Year :
2001
Title :
Mathematics (Core)
Exam :
JAMB Exam
Paper 1 | Objectives
41 - 50 of 50 Questions
| # | Question | Ans |
|---|---|---|
| 41. |
 The identity element with respect to the multiplication shown in the table above is A. o B. m C. l D. k |
B |
| 42. |
 In the figure above, PQR is a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, ∠SQR is 75o and ∠QPT is 25o. Calculate the value of ∠RST. A. 45o B. 55o C. 25o D. 50o Detailed SolutionIn Δ PQT,∠PTQ = 25o(base ∠s of isosceles Δ) In Δ QSR, ∠RQS = ∠QPT + ∠QTP (Extr = sum of interior opposite ∠s) ∠RQS = 25 + 25 = 50o Also in Δ QSR, 75 + ∠RQS + ∠QSR = 180o (sum of ∠s of Δ) ∴75 + 50 + ∠QSR = 180 125 + ∠QSR = 180 ∠QSR = 180 - 125 ∠QSR = 55o But ∠QSR and ∠RST are the same ∠RST = 55o |
|
| 43. |
 The histogram above shows the distribution of passengers in taxis of a certain motor park. How many taxis have more than 4 passengers A. 16 B. 17 C. 14 D. 15 |
B |
| 44. |
 The bar chart above shows different colours of passing a particular point of a certain street in two minutes. What fraction of the total number of cars is yellow? A. 3/25 B. 2/25 C. 1/5 D. 4/15 Detailed SolutionNumber of yellow cars = 3Total number of cars = 3 + 4 + 8 + 2 + 6 + 2 = 25 Fraction of yellow cars = 3/25 |
|
| 45. |
 Triangle SPT is the solution of the linear inequalities A. 2y - x - 2 \(\leq\) 0, y + 2x + 2 \(\geq\) 0, x \(\geq\) 0 B. 2y - x - 2 \(\geq\) 0, y + 2x + 2 \(\leq\) 0, -2 \(\geq\) x \(\geq\) -1 C. -2 \(\geq\) x \(\geq\) 2, y \(\leq\) 0, y + 2x + 2 \(\geq\) 0, x \(\geq\) 0 D. 2y - x - 2 \(\geq\) 0, y + 2x + 2 \(\geq\) 0, y \(\leq\) 0, x \(\geq\) 0 |
C |
| 46. |
 In the figure PQR a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, < SRQ is 75o and < QPT IS 25o. Calculate the value of < RST A. 50o B. 25o C. 55o D. 45o Detailed Solution< T = \(\frac{x}{1}\) = 25o (PQ = QT)< SQR = 2(25o) = 50o (sum of interior angle) < Q + < R + < S = 180o 50o + 75o + < S = 180o = 125o + < S = 180o < S = 180o - 125o = 55o |
|
| 47. |
 Find the value of \(\theta\) in the diagram A. 60o B. 100o C. 120o D. 30o Detailed SolutionUsing cosine formula (t\(\sqrt{3}\))2 = t2 + t2 - 2t2 cos\(\theta\)3t2 = 2t2 - 2t2 cos\(\theta\) = 2t2(1 - cos\(\theta\)) 1 - cos\(\theta\) = \(\frac{3t^2}{2t^2}\) = \(\frac{3}{2}\) cos = 1 - \(\frac{3}{2} = -\frac{1}{2}\) \(\theta\) = cos-1(-\(\frac{1}{2}\)) = 120o and 240o N.B 0 \(\geq\) \(\theta\) 360 |
|
| 48. |
 The bar chart shows different colours of cars passing a particular point of a certain street in two minutes. What fraction of the cars is yellow A. \(\frac{1}{5}\) B. \(\frac{2}{25}\) C. \(\frac{4}{15}\) D. \(\frac{3}{25}\) Detailed Solution\(\begin{array}{c|c} \text{colour of cars} & \text{Number (frequency)} \\ \hline yellow & 3 \\white & 4\\ red & 8\\ green & 2\\ blue & 6\\ black & 2\\ \hline & 25 \\ \hline\end{array}\)Thus, the fraction of the total numbers that are yellow is \(\frac{3}{25}\) |
|
| 49. |
 The graph shows the cumulative frequency of the distribution of masses of fertilizer for 48 workers in one institution. Which of the following gives the inter-quartile range? A. \(\frac{1}{2}(Q_3 - Q_1)\) B. Q3 - Q2 C. Q3 - Q2 D. Q3 - Q1 |
A |
| 50. |
 The histogram shows the distribution of passengers in taxis at a certain motor park. How many taxis have more than 4 passengers? A. 17 B. 16 C. 15 D. 14 Detailed Solution\(\begin{array}{c|c} \text{no. of passengers} & \text{Number of taxis}\\ \hline 0.5 - 2.5 & 3\\ 2.5 - 4.5 & 4 \\ 4.5 - 6.5 & 7\\ 6.5 - 8.5 & 5\\ 8.5 - 10.5 & 4 \\ 10.5 - 12.5 & 1\\ \hline \text{Total} & 24 \end{array}\)Thus, the taxi with more than 4 passengers = 7 + 5 + 4 + 1 = 17 |
