Year :
2000
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
1 - 10 of 45 Questions
| # | Question | Ans |
|---|---|---|
| 1. |
Let P = {1, 2, u, v, w, x}; Q = {2, 3, u, v, w, 5, 6, y} and R = {2, 3, 4, v, x, y}. A. {1, x} B. {x y} C. {x} D. ɸ Detailed SolutionP = {1,2,u,v,w,x}Q = {2,3,u,v,w,5,6,y} R = {2,3,4,v,x,y} P - Q = {1,x} (P - Q) ∩ R = {1,x} ∩ {2,3,4,v,x,y} = {x} NB: The set P−Q consists of elements that are in P but not in Q. |
|
| 2. |
If the population of a town was 240,000 in January 1998 and it increased by 2% each year, what would be the population of the town in January, 2000? A. 480,000 B. 249,696 C. 249,600 D. 244,800 Detailed Solution1st year, Population = 240,000 x (2/100) = 4800.Being the 2nd year population = 240,000 + 4800 = 244800. Increase in Pop. in 2nd year = 244800 x (2/100) = 4896 Jan 2000, Pop. = 244800 + 4896 = 249,696 |
|
| 3. |
If \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = m +n\sqrt{6}\), find the values of m and n respectively. A. 1, -2 B. -2, 1 C. \(\frac{-2}{5}\), 1 D. 2, 3/5 Detailed SolutionRationalize \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})}\) and equate to \(m +n\sqrt{6}\). Such that m = -2, and n = 1.Use \(\sqrt{3}-2\sqrt{2}\) as the conjugate for Rationalization \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})}\) X \(\frac{(\sqrt{3}-2\sqrt{2})}{(\sqrt{3}-2\sqrt{2})}\) \(\frac{6 - 4\sqrt{6} - \sqrt{6} + 4}{3 - 2\sqrt{6} + 2\sqrt{6} - 8}\) =\(\frac{10 - 5\sqrt{6}}{-5}\) = -2 + \(\sqrt{6}\) |
|
| 4. |
In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music? A. 8 B. 24 C. 62 D. 86 Detailed Solutionx = no. of ppl that like none.no. of ppl that like both Traditional and Modern music, which is equal to 3x Modern Music = 60 - 3x Traditional Music = 50 - 3x 60-3x + 50 - 3x + 3x + x = 94 110 - 3x + x = 94 -2x = 94 - 110 =>-2x = -16, this x = 8. Members that like only one game: = 60 - 3x + 50 - 3x = 60 - 3[8] + 50 - 3[8] = 60 - 24 + 50 - 24 = 36 + 26 = 62 Members that like only one type of music = 62 |
|
| 5. |
Evaluate \(\frac{(2.813 \times 10^{-3} \times 1.063)}{(5.637 \times 10^{-2})}\) reducing each number to two significant figures and leaving your answer in two significant figures. A. 0.056 B. 0.055 C. 0.054 D. 0.54 Detailed Solution\(\frac{2.813 \times 10^{-3} \times 1.063}{5.637 \times 10^{-2}}\)= \(\frac{0.002813 \times 1.063}{0.05637}\) \(\approxeq \frac{0.0028 \times 1.1}{0.056}\) = \(0.055\) |
|
| 6. |
A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for N150,000. How much does he need to deposit? A. N112,000.50 B. N96,000.00 C. N85,714.28 D. N76,800.00 Detailed SolutionAmount A = P(1+r)n;A = N150,000, r = 25%, n = 3. 150,000 = P(1+0.25)3 = P(1.25)3 P = 150,000/1.253 =N76,800.00 |
|
| 7. |
If 31410 - 2567 = 340x, find x. A. 7 B. 8 C. 9 D. 10 Detailed Solution31410 - 2567 = 340x,Convert 2567 and 340x to base 10, such that: 314 - 139 = 3x2 + 4x => 3x2 + 4x - 175 = 0 (quadratic) Factorising, (x - 7) (3x + 25) = 0, either x = 7 or x = -25/3 ( but x cannot be negative) Therefore, x = 7. |
|
| 8. |
Simplify \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\) A. 2n+1 B. 2n-1 C. 4 D. 1/4 Detailed SolutionStart by expanding \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\):\(\frac{3 \times 2^n \times 2^1 - 2^2 \times 2^n \times 2^{-1}}{2^n \times 2 - 2^n}\) NUMERATOR : 2\(^n\) ( 3\(^1\) X 2\(^1\) - 2\(^2\) X 2\(^-1\) ) --> 2\(^n\) ( 3 X 2 — 4 X \(\frac{1}{2}\) ) --> 2\(^n\) ( 6 - 2 ) --> 2\(^n\) (4) DENOMINATOR : 2\(^n\) ( 2\(^1\) - 1 ) --> 2\(^n\) ( 2 - 1) --> 2\(^n\) : [ 2\(^n\) ( 4) ] ÷ 2\(^n\) = 4 |
|
| 9. |
If \(P344_{6} - 23P2_{6} = 2PP2_{6}\), find the value of the digit P. A. 2 B. 3 C. 4 D. 5 Detailed SolutionConvert everything to base 10 and collect like terms, such that:\(210P - 42P = 434 + 406\) \(168P = 840\) \(P = 840/168 = 5\) |
|
| 10. |
A binary operation * is defined by a * b = a\(^b\). If a * 2 = 2 - a, find the possible values of a. A. 1, -1 B. 1, 2 C. 2, -2 D. 1, -2 Detailed Solutiona * b = a\(^b\)a * 2 = a\(^2\) = 2 - a a\(^2\) + a - 2 = 0 a\(^2\) + 2a - a - 2 = 0 a(a+2) - 1(a+2) = 0 (a-1)(a+2) = 0 a = 1, -2 |
