Mathematics questions and answers

Mathematics Questions and Answers

How good are you with figures and formulas? Find out with these Mathematics past questions and answers. This Test is useful for both job aptitude test candidates and students preparing for JAMB, WAEC, NECO or Post UTME.

606.

The diagram shows a trapezium inscribed in a semi-circle. If O is the mid-point of WZ and |WX| = |XY| = |YZ|, calculate the value of m

A.

90\(^o\)

B.

60\(^o\)

C.

45\(^o\)

D.

30\(^o\)

Correct answer is B

In the diagram, < WOZ = 180\(^o\) (angle on a straight line)

< WOX = < XOY = < YOZ

(|WX| = |XY| = |YZ|)

\(\frac{180^o}{3}\) = 60\(^o\)

= 60\(^o\)

M + m =2m (base angles of isosceles \(\bigtriangleup\), |OY| and |OZ| are radii)

< YOZ + 2m (base angles of a \(\bigtriangleup\))

60\(^o\) + 2m = 180\(^o\) (sum of a \(\bigtriangleup\))

60\(^o\) + 2m = 180\(^o\)

2m = 180\(^o\) - 60\(^o\)

2m = 120\(^o\)

m = \(\frac{120^o}{2}\)

= 60\(^o\)

 

607.

The solution of x + 2 \(\geq\) 2x + 1 is illustrated

A.

i

B.

ii

C.

iii

D.

iv

Correct answer is A

x + 2 \(\geq\) 2x + 1

x - 2x \(\geq\) 1 - 2

-x \(\geq\) -1

\(\frac{-x}{-1}\) \(\geq\) \(\frac{-1}{-1}\)

x \(\leq\) 1

608.

In the diagram, WXYZ is a rectangle with diamension 8cm by 6cm. P, Q, R and S are the midpoints of the rectangle as shown. Using this information calculate the area of the part of the rectangle that is not shaded

A.

25cm\(^2\)

B.

24cm\(^2\)

C.

16cm\(^2\)

D.

12cm\(^2\)

Correct answer is B

Area of shaded part = 2 x area of \(\bigtriangleup\)SPQ

= 2 x \(\frac{1}{2}\) 8 x 3 =24cm

Hence, area of the unshaded part of the rectangle = area of rectangle - area of shaded part

= 8 x 6 - 24

= 48 - 24

= 24 cm\(^2\)

609.

In the diagram, PS and RS are tangents to the circle centre O. ∠PSR = 70°, ∠POR = m, and ∠PSR =n. Find ( m + n ).

A.

110\(^o\)

B.

135\(^o\)

C.

165\(^o\)

D.

225\(^o\)

Correct answer is C

In the diagram,

 

Thus, m = 2 x 55\(^o\) (is a bisector of obtuse

m = 110\(^o\)

n = \(\frac{1}{2}\) x 110\(^o\) (angle at centre = 2 x angle at circum)

n = 55\(^o\)

m + n =  110 + 55 = 165\(^o\)