| 41. |
The identity element with respect to the multiplication shown in the table above is A. o B. m C. l D. k |
B |
| 42. |
In the figure above, PQR is a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, ∠SQR is 75o and ∠QPT is 25o. Calculate the value of ∠RST. A. 45o B. 55o C. 25o D. 50o Detailed SolutionIn Δ PQT,∠PTQ = 25o(base ∠s of isosceles Δ) In Δ QSR, ∠RQS = ∠QPT + ∠QTP (Extr = sum of interior opposite ∠s) ∠RQS = 25 + 25 = 50o Also in Δ QSR, 75 + ∠RQS + ∠QSR = 180o (sum of ∠s of Δ) ∴75 + 50 + ∠QSR = 180 125 + ∠QSR = 180 ∠QSR = 180 - 125 ∠QSR = 55o But ∠QSR and ∠RST are the same ∠RST = 55o |
|
| 43. |
The histogram above shows the distribution of passengers in taxis of a certain motor park. How many taxis have more than 4 passengers A. 16 B. 17 C. 14 D. 15 |
B |
| 44. |
The bar chart above shows different colours of passing a particular point of a certain street in two minutes. What fraction of the total number of cars is yellow? A. 3/25 B. 2/25 C. 1/5 D. 4/15 Detailed SolutionNumber of yellow cars = 3Total number of cars = 3 + 4 + 8 + 2 + 6 + 2 = 25 Fraction of yellow cars = 3/25 |
|
| 45. |
Triangle SPT is the solution of the linear inequalities A. 2y - x - 2 \(\leq\) 0, y + 2x + 2 \(\geq\) 0, x \(\geq\) 0 B. 2y - x - 2 \(\geq\) 0, y + 2x + 2 \(\leq\) 0, -2 \(\geq\) x \(\geq\) -1 C. -2 \(\geq\) x \(\geq\) 2, y \(\leq\) 0, y + 2x + 2 \(\geq\) 0, x \(\geq\) 0 D. 2y - x - 2 \(\geq\) 0, y + 2x + 2 \(\geq\) 0, y \(\leq\) 0, x \(\geq\) 0 |
C |
| 46. |
In the figure PQR a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, < SRQ is 75o and < QPT IS 25o. Calculate the value of < RST A. 50o B. 25o C. 55o D. 45o Detailed Solution< T = \(\frac{x}{1}\) = 25o (PQ = QT)< SQR = 2(25o) = 50o (sum of interior angle) < Q + < R + < S = 180o 50o + 75o + < S = 180o = 125o + < S = 180o < S = 180o - 125o = 55o |
|
| 47. |
Find the value of \(\theta\) in the diagram A. 60o B. 100o C. 120o D. 30o Detailed SolutionUsing cosine formula (t\(\sqrt{3}\))2 = t2 + t2 - 2t2 cos\(\theta\)3t2 = 2t2 - 2t2 cos\(\theta\) = 2t2(1 - cos\(\theta\)) 1 - cos\(\theta\) = \(\frac{3t^2}{2t^2}\) = \(\frac{3}{2}\) cos = 1 - \(\frac{3}{2} = -\frac{1}{2}\) \(\theta\) = cos-1(-\(\frac{1}{2}\)) = 120o and 240o N.B 0 \(\geq\) \(\theta\) 360 |
|
| 48. |
The bar chart shows different colours of cars passing a particular point of a certain street in two minutes. What fraction of the cars is yellow A. \(\frac{1}{5}\) B. \(\frac{2}{25}\) C. \(\frac{4}{15}\) D. \(\frac{3}{25}\) Detailed Solution\(\begin{array}{c|c} \text{colour of cars} & \text{Number (frequency)} \\ \hline yellow & 3 \\white & 4\\ red & 8\\ green & 2\\ blue & 6\\ black & 2\\ \hline & 25 \\ \hline\end{array}\)Thus, the fraction of the total numbers that are yellow is \(\frac{3}{25}\) |
|
| 49. |
The graph shows the cumulative frequency of the distribution of masses of fertilizer for 48 workers in one institution. Which of the following gives the inter-quartile range? A. \(\frac{1}{2}(Q_3 - Q_1)\) B. Q3 - Q2 C. Q3 - Q2 D. Q3 - Q1 |
A |
| 50. |
The histogram shows the distribution of passengers in taxis at a certain motor park. How many taxis have more than 4 passengers? A. 17 B. 16 C. 15 D. 14 Detailed Solution\(\begin{array}{c|c} \text{no. of passengers} & \text{Number of taxis}\\ \hline 0.5 - 2.5 & 3\\ 2.5 - 4.5 & 4 \\ 4.5 - 6.5 & 7\\ 6.5 - 8.5 & 5\\ 8.5 - 10.5 & 4 \\ 10.5 - 12.5 & 1\\ \hline \text{Total} & 24 \end{array}\)Thus, the taxi with more than 4 passengers = 7 + 5 + 4 + 1 = 17 |