JAMB Mathematics Past Questions & Answers - Page 165

821.

If x varies inversely as y, and y varies directly as the square root of z, and z varies directly \(\frac{1}{w^2}\) write down in words how x varies with w

A.

x varies inversely as w2

B.

x varies directly as w2

C.

x varies directly as w

D.

x varies inversely as w

E.

x varies directly as square root of w

Correct answer is B

No explanation has been provided for this answer.

822.

A cylindrical motor of height 12cm has uniform thickness of 2cm. If the diameter of its outer cross section is 10cm, Find the volume of the constituent material. (take \(\pi\) = \(\frac{22}{7}\)

A.

\(\frac{6600}{7}\)cm3

B.

270cm3

C.

660cm3

D.

\(\frac{4224}{7}\)cm3

E.

\(\frac{1980}{7}\)cm3

Correct answer is D

V = \(\pi\)r2h

= \(\frac{22}{7}\) x 52 x 12 - \(\frac{22}{7}\) x 32 x 12

= \(\frac{22}{7}\) x 12(52 - 32)

= \(\frac{4224}{7}\)

823.

If a function is defined by f(x + 1) = 3x2 - x + 4, Find f(0).

A.

4

B.

6

C.

9

D.

8

E.

2

Correct answer is D

f(x + 1) = 3x2 - x + 4

f(0) = f(x + 1)

x + 1 = 0 ===> x = -1

f(0) = 3(-1)2 - (-1) + 4

f(0) = 3 + 1 + 4

= 8

824.

The expression x\(^3\) - 4x\(^2\) + cx + d is such that x + 1 is its factor, and its value is 1 when x is -2. Find c and d.

A.

c = 4 and d = -9

B.

c = -4 and d = 9

C.

c = -20 and d = -15

D.

c = 20 and d = -15

E.

c = -20 and d = 15

Correct answer is C

F(X) = x\(^3\) - 4x\(^2\) + cx + d

= (X + 1) Q(X) + R

x = -1, R = 0,f(-1) = -1\(^3\) - 4(-1)\(^2\) + c(-1) + d = 0

-1 - 4 - c + d = 0

d - c = 5................(i)

f(-2) = -2\(^3\) - 4(-2)\(^2\) + c(-2) + d = 1

= -8 - 16 - 2c + d

= 1

-8 - 16 - 2c + d = 1

-24 - 2c + d = 1

d - 2c = 1 + 24

d - 2c = 25.................(ii)

\(\frac{d - c = 5}{-c = 20}\) d - c = 5

c = -20

d - (-20) = 5

d + 20 = 5

d = 5 - 20

= -15

c = -20, d = -15

825.

Find the missing numerator \(\frac{5}{x + 1}\) - \(\frac{3}{1 - x}\) - \(\frac{7x - 1}{x^2 - 1}\) = \(\frac{?}{x + 1}\).

A.

-1

B.

x - 1

C.

\(\frac{3(1 - 5x)}{x + 1}\)

D.

1

E.

3(1 - 5x)

Correct answer is D

\(\frac{5}{x + 1} - \frac{3}{1 - x} - \frac{7x - 1}{x^{2} - 1} = \frac{?}{x + 1}\)

\(\frac{5(x - 1) - 3(- (x + 1)) - 7x - 1}{x^{2} - 1}\)

= \(\frac{5x - 5 + 3x + 3 - 7x - 1}{x^{2} - 1}\)

= \(\frac{x - 1}{x^{2} - 1}\)

= \(\frac{x - 1}{(x - 1)(x + 1)}\)

= \(\frac{1}{x + 1}\).

The numerator = 1.