Year :
1978
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
1 - 10 of 48 Questions
| # | Question | Ans |
|---|---|---|
| 1. |
A rectangular picture 6cm by 8cm is enclosed by a frame \(\frac{1}{2}\)cm wide. Calculate the area of the frame A. 15sq.cm B. 20sq.cm C. 13sq.cm D. 16sq.cm E. 17sq.cm Detailed SolutionArea of the rectangular picture = L x B = 8 x 6= 48 sq.cm. Area of the whole surface (which is gotten by adding \(\frac{1}{2}\) on every side to the original picture size) is 9 x 7 = 63 sq. cm area of the frame is 63 - 48 = 15 sq. cm |
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| 2. |
The sum of \(3\frac{7}{8}\) and \(1\frac{1}{3}\) is less than the difference between \(\frac{1}{8}\) and \(1\frac{2}{3}\) by: A. 3\(\frac{2}{3}\) B. 5\(\frac{1}{4}\) C. 6\(\frac{1}{2}\) D. 8 E. 8\(\frac{1}{8}\) Detailed Solution\(3\frac{7}{8} + 1\frac{1}{3} = 4\frac{21 + 8}{24}\)= \(4\frac{29}{24}\) \(\equiv 5\frac{5}{24}\) \(1\frac{2}{3} - \frac{1}{8} = \frac{5}{3} - \frac{1}{8}\) = \(\frac{40 - 3}{24}\) = \(\frac{37}{24}\) \(5\frac{5}{24} - \frac{37}{24} = \frac{125}{24} - \frac{37}{24}\) = \(\frac{88}{24}\) = 3\(\frac{2}{3}\) |
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| 3. |
Multiply (x + 3y + 5) by (2x2 + 5y + 2) A. 2x2 + 3yx2 + 10xy + 15y2 + 13y + 10x2 + 2x + 10 B. 2x3 + 6yx2 + 5xy + 15y2 + 31y + 5x2 + 2x + 10 C. 2x3 + 6xy2 + 5xy + 15y2 + 12y + 10x2 + 2x = 10 D. 2x2 + 6xy2 + 5xy + 15y2 + 13y + 10x2 + 2x + 10 E. 2x3 + 2yx2 + 10xy + 10y2 + 31y + 5x2 + 10 Detailed Solution\((x + 3y + 5)(2x^{2} + 5y + 2)\)= \(2x^{3} + 5xy + 2x + 6yx^{2} + 15y^{2} + 6y + 10x^{2} + 25y + 10\) = \(2x^{3} + 5xy + 2x + 6yx^{2} + 15y^{2} + 31y + 10x^{2} + 10\) |
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| 4. |
Arrange \(\frac{3}{5}\),\(\frac{9}{16}\), \(\frac{34}{59}\) and \(\frac{71}{97}\) in ascending order of magnitude. A. \(\frac{3}{5}\), \(\frac{9}{16}\), \(\frac{34}{59}\), \(\frac{71}{97}\) B. \(\frac{9}{16}\), \(\frac{34}{59}\), \(\frac{3}{5}\) , \(\frac{71}{97}\) C. \(\frac{3}{5}\), \(\frac{9}{16}\), \(\frac{71}{97}\), \(\frac{34}{59}\) D. \(\frac{9}{16}\), \(\frac{3}{5}\), \(\frac{71}{97}\), \(\frac{34}{59}\) Detailed Solution\(\frac{3}{5}\) = 0.60, \(\frac{9}{16}\) = 0.56, \(\frac{34}{59}\) = 0.58, \(\frac{71}{97}\) = 0.73Hence, \(\frac{9}{16} < \frac{34}{59} < \frac{3}{5} < \frac{71}{97}\) |
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| 5. |
The sum of the progression is 1 + x + x2 + x3 + ...... A. \(\frac{1}{1 - x}\) B. \(\frac{1}{1 + x}\) C. \(\frac{1}{x - 1}\) D. \(\frac{1}{x}\) Detailed SolutionSum of n terms of Geometric progression is \(S_{n} = \frac{a(1 - r^n)}{1 - r}\)In the given series, a (the first term) = 1 and r (the common ratio) = x. \(S_{n} = \frac{1(1 - x^{n})}{1 - x}\) a = 1, and as n tends to infinity \(S_{n} = \frac{1}{1 - x}\) |
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| 6. |
The number of telephone calls N between two cities A and B varies directly as the population P\(_{A}\), P\(_B\) respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation? A. N = \(\frac{kp_A}{D^2} + {cp_B}{D^2}\) B. N = \(\frac{k P_{A} P_{B} }{D^2}\) C. N = \(\frac{kD_AP_D}{B^2}\) D. N = \(\frac{kD^2_AP_D}{B}\) Detailed Solution\(N \propto P_{A}\); \(N \propto P_{B}\); \(N \propto \frac{1}{D^{2}}\)\(\therefore N \propto \frac{P_{A} P_{B}}{D^{2}}\) \(N = \frac{k P_{A} P_{B}}{D^{2}}\) |
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| 7. |
