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.

1,846.

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

1,847.

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

1,848.

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.

1,849.

Simplify 102 + log105

A.

500

B.

2 log10 5

C.

10

D.

25

E.

log105 x 10100

Correct answer is E

102 + log105 = log10 10100 + log105

= log105 x 10100

1,850.

Given log 2 = 0.69, log3 = 1, 10 and log7 = 1.90, all to a fixed base, find log 10.5 to the same base without using tables.

A.

1.03

B.

2.31

C.

3.69

D.

10.5

E.

25

Correct answer is B

log 10.5 = log \(\frac{21}{2}\)

= log 21 - log 2

= log(3 x 7) - log 2

= log 3 + log 7 - log 2

= 1.10 + 1.90 - 0.69

= 3 - 0.69

= 2.31