Mathematics (Core), 1986, JAMB Exam, Exam, Paper 1 | Objectives

Paper Info

Year :

1986

Title :

Mathematics (Core)

Exam :

JAMB Exam

Paper 1 | Objectives

41 - 48 of 48 Questions

#	Question	Ans
41.	The table below gives the scores of a group of students in a Mathematical test. \(\begin{array}{c\|c} Scores & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline Frequency & 2 & 4 & 7 & 14 & 12 & 6 & 4 & 1\end{array}\) If the mode in m and the number of students who scored 4 or less is s. What is (s, m)? A. (27, 4) B. (14,4) C. (13,4) D. (4,4) Show Content Detailed Solution M = mode = the number having the highest frequency = 4 S = Number of students with 4 or less marks = 14 + 7 + 4 + 2 = 27 ∴ (M,S) = (27, 4)	A
42.	In the diagram, PQ and RS are chords of a circle centre O which meet at T outside the circle. If TP = 24cm. TQ = 8cm and TS = 12cm, find TR. A. 16cm B. 14cm C. 12cm D. 8cm Show Content Detailed Solution PT x QT = TR x TS 24 x 8 = TR x 12 TR = \(\frac{24 \times 8}{12}\) = = 16cm	A
43.	The figure is a solid with the trapezium PQRS as its uniform cross-section. Find its volume A. 120m² B. 576m³ C. 816m³ D. 1056m³ Show Content Detailed Solution Volume of solid = cross section x H Since the cross section is a trapezium = \(\frac{1}{2} (6 + 11) \times 12 \times 8\) = 6 x 17 x 8 = 816m³	C
44.	PQ and PR are tangents from P to a circle centre O as shown in the figure. If QRP = 34^o, find the angle marked x A. 34^o B. 56^o C. 68^o D. 112^o Show Content Detailed Solution From the circle centre 0, if PQ & PR are tangents from P and QRP = 34^o Then the angle marked x i.e. QOP 34^o x 2 = 68^o	C
45.	In the figure, \(\bigtriangleup\)PQT is isosceles. PQ = QT, SRQ = 35^o, TPQ = 20^o and PQR is a straight line.Calculate TSR A. 20^o B. 55^o C. 75^o D. 140^o Show Content Detailed Solution Given \(\bigtriangleup\) isosceles PQ = QT, SRQ = 35^o TPQ = 20^o PQR = is a straight line Since PQ = QT, angle P = angle T = 20^o Angle PQR = 180^o - (20 + 20) = 140^o TQR = 180^o - 140^o = 40^o < on a straight line QSR = 180^o - (40 + 35)&	C
46.	In the figure, PQ\|\|ST, RS\|\|UV. If PQR = 35^o and QRS = 65^o, find STV A. 30^o B. 35^o C. 55^o D. 65^o Show Content Detailed Solution Draw XW//PQ and ARW = 35^o (alternative angle) WRS = 60 - 30 = 30^o RSR = 30^o (Alternative angle) STV = 30^o (Alternative angle)	A
47.	The people in a city with a population of 0.9 million were grouped according to their ages. Use the diagram to determine the number of people in the 15 - 29 years group A. 29 x 10⁴ B. 26 x 10⁴ C. 16 x 10⁴ D. 13 x 10⁴ Show Content Detailed Solution 15 - 29 years is represented by 104^o Number of people in the group is \(\frac{104}{360}\) x 0.9m = 260000 = 26 x 10⁴	B
48.	In \(\bigtriangleup\)XYZ, determine the cosine of angle Z. A. \(\frac{3}{39}\) B. \(\frac{29}{36}\) C. \(\frac{14}{5}\) D. \(\frac{7}{5}\) Show Content Detailed Solution cos z = \(\frac{y^2 + x^2 -z^2}{2yx}\) = \(\frac{9 + 36 - 16}{2(3)(6)}\) = \(\frac{29}{36}\)	B

41.	The table below gives the scores of a group of students in a Mathematical test. \(\begin{array}{c\|c} Scores & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline Frequency & 2 & 4 & 7 & 14 & 12 & 6 & 4 & 1\end{array}\) If the mode in m and the number of students who scored 4 or less is s. What is (s, m)? A. (27, 4) B. (14,4) C. (13,4) D. (4,4) Show Content Detailed Solution M = mode = the number having the highest frequency = 4 S = Number of students with 4 or less marks = 14 + 7 + 4 + 2 = 27 ∴ (M,S) = (27, 4)	A
42.	In the diagram, PQ and RS are chords of a circle centre O which meet at T outside the circle. If TP = 24cm. TQ = 8cm and TS = 12cm, find TR. A. 16cm B. 14cm C. 12cm D. 8cm Show Content Detailed Solution PT x QT = TR x TS 24 x 8 = TR x 12 TR = \(\frac{24 \times 8}{12}\) = = 16cm	A
43.	The figure is a solid with the trapezium PQRS as its uniform cross-section. Find its volume A. 120m² B. 576m³ C. 816m³ D. 1056m³ Show Content Detailed Solution Volume of solid = cross section x H Since the cross section is a trapezium = \(\frac{1}{2} (6 + 11) \times 12 \times 8\) = 6 x 17 x 8 = 816m³	C
44.	PQ and PR are tangents from P to a circle centre O as shown in the figure. If QRP = 34^o, find the angle marked x A. 34^o B. 56^o C. 68^o D. 112^o Show Content Detailed Solution From the circle centre 0, if PQ & PR are tangents from P and QRP = 34^o Then the angle marked x i.e. QOP 34^o x 2 = 68^o	C

45.	In the figure, \(\bigtriangleup\)PQT is isosceles. PQ = QT, SRQ = 35^o, TPQ = 20^o and PQR is a straight line.Calculate TSR A. 20^o B. 55^o C. 75^o D. 140^o Show Content Detailed Solution Given \(\bigtriangleup\) isosceles PQ = QT, SRQ = 35^o TPQ = 20^o PQR = is a straight line Since PQ = QT, angle P = angle T = 20^o Angle PQR = 180^o - (20 + 20) = 140^o TQR = 180^o - 140^o = 40^o < on a straight line QSR = 180^o - (40 + 35)&	C
46.	In the figure, PQ\|\|ST, RS\|\|UV. If PQR = 35^o and QRS = 65^o, find STV A. 30^o B. 35^o C. 55^o D. 65^o Show Content Detailed Solution Draw XW//PQ and ARW = 35^o (alternative angle) WRS = 60 - 30 = 30^o RSR = 30^o (Alternative angle) STV = 30^o (Alternative angle)	A
47.	The people in a city with a population of 0.9 million were grouped according to their ages. Use the diagram to determine the number of people in the 15 - 29 years group A. 29 x 10⁴ B. 26 x 10⁴ C. 16 x 10⁴ D. 13 x 10⁴ Show Content Detailed Solution 15 - 29 years is represented by 104^o Number of people in the group is \(\frac{104}{360}\) x 0.9m = 260000 = 26 x 10⁴	B
48.	In \(\bigtriangleup\)XYZ, determine the cosine of angle Z. A. \(\frac{3}{39}\) B. \(\frac{29}{36}\) C. \(\frac{14}{5}\) D. \(\frac{7}{5}\) Show Content Detailed Solution cos z = \(\frac{y^2 + x^2 -z^2}{2yx}\) = \(\frac{9 + 36 - 16}{2(3)(6)}\) = \(\frac{29}{36}\)	B