Year :
2019
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
1 - 10 of 80 Questions
| # | Question | Ans |
|---|---|---|
| 1. |
Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\) A. \(q = \frac{b^2(mn - a^2)}{a^2 p}\) B. \(q = \frac{m^2 n - a^2}{p^2}\) C. \(q = \frac{mn - 2b^2}{a^2}\) D. \(q = \frac{b^2 (n^2 - ma^2)}{n}\) Detailed Solution\(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)\(\frac{mn}{a^2} - 1 = \frac{pq}{b^2}\) \(\frac{mn - a^2}{a^2} = \frac{pq}{b^2}\) \(pq = \frac{b^2 (mn - a^2)}{a^2}\) \(q = \frac{b^2(mn - a^2)}{a^2 p}\) There is an explanation video available below. |
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| 2. |
The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number. A. 148m B. 382m C. 282m D. 248m Detailed Solution \(\tan 78 = \frac{h}{60}\) \(h = 60 \tan 78\) \(h = 60 \times 4.705 = 282.27m\) \(\approxeq\) 282m to the nearest whole number. There is an explanation video available below. |
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| 3. |
A binary operation \(\otimes\) is defined by \(m \otimes n = mn + m - n\) on the set of real numbers, for all m, n \(\in\) R. Find the value of 3 \(\otimes\) (2 \(\otimes\) 4). A. 6 B. 25 C. 15 D. 18 Detailed Solution\(m \otimes n = mn + m - n\)3 \(\otimes\) (2 \(\otimes\) 4) 2 \(\otimes\) 4 = 2(4) + 2 - 4 = 6 3 \(otimes\) 6 = 3(6) + 3 - 6 = 15 There is an explanation video available below. |
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| 4. |
 Table:The table above shows the number of pupils in a class with respect to their ages. If a pie chart is constructed to represent the age, the angle corresponding to 8 years old is A. 48.6° B. 56.3° C. 46.8° D. 13° Detailed SolutionTotal number of pupils : 4 + 13 + 30 + 44 + 9 = 100The number of 8 - year olds = 13 The angle represented by the 8-year olds on the pie chart = \(\frac{13}{100} \times 360°\) = 46.8° There is an explanation video available below. |
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| 5. |
In a class of 50 students, 40 students offered Physics and 30 offered Biology. How many offered both Physics and Biology? A. 42 B. 20 C. 70 D. 54 Detailed Solutionn(Total) = 50n(Physics) = 40 n(Biology) = 30 Let n(Physics and Biology) = x n(Physics only) = 40 -x n(Biology only) = 30 - x 40 - x + 30 - x + x = 50 70 - x = 50 x = 20 There is an explanation video available below. |
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| 6. |
Rationalize \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\) A. \(-5 - 2\sqrt{6}\) B. \(-5 + 3\sqrt{2}\) C. \(5 - 2\sqrt{3}\) D. \(5 + 2\sqrt{6}\) Detailed Solution\(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)= \((\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}})(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}})\) = \(\frac{2 + \sqrt{6} + \sqrt{6} + 3}{2 - \sqrt{6} + \sqrt{6} - 3}\) = \(\frac{5 + 2\sqrt{6}}{-1}\) = \(- 5 - 2\sqrt{6}\) There is an explanation video available below. |
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| 7. |
OPEN_PHOTO Find the length of the chord |AB| in the diagram shown above. A. 4.2 cm B. 4.3 cm C. 3.2 cm D. 3.4 cm Detailed SolutionLength of chord = \(2r \sin (\frac{\theta}{2})\)= \(2(3) \sin (\frac{68}{2})\) = \(6 \sin 34\) = \(6 \times 0.559\) = 3.354 cm \(\approxeq\) 3.4 cm There is an explanation video available below. |
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| 8. |
Given \(\sin 58° = \cos p°\), find p. A. 48° B. 58° C. 32° D. 52° Detailed Solution\(\sin \theta = \cos (90 - \theta)\)\(\sin \theta = \cos (90 - 58)\) = \(\cos 32\) There is an explanation video available below. |
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| 9. |
\(\frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}}\) A. \(\frac{31}{50}\) B. \(\frac{20}{31}\) C. \(\frac{31}{20}\) D. \(\frac{50}{31}\) Detailed Solution\(\frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}}\)\(\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4}\) = \(\frac{5}{6}\) \(\frac{1}{4} + \frac{3}{5} - \frac{1}{3} = \frac{15 + 36 - 20}{60}\) = \(\frac{31}{60}\) \(\therefore \frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}} = \frac{5}{6} \div \frac{31}{60}\) = \(\frac{5}{6} \times \frac{60}{31}\) = \(\frac{50}{31}\) There is an explanation video available below. |
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| 10. |
