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.

2,496.

Each of the base angles of a isosceles triangle is 58° and the verticles of the triangle lie on a circle. Determine the angle which the base of the triangle subtends at the centre of the circle.

A.

128o

B.

16o

C.

64o

D.

58o

Correct answer is A

Base angle of the triangle = 58°.

The third angle = 180° - (58° + 58°)

= 64°

Angle subtended at the centre = \(2 \times 64° = 128°\) (angle at the centre is twice the angle at the circumference).

2,497.
2,498.

Determine x + y if \(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix}\) \(\begin{pmatrix} x \\ y \end{pmatrix}\) = \(\begin{pmatrix}-1 \\ 8 \end{pmatrix}\)

A.

3

B.

4

C.

7

D.

12

Correct answer is C

\(\begin{pmatrix} 2 & -3 \\ -1 & 4 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -1 \\ 8 \end{pmatrix}\)

\(\begin{pmatrix} 2x - 3y \\ -x + 4y \end{pmatrix} = \begin{pmatrix} -1 \\ 8 \end{pmatrix}\)

\(2x - 3y = -1 ... (i)\)

\(-x + 4y = 8 ... (ii)\)

From (ii), x = 4y - 8.

\(2(4y - 8) - 3y = -1 \implies 8y - 16 - 3y = -1\)

\(5y = -1 + 16 = 15 \implies y = 3\)

\(x = 4(3) - 8 = 12 - 8 = 4\)

\(\therefore x + y = 3 + 4 = 7\)

2,499.

If X \(\ast\) Y = X + Y - XY, find x when (x \(\ast\) 2) + (x \(\ast\) 3) = 68

A.

24

B.

22

C.

-12

D.

-21

Correct answer is D

x \(\ast\) y = x + y - xy

(x \(\ast\) 2) + (x \(\ast\) 3) = 68

= x + 2 - 2x + x + 3 - 3x

= 86

3x = 63

x = -21

2,500.

Two binary operations \(\ast\) and \(\oplus\) are defined as m \(\ast\) n = mn - n - 1 and m \(\oplus\) n = mn + n - 2 for all real numbers m, n.

Find the value of 3 \(\oplus\) (4 \(\ast\) 50)

A.

60

B.

57

C.

54

D.

42

Correct answer is C

m \(\ast\) n = mn - n - 1, m \(\oplus\) n = mn + n - 2

3 \(\oplus\) (4 \(\ast\) 5) = 3 \(\oplus\) (4 x 5 - 5 - 1) = 3 \(\oplus\) 14

3 \(\oplus\) 14 = 3 x 14 + 14 - 2

= 54