JAMB Mathematics Past Questions & Answers - Page 79

391.

Find the gradient of the line joining the points (3, 2) and (1, 4)

A.

3/2

B.

2/1

C.

-1

D.

3/2

Correct answer is C

Gradient of line joining points (3, 2), (1, 4)

Gradient = \(\frac{\text{Change in Y}}{\text{Change in X}}\)

= \(\frac{y_2 - Y_1}{x_2 - x_1}\)\)

(X1, Y1) = (3, 2)

(X2, Y2) = (1, 4)

Gradient = \(\frac{4 − 2}{1 + 3}\)

= \(\frac{2}{-2}\)

= −1

392.

The operation * on the set R of real number is defined by x * y = 3x + 2y − 1, find 3* − 1

A.

9

B.

- 9

C.

6

D.

- 6

Correct answer is C

x * y is an operation on 3x + 2y − 1

Find 3A − 1

x = 3, y = −1

3 * − 1 on 3x + 2y − 1

3(3) + 2(−1) −1

= 9 − 2 − 1

= 6

393.

Make S the subject of the relation
p = s + \(\frac{sm^2}{nr}\)

A.

s = \(\frac{nrp}{nr + m^2}\)

B.

s = nr + \(\frac{m^2}{mrp}\)

C.

s = \(\frac{nrp}{mr}\) + m2

D.

s = \(\frac{nrp}{nr}\) + m2

Correct answer is A

p = s + \(\frac{sm^2}{nr}\)

p = s + ( 1 + \(\frac{m^2}{nr}\))

p = s (1 + \(\frac{nr + m^2}{nr}\))

nr × p = s (nr + m2)

s = \(\frac{nrp}{nr + m^2}\)

394.

Factorize completely X2+2XY+Y2+3X+3Y-18

A.

(x + y + 6)(x + y -3)

B.

(x - y - 6)(x - y + 3)

C.

(x - y + 6)(x - y - 3)

D.

(x + y - 6)(x + y + 3)

Correct answer is A

\(x^{2} + 2xy + y^{2} + 3x + 3y - 18\)

\(x^{2} + 2xy + 3x + y^{2} + 3y -18\)

\(x^{2} + 2xy - 3x + 6x + y^{2} -3y + 6y -18\)

\(x^{2} + 2xy -3x + y^{2} -3y + 6x + 6y -18\)

\(x^{2} + xy -3x + xy + y^{2} - 3y + 6x + 6y -18\)

x(x + y - 3) + y(x + y - 3) + 6(x + y - 3)

= (x + y - 3)(x + y + 6)

= (x + y + 6)(x + y -3)

395.

In the diagram above MN is a chord of a circle KMN centre O and radius 10cm. If < MON = 140°, find, to the nearest cm, the length of the chord MN.

A.

10cm

B.

19cm

C.

17cm

D.

12cm

Correct answer is B

Find the diagram
Sin 70°

x = 10 Sin 70°

= 9.3969

Hence, length of chord MN = 2x

= 2 × 9.3969

= 18.79

= 19cm (nearest cm)