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JAMB Mathematics Past Questions & Answers - Page 112

556.

find the length XZ in the triangle

$\sqrt{7m}$

$\sqrt{6m}$

$\sqrt{5m}$

$\sqrt{3m}$

View answer & explanation

Correct answer is A

xz² = xy² + yx² - 2(xy) (yz) cos 120^o

= 2² + 1² - 2(2) (1) cos 120²

= 4 + 1 - 4x - cos 60 = 5 - 4x - $\frac{1}{2}$

5 + 2 = 7

xz = $\sqrt{7}$ m

557.

Find the value of L in the frustum

5cm

6cm

7cm

8cm

View answer & explanation

Correct answer is A

No explanation has been provided for this answer.

558.

In the figure, TZ is tangent to the circle QPZ. Find x if TZ = 6 units and PQ = 9 units

View answer & explanation

Correct answer is A

In $\bigtriangleup$ WOP, b² = r² - (4.50²...........(i)

In $\bigtriangleup$ WOT, b $\bigtriangleup$ + (4.5 + x)² = a²...........(ii)

In $\bigtriangleup$ ZOT, a² = 6² + r² ..........(iii)

subst. equation (iii) and (i) in eqn (ii)

r² - (4.5)² + (4.5 + x)² = 36 = 20.25

= (4.5 + x)² = $\sqrt{56.25}$ = (4.5 + x)

= 56.25

= 4.5 + x = 7.5

x = 3.0m

559.

In the figure, PQRS is a circle with ST||RQ. Find the value of x if PT = pS

70^o

55^o

40^o

35^o

View answer & explanation

Correct answer is B

< PST = < RQT = x(corresponding angle)

< PST = < PTS = < PTS x (PS = PT0

< SRQ = < SPT = 180^o (sum of < on straight line)

< SPT = 180^o - 110^o = 70^o

in < SPT, < PST = PTS = < PSt = 180^o

2x + 70 = 180^o

2x = 180^o - 70^o = 110^o

x = $\frac{110^o}{2}$ = 55^o

560.

In the diagram, EFGH is a cyclic quadrilateral in which EH || FG, EG, and FH are chords. If < FHG = 42º and < EFH = 34º, calculate < HEG.

34^o

42^o

52^o

76^o

View answer & explanation

Correct answer is C

< EFH = < EGH = 34º (angles n the same segment)

< GHF = < GEF = 42º(angles in the same segment)

< FOG = 42 + 34 = 76º (exterior angle)

< FOG = < EOH = 76º (vertically opposite angle)

< EDO = 90º, < DOE = $\frac{76}{2}$ = 38º

< HEG = 90º - 38º = 52º