| 1. |
Let P = {1, 2, u, v, w, x}; Q = {2, 3, u, v, w, 5, 6, y} and R = {2, 3, 4, v, x, y}. A. {1, x} B. {x y} C. {x} D. ɸ Detailed SolutionP = {1,2,u,v,w,x}Q = {2,3,u,v,w,5,6,y} R = {2,3,4,v,x,y} P - Q = {1,x} (P - Q) ∩ R = {1,x} ∩ {2,3,4,v,x,y} = {x} NB: The set P−Q consists of elements that are in P but not in Q. |
|
| 2. |
If the population of a town was 240,000 in January 1998 and it increased by 2% each year, what would be the population of the town in January, 2000? A. 480,000 B. 249,696 C. 249,600 D. 244,800 Detailed Solution1st year, Population = 240,000 x (2/100) = 4800.Being the 2nd year population = 240,000 + 4800 = 244800. Increase in Pop. in 2nd year = 244800 x (2/100) = 4896 Jan 2000, Pop. = 244800 + 4896 = 249,696 |
|
| 3. |
If \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})} = m +n\sqrt{6}\), find the values of m and n respectively. A. 1, -2 B. -2, 1 C. \(\frac{-2}{5}\), 1 D. 2, 3/5 Detailed SolutionRationalize \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})}\) and equate to \(m +n\sqrt{6}\). Such that m = -2, and n = 1.Use \(\sqrt{3}-2\sqrt{2}\) as the conjugate for Rationalization \(\frac{(2\sqrt{3}-\sqrt{2})}{(\sqrt{3}+2\sqrt{2})}\) X \(\frac{(\sqrt{3}-2\sqrt{2})}{(\sqrt{3}-2\sqrt{2})}\) \(\frac{6 - 4\sqrt{6} - \sqrt{6} + 4}{3 - 2\sqrt{6} + 2\sqrt{6} - 8}\) =\(\frac{10 - 5\sqrt{6}}{-5}\) = -2 + \(\sqrt{6}\) |
|
| 4. |
In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music? A. 8 B. 24 C. 62 D. 86 Detailed Solutionx = no. of ppl that like none.no. of ppl that like both Traditional and Modern music, which is equal to 3x Modern Music = 60 - 3x Traditional Music = 50 - 3x 60-3x + 50 - 3x + 3x + x = 94 110 - 3x + x = 94 -2x = 94 - 110 =>-2x = -16, this x = 8. Members that like only one game: = 60 - 3x + 50 - 3x = 60 - 3[8] + 50 - 3[8] = 60 - 24 + 50 - 24 = 36 + 26 = 62 Members that like only one type of music = 62 |
|
| 5. |
Evaluate \(\frac{(2.813 \times 10^{-3} \times 1.063)}{(5.637 \times 10^{-2})}\) reducing each number to two significant figures and leaving your answer in two significant figures. A. 0.056 B. 0.055 C. 0.054 D. 0.54 Detailed Solution\(\frac{2.813 \times 10^{-3} \times 1.063}{5.637 \times 10^{-2}}\)= \(\frac{0.002813 \times 1.063}{0.05637}\) \(\approxeq \frac{0.0028 \times 1.1}{0.056}\) = \(0.055\) |
| 6. |
A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for N150,000. How much does he need to deposit? A. N112,000.50 B. N96,000.00 C. N85,714.28 D. N76,800.00 Detailed SolutionAmount A = P(1+r)n;A = N150,000, r = 25%, n = 3. 150,000 = P(1+0.25)3 = P(1.25)3 P = 150,000/1.253 =N76,800.00 |
|
| 7. |
If 31410 - 2567 = 340x, find x. A. 7 B. 8 C. 9 D. 10 Detailed Solution31410 - 2567 = 340x,Convert 2567 and 340x to base 10, such that: 314 - 139 = 3x2 + 4x => 3x2 + 4x - 175 = 0 (quadratic) Factorising, (x - 7) (3x + 25) = 0, either x = 7 or x = -25/3 ( but x cannot be negative) Therefore, x = 7. |
|
| 8. |
Simplify \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\) A. 2n+1 B. 2n-1 C. 4 D. 1/4 Detailed SolutionStart by expanding \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\):\(\frac{3 \times 2^n \times 2^1 - 2^2 \times 2^n \times 2^{-1}}{2^n \times 2 - 2^n}\) NUMERATOR : 2\(^n\) ( 3\(^1\) X 2\(^1\) - 2\(^2\) X 2\(^-1\) ) --> 2\(^n\) ( 3 X 2 — 4 X \(\frac{1}{2}\) ) --> 2\(^n\) ( 6 - 2 ) --> 2\(^n\) (4) DENOMINATOR : 2\(^n\) ( 2\(^1\) - 1 ) --> 2\(^n\) ( 2 - 1) --> 2\(^n\) : [ 2\(^n\) ( 4) ] ÷ 2\(^n\) = 4 |
|
| 9. |
If \(P344_{6} - 23P2_{6} = 2PP2_{6}\), find the value of the digit P. A. 2 B. 3 C. 4 D. 5 Detailed SolutionConvert everything to base 10 and collect like terms, such that:\(210P - 42P = 434 + 406\) \(168P = 840\) \(P = 840/168 = 5\) |
|
| 10. |
A binary operation * is defined by a * b = a\(^b\). If a * 2 = 2 - a, find the possible values of a. A. 1, -1 B. 1, 2 C. 2, -2 D. 1, -2 Detailed Solutiona * b = a\(^b\)a * 2 = a\(^2\) = 2 - a a\(^2\) + a - 2 = 0 a\(^2\) + 2a - a - 2 = 0 a(a+2) - 1(a+2) = 0 (a-1)(a+2) = 0 a = 1, -2 |