Mathematics Questions & Answers - Free Online Practice

1,646.

In the diagram, O is the centre of the circle and POQ a diameter. If POR = 96^o, find the value of ORQ.

84^o

48^o

45^o

42^o

View answer & explanation

Correct answer is B

OQ = OR = radii

< ROQ = 180 - 86 = 84^o

\(\bigtriangleup\)OQR = Isosceles

R = Q

R + Q + 84 = 180(angle in a \(\bigtriangleup\))

2R = 96 since R = Q

R = 48^o

ORQ = 48^o

1,647.

In the diagram, PQRS is a circle with O as centre and PQ/RT. If RTS = 32°. Find PSQ

32^o

45^o

58^o

90^o

View answer & explanation

Correct answer is C

< PSO = \(\frac{1}{2}\) < SOQ = \(\frac{1}{2}\)(180) = 90°

< RTS = < PQS = 32° (Alternative angle)

< PSQ = 90 - < PSQ = 90° - 32°

= 58°

1,648.

PQRST is a regular pentagon and PQVU is a rectangle with U and V lying on TS and SR respectively as shown in the diagram. Calculate TUP

18^o

54^o

90^o

108^o

View answer & explanation

Correct answer is B

The total angle in a regular pentagon = \((2(5) - 4) \times 90\)

= \(6 \times 90 = 540°\)

Each interior angle = \(\frac{540}{5} = 108°\)

While the interior of a quadrilateral = \(\frac{360}{4} = 90°\)

\(PTU + TPU + TUP = 180°\)

\(108° + (180° - 90°) + TUP = 180°\)

\(TUP = 180° - (108° + 18°) = 54°\)

1,649.

The figure represents the graphs of y = x(2 - x) and y = (x - 1)(x - 3). What are the x-coordinates of P, Q and F respectively?

1, 3, 2

0, 0, 0

0, 2, 3

1, 2, 3

View answer & explanation

Correct answer is D

The two equations are y = x(2 - x) and y = (x - 1)(x - 3)

The root of these equations are points where the graph of the equations cuts the x axis; but at these points = 0

put y = 0; 0 = x(2 - x)

0 = (x - 1)(x - 3)

x = 0 or x = 2; x = 1 or x = 3

The values of x at P, Q, R are increasing towards the positive direction of x-axis

at P, x = 1 at Q, x = 2 at R, x = 3

P, Q, R are respectively (1, 2, 3)