JAMB Mathematics Past Questions & Answers - Page 133

661.

In the figure, \(\bigtriangleup\)PQT is isosceles. PQ = QT, SRQ = 35o, TPQ = 20o and PQR is a straight line.Calculate TSR

A.

20o

B.

55o

C.

75o

D.

140o

Correct answer is C

Given \(\bigtriangleup\) isosceles PQ = QT, SRQ = 35o

TPQ = 20o

PQR = is a straight line

Since PQ = QT, angle P = angle T = 20o

Angle PQR = 180o - (20 + 20) = 140o

TQR = 180o - 140o = 40o < on a straight line

QSR = 180o - (40 + 35)o = 105o

TSR = 180o - 105o

= 75o

662.

In the figure, PQRS is a circle. If chords QR and RS are equal, calculate the value of x

A.

80o

B.

60o

C.

45o

D.

40o

Correct answer is D

SRT is a straight line, where QRT = 120

SRQ = 180o - 120o = 60o - (angle on a straight line)

also angle QRS = 180o - 100o (angle on a straight line) . In angles where QR = SR and angle SRQ = 60o

x = 100 - 60 = 40o

663.

PQ and PR are tangents from P to a circle centre O as shown in the figure. If QRP = 34o, find the angle marked x

A.

34o

B.

56o

C.

68o

D.

112o

Correct answer is C

From the circle centre 0, if PQ & PR are tangents from P and QRP = 34o

Then the angle marked x i.e. QOP

34o x 2 = 68o

664.

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

Correct answer is C

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

665.

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

Correct answer is A

PT x QT = TR x TS

24 x 8 = TR x 12

TR = \(\frac{24 \times 8}{12}\)

= = 16cm