JAMB Mathematics Past Questions & Answers - Page 290

1,446.

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).

1,447.
1,448.

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.

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

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

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

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

1,449.

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

1,450.

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