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JAMB Mathematics Past Questions & Answers - Page 137

681.

The diagram is the distance time graph of a vehicle. Find its average speed in kilometers per hour during the journey

A.

155km/hr

B.

50km/hr

C.

40km/hr

D.

124km/hr

E.

84km/hr

View answer & explanation

Correct answer is E

Distance = 155 - 50 = 105km

Time = 75mins

= $\frac{75}{60}$ hr = $\frac{5}{4}$ hr

Average speed = $\frac{Distance}{time}$ = $\frac{105}{\frac{5}{4}}$

= $\frac{105 \times 4}{5}$

= 84km\h

682.

In the diagram, angle QPR = 90^o, angle PSR = 90^o and PR = 5 units. Find the length of QS.

A.

5 tan 25^o sin 65^o

B.

5 cos 25^o sin 65^o

C.

5 tan 25^o cos 65^o

D.

cos 25^o cos 65^o

E.

5 cosec 25^o

View answer & explanation

Correct answer is C

From $\bigtriangleup$ QPR, < R = 180^o - (25^o + 90^o)

180^o - 115^o = 65^o

From $\bigtriangleup$ PSQ, Sin 65^o = $\frac{QPR}{hyp}$ = $\frac{PS}{5}$

PS = 5 sin 65^o

From $\bigtriangleup$ PSR, tan = $\frac{OPP}{adj}$ = $\frac{PS}{QS}$

but PS = 5 sin 65^o

QS tan 25^o = PS

QS tan 25^o = 5 sin 65^o

QS = $\frac{5 sin 65^o}{tan 25^o}$

= 5 tan 25^o cos 65^o

683.

In the figure, WU//YZ, WY//YZ = 12cm, VZ = 6cm, XU = 8cm. Determine the length of WU.

A.

1cm``3cm

B.

6cm

C.

2cm

D.

4cm

View answer & explanation

Correct answer is D

From similar triangle, $\frac{x}{6}$ = $\frac{8}{12}$

12x = 48

x = $\frac{48}{12}$

= 4

684.

In the diagram, XZ is the diameter of a circle's radius $\frac{5}{2}$ . If XY is 4cm, then the area of the triangle XYZ is

A.

12cm²

B.

28 $\frac{1}{2}$ cm²

C.

16cm²

D.

10cm²

E.

6cm²

View answer & explanation

Correct answer is E

Area of the triangle XYZ = $\frac{1}{2}$ bh = $\frac{1}{2}$ ZY x XY

= $\frac{1}{2}$ x 3 x 4

= 6cm2.

685.

In the figure, find x in terms of a, b and c.

A.

a + b + c

B.

180^o - (a + b + c)

C.

a - b - c

D.

a + b

E.

a + c

View answer & explanation

Correct answer is A

180 - x + a + b + c

= 180(sum of interior angle in triangle)

a + b + c = x.

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