Year :
2007
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
21 - 30 of 47 Questions
| # | Question | Ans |
|---|---|---|
| 21. |
A binary operation Δ is defined by aΔb = a + b + 1 for any numbers a and b. Find the inverse of the real number 7 under the operation Δ, if the identity element is -1 A. -7 B. -9 C. 5 D. 9 Detailed Solutiona*e = a + e + 1 = aimplies e+ 1 = 0 ∴ e = -1 7 * e = -1 ∴ a + 7 + 1 = -1 a + 8 = -1 a+8 = -1 a = -1-8 a = -9 |
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| 22. |
The nth term of the sequence 3/2, 3, 7, 16, 35, 74 ..... is A. 2n-2 - n B. 2n-2 - (n+1) / 2 C. 2n-2 D. 3/2 n Detailed Solution3/2, 3, 7, 16, 35, 74, ....Using the method of substitution When n = 1, 5 . 2n-2 - 1 = 5 . 21-2 - 1 = 5 x 2-1 - 1 = 5 x 1/2 - 1 = 5/2 - 1 = 3/2 When n = 1, 5 . 2n-2 - n = 5 . 22-2 - 2 = 5 x 20 - 2 = 5 x 1 – 2 = 3 When n = 3, 5 . 2n-2 - n = 5 . 23-2 - 3 = |
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| 23. |
Find the sum to infinity of the series \(2+\frac{3}{2}+\frac{9}{8}+\frac{27}{32}+......\) A. 1 B. 2 C. 8 D. 4 Detailed Solution\(a=2\\r = \frac{3}{4}\\ S = \frac{a}{1-r}\\ S= \frac{2}{1-\frac{3}{4}}\\ = \frac{2}{\frac{1}{4}}\\ S = \frac{2}{1}\times \frac{4}{1}\\ = 8\) |
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| 24. |
Find y, if \(\sqrt{12}-\sqrt{147}+y\sqrt{3} = 0\) A. 5 B. 1 C. 7 D. 3 Detailed Solution\(\sqrt{12}-\sqrt{147}+y\sqrt{3} = 0\\\sqrt{4\times 3}-\sqrt{49\times 3}+y\sqrt{3} = 0\\ 2\sqrt{3}-7\sqrt{3}+y\sqrt{3} = 0\\ y\sqrt{3} = 7\sqrt{3} - 2\sqrt{3}\\ y=\frac{5\sqrt{3}}{\sqrt{3}}\\ y = 5\) |
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| 25. |
If x10 = 12145 find x A. 124 B. 121 C. 184 D. 180 Detailed Solutionx10 = 12145= x10 = 1 x 53 + 2 x 52 + 1 * 51 + 4 x 50 = 1 x 125 + 2 x 25 + 1 x 5 + 4 x 1 = 125 + 50 + 5 + 4 = 184 |
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| 26. |
Evaluate \(\frac{(05652 - 04375)^2}{0.04}\) correct to three significant figures A. 3.11 B. 3.13 C. 0.313 D. 3.12 Detailed Solution\(\frac{(0.5652 - 0.4375)^2}{0.04}\\\frac{(0.5625+0.4375)(0.5625-0.4375)}{0.04}\\ \frac{1.000\times 0.125}{0.04}\\ =3.125\\ =3.13\) |
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| 27. |
Find the value of x for which 2(32x-1) = 162 A. 5/2 B. 3/2 C. 2/5 D. 1/2 Detailed Solution2(32x-1) = 16232x-1 = 162/2 32x-1 = 81 32x-1 = 32 2x - 1 = 4 (equating the indices) 2x = 5 5/2 x = |
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| 28. |
Simplify \(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\) A. \(\frac{4}{5}\) B. \(\frac{7}{10}\) C. \(\frac{6}{6}\) D. \(\frac{21}{6}\) Detailed Solution\(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\\=\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \times \frac{9}{4}\right)\\ =\frac{3}{5} \div \frac{6}{7}\\ =\frac{3}{5} \times \frac{7}{6}\\ =\frac{7}{10}\) |
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| 29. |
If log102 = x, express log1012.5 in terms of x A. 2(1 + x) B. 2 + 3x C. 2(1 - x) D. 2 - 3x Detailed Solutionlog1012.5 = log10 121/2= log1025/2 = log1025 - log102 = log1052 - log102 = 2log105 - log102 = 2log1010/2 - log102 = 2(1-x)- x = 2 - 2x – x = 2 – 3x |
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| 30. |
A man made a profit of 5% when he sold an article for N60,000.00. How much would he have sell the article to make a profit of 26% A. N68,000 B. N72,000 C. N65,000 D. N70,000 Detailed Solution5% profit = 100 + 5 = 105%26% profit = 100 + 26 = 126% ∴ 105% → N60,000 1% → 60000/15 126% = 1000/105 x 126/1 =N72,000 |
