JAMB Mathematics Past Questions & Answers - Page 295

1,471.

An arc of a circle subtends an angle 70° at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle.(\(\pi\) = \(\frac{22}{7}\))

A.

22cm2

B.

44cm2

C.

66cm2

D.

88cm2

Correct answer is A

Area of a sector = \(\frac{\theta}{360°} \times \pi r^{2}\)

r = 6cm; \(\theta\) = 70°.

Area of the sector = \(\frac{70}{360} \times \frac{22}{7} \times 6^{2}\)

= \(22 cm^{2}\)

1,472.

A chord of a circle of a diameter 42cm subtends an angle of 60° at the centre of the circle. Find the length of the mirror arc

A.

22cm

B.

44cm

C.

110cm

D.

220cm

Correct answer is A

Diameter = 42cm

Length of the arc = \(\frac{\theta}{360°} \times \pi d\)

= \(\frac{60}{360} \times \frac{22}{7} \times 42cm\)

= \(22cm\)

1,473.

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).

1,474.
1,475.

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.

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

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

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

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