for sets A and B, in a universal set E, A \(\subseteq\) B then A \(\cap\)(A \(\cap\) B)' is A. A B. \(\phi\) C. B D. E Detailed SolutionA \(\subset\) B means A is contained in B i.e. A is a subset of B(A \(\cap\) B)' = A'A(A \(\cap\) B)' = A \(\cap\) A' The intersection of complement of a set P and P' has no element i.e. n(A \(\cap\) A') = \(\phi\) |
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| 10. |
Simplify \(\frac{(2m - u)^2 - (m - 2u)^2}{5m^2 - 5u^2}\) A. \(\frac{3}{5}\) B. \(\frac{2}{5}\) C. \(\frac{2m - u}{5m + u}\) D. \(\frac{m - 2u}{m + 5u}\) Detailed Solution\(\frac{(2m - u)^2 - (m - 2u)^2}{5m^2 - 5u^2}\)= \(\frac{2m - u + m - 2u)(2m - u - m + 2u)}{5(m + u)(m - u)}\) = \(\frac{3(m - u)(m + u)}{5(m + u)(m - u)}\) = \(\frac{3}{5}\) |
| 1. |
Solve for x if \(25^{x} + 3(5^{x}) = 4\) A. 1 or -4 B. 0 C. 1 D. -4 or 0 Detailed Solution\(25^{x} + 3(5^{x}) = 4\)Let \(5^{x}\) = y. \((5^{2})^{x} + 3(5^{x}) - 4 = 0\) \(y^{2} + 3y - 4 = 0\) \(y^{2} - y + 4y - 4 = 0\) \(y(y - 1) + 4(y - 1) = 0\) \((y + 4)(y - 1) = 0\) \(y = -4 ; y = 1\) y = -4 is not possible. y = 1 \(\implies\) x = 0. |
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| 2. |
The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number A. 29 B. 26 C. 25 D. 24 Detailed SolutionLet the sum of the 12 numbers be x and the 13th number be y.\(\frac{x}{12} = 3 \implies x = 36\) \(\frac{36 + y}{13} = 5 \implies 36 + y = 65\) \(y = 65 - 36 = 29\) |
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| 3. |
Evaluate \(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\) A. \(\frac{28}{39}\) B. \(\frac{13}{39}\) C. \(\frac{39}{28}\) D. \(\frac{84}{13}\) Detailed Solution\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} -1 + \frac{3}{4})]\)\(\frac{1}{3} \div [\frac{5}{7}(\frac{9}{10} - \frac{10}{10} + \frac{3}{4})]\) = \(\frac{1}{3} \div [\frac{5}{7}(\frac{-1}{10} + \frac{3}{4})]\) = \(\frac{1}{3} \div [\frac{5}{7}(\frac{-2 + 15}{20})]\) = \(\frac{1}{3} \div [\frac{5}{7} \times \frac{13}{20}]\) \(\frac{1}{3} + [\frac{13}{28}]\) = \(\frac{1}{3} \times \frac{28}{13}\) = \(\frac{28}{39}\) |
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| 4. |
Evaluate \(\frac{0.36 \times 5.4 \times 0.63}{4.2 \times 9.0 \times 2.4}\) A. 0.013 B. 0.014 C. 0.14 D. 0.13 Detailed Solution\(\frac{0.36 \times 5.4 \times 0.63}{4.2 \times 9.0 \times 2.4}\)= \(\frac{36}{420} \times \frac{54}{90} \times \frac{63}{240}\) = \(\frac{6}{70} \times \frac{18}{30} \times \frac{21}{80}\) = \(\frac{27}{2000}\) = 0.0135 \(\approx\) = 0.014 |
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| 5. |
Evaluate \(\frac{log_5 (0.04)}{log_3 18 - log_3 2}\) A. 1 B. -1 C. \(\frac{2}{3}\) D. -\(\frac{2}{3}\) Detailed Solution\(\frac{log_5 0.04}{log_3 18 - log_3 2}\)= \(\frac{log_5 0.04}{log_3(\frac{18}{2})}\) = \(\frac{log_5 0.04}{log_3 9}\) = \(\frac{-2}{2}\) = -1 Let log5 0.04 = x 5x = 0.04 x = \(\frac{4}{100}\) = 5-2 Let log3 9 = z 32 = 32 z = 3 |
| 6. |
Without using table, solve the equation 8x-2 = \(\frac{2}{25}\) A. 4 B. 6 C. 8 D. 10 Detailed Solution8x-2 = \(\frac{2}{25}\)= 200x-2 = 2 = 100x-2 = 1 x-2 = \(\frac{1}{100}\) x-2 = 10-2 x = 10 |
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| 7. |
Simplify \(\sqrt{48}\) - \(\frac{9}{\sqrt{3}}\) + \(\sqrt{75}\) A. 5√3 B. 6√3 C. 8√3 D. 18√3 Detailed Solution\(\sqrt{48}\) - \(\frac{9}{\sqrt{3}}\) + \(\sqrt{75}\)Rearrange = \(\sqrt{48}\) + \(\sqrt{75}\) - \(\frac{9}{\sqrt{3}}\) = (√16 x √3) + (√25 x √3) - \(\frac{9}{\sqrt{3}}\) =4√3 + 5√3 - \(\frac{9}{\sqrt{3}}\) Rationalize \(\to\) 9√3 = \(\frac{9}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\) = \(\frac{9\sqrt{3}}{\sqrt{9}}\) - \(\frac{9\sqrt{3}}{\sqrt{3}}\) = 3√3 |
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| 8. |
Given that \(\sqrt{2} = 1.414\), find without using tables, the value of \(\frac{1}{\sqrt{2}}\) A. 0.141 B. 0.301 C. 0.667 D. 0.707 Detailed Solution\(\frac{1}{\sqrt{2}}\) = \(\frac{1}{\sqrt{2}}\) x \(\frac{\sqrt{2}}{\sqrt{2}}\)= \(\frac{\sqrt{2}}{2}\) = \(\frac{1.414}{2}\) = 0.707 |
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| 9. |
Given that for sets A and B, in a universal set E, A \(\subseteq\) B then A \(\cap\)(A \(\cap\) B)' is A. A B. \(\phi\) C. B D. E Detailed SolutionA \(\subset\) B means A is contained in B i.e. A is a subset of B(A \(\cap\) B)' = A'A(A \(\cap\) B)' = A \(\cap\) A' The intersection of complement of a set P and P' has no element i.e. n(A \(\cap\) A') = \(\phi\) |
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| 10. |
Simplify \(\frac{(2m - u)^2 - (m - 2u)^2}{5m^2 - 5u^2}\) A. \(\frac{3}{5}\) B. \(\frac{2}{5}\) C. \(\frac{2m - u}{5m + u}\) D. \(\frac{m - 2u}{m + 5u}\) Detailed Solution\(\frac{(2m - u)^2 - (m - 2u)^2}{5m^2 - 5u^2}\)= \(\frac{2m - u + m - 2u)(2m - u - m + 2u)}{5(m + u)(m - u)}\) = \(\frac{3(m - u)(m + u)}{5(m + u)(m - u)}\) = \(\frac{3}{5}\) |