| 21. |
A binary operation Δ is defined by aΔb = a + b + 1 for any numbers a and b. Find the inverse of the real number 7 under the operation Δ, if the identity element is -1 A. -7 B. -9 C. 5 D. 9 Detailed Solutiona*e = a + e + 1 = aimplies e+ 1 = 0 ∴ e = -1 7 * e = -1 ∴ a + 7 + 1 = -1 a + 8 = -1 a+8 = -1 a = -1-8 a = -9 |
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| 22. |
The nth term of the sequence 3/2, 3, 7, 16, 35, 74 ..... is A. 2n-2 - n B. 2n-2 - (n+1) / 2 C. 2n-2 D. 3/2 n Detailed Solution3/2, 3, 7, 16, 35, 74, ....Using the method of substitution When n = 1, 5 . 2n-2 - 1 = 5 . 21-2 - 1 = 5 x 2-1 - 1 = 5 x 1/2 - 1 = 5/2 - 1 = 3/2 When n = 1, 5 . 2n-2 - n = 5 . 22-2 - 2 = 5 x 20 - 2 = 5 x 1 – 2 = 3 When n = 3, 5 . 2n-2 - n = 5 . 23-2 - 3 = |
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| 23. |
Find the sum to infinity of the series \(2+\frac{3}{2}+\frac{9}{8}+\frac{27}{32}+......\) A. 1 B. 2 C. 8 D. 4 Detailed Solution\(a=2\\r = \frac{3}{4}\\ S = \frac{a}{1-r}\\ S= \frac{2}{1-\frac{3}{4}}\\ = \frac{2}{\frac{1}{4}}\\ S = \frac{2}{1}\times \frac{4}{1}\\ = 8\) |
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| 24. |
Find y, if \(\sqrt{12}-\sqrt{147}+y\sqrt{3} = 0\) A. 5 B. 1 C. 7 D. 3 Detailed Solution\(\sqrt{12}-\sqrt{147}+y\sqrt{3} = 0\\\sqrt{4\times 3}-\sqrt{49\times 3}+y\sqrt{3} = 0\\ 2\sqrt{3}-7\sqrt{3}+y\sqrt{3} = 0\\ y\sqrt{3} = 7\sqrt{3} - 2\sqrt{3}\\ y=\frac{5\sqrt{3}}{\sqrt{3}}\\ y = 5\) |
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| 25. |
If x10 = 12145 find x A. 124 B. 121 C. 184 D. 180 Detailed Solutionx10 = 12145= x10 = 1 x 53 + 2 x 52 + 1 * 51 + 4 x 50 = 1 x 125 + 2 x 25 + 1 x 5 + 4 x 1 = 125 + 50 + 5 + 4 = 184 |
| 26. |
Evaluate \(\frac{(05652 - 04375)^2}{0.04}\) correct to three significant figures A. 3.11 B. 3.13 C. 0.313 D. 3.12 Detailed Solution\(\frac{(0.5652 - 0.4375)^2}{0.04}\\\frac{(0.5625+0.4375)(0.5625-0.4375)}{0.04}\\ \frac{1.000\times 0.125}{0.04}\\ =3.125\\ =3.13\) |
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| 27. |
Find the value of x for which 2(32x-1) = 162 A. 5/2 B. 3/2 C. 2/5 D. 1/2 Detailed Solution2(32x-1) = 16232x-1 = 162/2 32x-1 = 81 32x-1 = 32 2x - 1 = 4 (equating the indices) 2x = 5 5/2 x = |
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| 28. |
Simplify \(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\) A. \(\frac{4}{5}\) B. \(\frac{7}{10}\) C. \(\frac{6}{6}\) D. \(\frac{21}{6}\) Detailed Solution\(\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right)\\=\frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \times \frac{9}{4}\right)\\ =\frac{3}{5} \div \frac{6}{7}\\ =\frac{3}{5} \times \frac{7}{6}\\ =\frac{7}{10}\) |
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| 29. |
If log102 = x, express log1012.5 in terms of x A. 2(1 + x) B. 2 + 3x C. 2(1 - x) D. 2 - 3x Detailed Solutionlog1012.5 = log10 121/2= log1025/2 = log1025 - log102 = log1052 - log102 = 2log105 - log102 = 2log1010/2 - log102 = 2(1-x)- x = 2 - 2x – x = 2 – 3x |
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| 30. |
A man made a profit of 5% when he sold an article for N60,000.00. How much would he have sell the article to make a profit of 26% A. N68,000 B. N72,000 C. N65,000 D. N70,000 Detailed Solution5% profit = 100 + 5 = 105%26% profit = 100 + 26 = 126% ∴ 105% → N60,000 1% → 60000/15 126% = 1000/105 x 126/1 =N72,000 |