Find the square root of 170 - 20\(\sqrt{30}\) A. 2 \(\sqrt{10}\) - 5\(\sqrt{3}\) B. 2 \(\sqrt{5}\) - 5\(\sqrt{6}\) C. 5 \(\sqrt{10}\) - 2\(\sqrt{3}\) D. 3 \(\sqrt{5}\) - 8\(\sqrt{6}\) Detailed Solution\(\sqrt{170 - 20 \sqrt{30}} = \sqrt{a} - \sqrt{b}\)Squaring both sides, \(170 - 20\sqrt{30} = a + b - 2\sqrt{ab}\) Equating the rational and irrational parts, we have \(a + b = 170 ... (1)\) \(2 \sqrt{ab} = 20 \sqrt{30}\) \(2 \sqrt{ab} = 2 \sqrt{30 \times 100} = 2 \sqrt{3000} \) \(ab = 3000 ... (2)\) From (2), \(b = \frac{3000}{a}\) \(a + \frac{3000}{a} = 170 \implies a^{2} + 3000 = 170a\) \(a^{2} - 170a + 3000 = 0\) \(a^{2} - 20a - 150a + 3000 = 0\) \(a(a - 20) - 150(a - 20) = 0\) \(\text{a = 20 or a = 150}\) \(\therefore b = \frac{3000}{20} = 150 ; b = \frac{3000}{150} = 20\) \(\sqrt{170 - 20\sqrt{30}} = |
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| 8. |
If x\(^2\) + 4 = 0, then x ? A. 4 B. -4 C. 2 D. -2 E. None of the above Detailed Solutionx\(^2\) + 4 = 0x\(^2\) = -4 You can't apply a square root to a negative number. So the answer is None of the above. |
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| 9. |
What is the number whose logarithm to base 10 is 2.3482? A. 223 B. 2228 C. 2.235 D. 22.37 E. 0.2229 Detailed Solution\(\begin{array}{c|c} Nos. & log \\ \hline 222.9 & 2.3482\end{array}\)N : b Look for the antilog of .3482 which gives 222.9 |
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| 10. |
Five years ago, a father was 3 times as old as his son, now their combined ages amount to 110years. thus, the present age of the father is A. 75 years B. 60 years C. 98 years D. 80 years E. 105 years Detailed SolutionLet the present ages of father be x and son = yfive years ago, father = x - 5 son = y - 5 x - 5 = 3(y - 5) x - 5 = 3y - 15 x - 3y = -15 + 5 = -10 ......(i) x + y = 110......(ii) eqn(ii) - eqn(i) 4y = 120 y = 30 sub for y = 30 in eqn(i) x -10 = 3(30) x -10 = 90 x = 80 |
| 1. |
A rectangular picture 6cm by 8cm is enclosed by a frame \(\frac{1}{2}\)cm wide. Calculate the area of the frame A. 15sq.cm B. 20sq.cm C. 13sq.cm D. 16sq.cm E. 17sq.cm Detailed SolutionArea of the rectangular picture = L x B = 8 x 6= 48 sq.cm. Area of the whole surface (which is gotten by adding \(\frac{1}{2}\) on every side to the original picture size) is 9 x 7 = 63 sq. cm area of the frame is 63 - 48 = 15 sq. cm |
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| 2. |
The sum of \(3\frac{7}{8}\) and \(1\frac{1}{3}\) is less than the difference between \(\frac{1}{8}\) and \(1\frac{2}{3}\) by: A. 3\(\frac{2}{3}\) B. 5\(\frac{1}{4}\) C. 6\(\frac{1}{2}\) D. 8 E. 8\(\frac{1}{8}\) Detailed Solution\(3\frac{7}{8} + 1\frac{1}{3} = 4\frac{21 + 8}{24}\)= \(4\frac{29}{24}\) \(\equiv 5\frac{5}{24}\) \(1\frac{2}{3} - \frac{1}{8} = \frac{5}{3} - \frac{1}{8}\) = \(\frac{40 - 3}{24}\) = \(\frac{37}{24}\) \(5\frac{5}{24} - \frac{37}{24} = \frac{125}{24} - \frac{37}{24}\) = \(\frac{88}{24}\) = 3\(\frac{2}{3}\) |
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| 3. |
Multiply (x + 3y + 5) by (2x2 + 5y + 2) A. 2x2 + 3yx2 + 10xy + 15y2 + 13y + 10x2 + 2x + 10 B. 2x3 + 6yx2 + 5xy + 15y2 + 31y + 5x2 + 2x + 10 C. 2x3 + 6xy2 + 5xy + 15y2 + 12y + 10x2 + 2x = 10 D. 2x2 + 6xy2 + 5xy + 15y2 + 13y + 10x2 + 2x + 10 E. 2x3 + 2yx2 + 10xy + 10y2 + 31y + 5x2 + 10 Detailed Solution\((x + 3y + 5)(2x^{2} + 5y + 2)\)= \(2x^{3} + 5xy + 2x + 6yx^{2} + 15y^{2} + 6y + 10x^{2} + 25y + 10\) = \(2x^{3} + 5xy + 2x + 6yx^{2} + 15y^{2} + 31y + 10x^{2} + 10\) |
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| 4. |