If \(6x^3 + 2x^2 - 5x + 1\) divides \(x^2 - x - 1\), find the remainder. A. 9x + 9 B. 2x + 6 C. 6x + 8 D. 5x - 3 |
| 1. |
Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\) A. \(q = \frac{b^2(mn - a^2)}{a^2 p}\) B. \(q = \frac{m^2 n - a^2}{p^2}\) C. \(q = \frac{mn - 2b^2}{a^2}\) D. \(q = \frac{b^2 (n^2 - ma^2)}{n}\) Detailed Solution\(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)\(\frac{mn}{a^2} - 1 = \frac{pq}{b^2}\) \(\frac{mn - a^2}{a^2} = \frac{pq}{b^2}\) \(pq = \frac{b^2 (mn - a^2)}{a^2}\) \(q = \frac{b^2(mn - a^2)}{a^2 p}\) There is an explanation video available below. |
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| 2. |
The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number. A. 148m B. 382m C. 282m D. 248m Detailed Solution\(\tan 78 = \frac{h}{60}\) \(h = 60 \tan 78\) \(h = 60 \times 4.705 = 282.27m\) \(\approxeq\) 282m to the nearest whole number. There is an explanation video available below. |
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| 3. |
A binary operation \(\otimes\) is defined by \(m \otimes n = mn + m - n\) on the set of real numbers, for all m, n \(\in\) R. Find the value of 3 \(\otimes\) (2 \(\otimes\) 4). A. 6 B. 25 C. 15 D. 18 Detailed Solution\(m \otimes n = mn + m - n\)3 \(\otimes\) (2 \(\otimes\) 4) 2 \(\otimes\) 4 = 2(4) + 2 - 4 = 6 3 \(otimes\) 6 = 3(6) + 3 - 6 = 15 There is an explanation video available below. |
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| 4. |
Table:The table above shows the number of pupils in a class with respect to their ages. If a pie chart is constructed to represent the age, the angle corresponding to 8 years old is A. 48.6° B. 56.3° C. 46.8° D. 13° Detailed SolutionTotal number of pupils : 4 + 13 + 30 + 44 + 9 = 100The number of 8 - year olds = 13 The angle represented by the 8-year olds on the pie chart = \(\frac{13}{100} \times 360°\) = 46.8° There is an explanation video available below. |
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| 5. |
In a class of 50 students, 40 students offered Physics and 30 offered Biology. How many offered both Physics and Biology? A. 42 B. 20 C. 70 D. 54 Detailed Solutionn(Total) = 50n(Physics) = 40 n(Biology) = 30 Let n(Physics and Biology) = x n(Physics only) = 40 -x n(Biology only) = 30 - x 40 - x + 30 - x + x = 50 70 - x = 50 x = 20 There is an explanation video available below. |
| 6. |
Rationalize \(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\) A. \(-5 - 2\sqrt{6}\) B. \(-5 + 3\sqrt{2}\) C. \(5 - 2\sqrt{3}\) D. \(5 + 2\sqrt{6}\) Detailed Solution\(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}}\)= \((\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} - \sqrt{3}})(\frac{\sqrt{2} + \sqrt{3}}{\sqrt{2} + \sqrt{3}})\) = \(\frac{2 + \sqrt{6} + \sqrt{6} + 3}{2 - \sqrt{6} + \sqrt{6} - 3}\) = \(\frac{5 + 2\sqrt{6}}{-1}\) = \(- 5 - 2\sqrt{6}\) There is an explanation video available below. |
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| 7. |
OPEN_PHOTO Find the length of the chord |AB| in the diagram shown above. A. 4.2 cm B. 4.3 cm C. 3.2 cm D. 3.4 cm Detailed SolutionLength of chord = \(2r \sin (\frac{\theta}{2})\)= \(2(3) \sin (\frac{68}{2})\) = \(6 \sin 34\) = \(6 \times 0.559\) = 3.354 cm \(\approxeq\) 3.4 cm There is an explanation video available below. |
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| 8. |
Given \(\sin 58° = \cos p°\), find p. A. 48° B. 58° C. 32° D. 52° Detailed Solution\(\sin \theta = \cos (90 - \theta)\)\(\sin \theta = \cos (90 - 58)\) = \(\cos 32\) There is an explanation video available below. |
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| 9. |
\(\frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}}\) A. \(\frac{31}{50}\) B. \(\frac{20}{31}\) C. \(\frac{31}{20}\) D. \(\frac{50}{31}\) Detailed Solution\(\frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}}\)\(\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4}\) = \(\frac{5}{6}\) \(\frac{1}{4} + \frac{3}{5} - \frac{1}{3} = \frac{15 + 36 - 20}{60}\) = \(\frac{31}{60}\) \(\therefore \frac{\frac{2}{3} \div \frac{4}{5}}{\frac{1}{4} + \frac{3}{5} - \frac{1}{3}} = \frac{5}{6} \div \frac{31}{60}\) = \(\frac{5}{6} \times \frac{60}{31}\) = \(\frac{50}{31}\) There is an explanation video available below. |
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| 10. |
If \(6x^3 + 2x^2 - 5x + 1\) divides \(x^2 - x - 1\), find the remainder. A. 9x + 9 B. 2x + 6 C. 6x + 8 D. 5x - 3 |