Arrange \(\frac{3}{5}\),\(\frac{9}{16}\), \(\frac{34}{59}\) and \(\frac{71}{97}\) in ascending order of magnitude. A. \(\frac{3}{5}\), \(\frac{9}{16}\), \(\frac{34}{59}\), \(\frac{71}{97}\) B. \(\frac{9}{16}\), \(\frac{34}{59}\), \(\frac{3}{5}\) , \(\frac{71}{97}\) C. \(\frac{3}{5}\), \(\frac{9}{16}\), \(\frac{71}{97}\), \(\frac{34}{59}\) D. \(\frac{9}{16}\), \(\frac{3}{5}\), \(\frac{71}{97}\), \(\frac{34}{59}\) Detailed Solution\(\frac{3}{5}\) = 0.60, \(\frac{9}{16}\) = 0.56, \(\frac{34}{59}\) = 0.58, \(\frac{71}{97}\) = 0.73Hence, \(\frac{9}{16} < \frac{34}{59} < \frac{3}{5} < \frac{71}{97}\) |
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| 5. |
The sum of the progression is 1 + x + x2 + x3 + ...... A. \(\frac{1}{1 - x}\) B. \(\frac{1}{1 + x}\) C. \(\frac{1}{x - 1}\) D. \(\frac{1}{x}\) Detailed SolutionSum of n terms of Geometric progression is \(S_{n} = \frac{a(1 - r^n)}{1 - r}\)In the given series, a (the first term) = 1 and r (the common ratio) = x. \(S_{n} = \frac{1(1 - x^{n})}{1 - x}\) a = 1, and as n tends to infinity \(S_{n} = \frac{1}{1 - x}\) |
| 6. |
The number of telephone calls N between two cities A and B varies directly as the population P\(_{A}\), P\(_B\) respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation? A. N = \(\frac{kp_A}{D^2} + {cp_B}{D^2}\) B. N = \(\frac{k P_{A} P_{B} }{D^2}\) C. N = \(\frac{kD_AP_D}{B^2}\) D. N = \(\frac{kD^2_AP_D}{B}\) Detailed Solution\(N \propto P_{A}\); \(N \propto P_{B}\); \(N \propto \frac{1}{D^{2}}\)\(\therefore N \propto \frac{P_{A} P_{B}}{D^{2}}\) \(N = \frac{k P_{A} P_{B}}{D^{2}}\) |
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| 7. |
Find the square root of 170 - 20\(\sqrt{30}\) A. 2 \(\sqrt{10}\) - 5\(\sqrt{3}\) B. 2 \(\sqrt{5}\) - 5\(\sqrt{6}\) C. 5 \(\sqrt{10}\) - 2\(\sqrt{3}\) D. 3 \(\sqrt{5}\) - 8\(\sqrt{6}\) Detailed Solution\(\sqrt{170 - 20 \sqrt{30}} = \sqrt{a} - \sqrt{b}\)Squaring both sides, \(170 - 20\sqrt{30} = a + b - 2\sqrt{ab}\) Equating the rational and irrational parts, we have \(a + b = 170 ... (1)\) \(2 \sqrt{ab} = 20 \sqrt{30}\) \(2 \sqrt{ab} = 2 \sqrt{30 \times 100} = 2 \sqrt{3000} \) \(ab = 3000 ... (2)\) From (2), \(b = \frac{3000}{a}\) \(a + \frac{3000}{a} = 170 \implies a^{2} + 3000 = 170a\) \(a^{2} - 170a + 3000 = 0\) \(a^{2} - 20a - 150a + 3000 = 0\) \(a(a - 20) - 150(a - 20) = 0\) \(\text{a = 20 or a = 150}\) \(\therefore b = \frac{3000}{20} = 150 ; b = \frac{3000}{150} = 20\) \(\sqrt{170 - 20\sqrt{30}} = |
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| 8. |
If x\(^2\) + 4 = 0, then x ? A. 4 B. -4 C. 2 D. -2 E. None of the above Detailed Solutionx\(^2\) + 4 = 0x\(^2\) = -4 You can't apply a square root to a negative number. So the answer is None of the above. |
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| 9. |
What is the number whose logarithm to base 10 is 2.3482? A. 223 B. 2228 C. 2.235 D. 22.37 E. 0.2229 Detailed Solution\(\begin{array}{c|c} Nos. & log \\ \hline 222.9 & 2.3482\end{array}\)N : b Look for the antilog of .3482 which gives 222.9 |
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| 10. |
Five years ago, a father was 3 times as old as his son, now their combined ages amount to 110years. thus, the present age of the father is A. 75 years B. 60 years C. 98 years D. 80 years E. 105 years Detailed SolutionLet the present ages of father be x and son = yfive years ago, father = x - 5 son = y - 5 x - 5 = 3(y - 5) x - 5 = 3y - 15 x - 3y = -15 + 5 = -10 ......(i) x + y = 110......(ii) eqn(ii) - eqn(i) 4y = 120 y = 30 sub for y = 30 in eqn(i) x -10 = 3(30) x -10 = 90 x = 80 |