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.

1,761.

What is the number whose logarithm to base 10 is 2.3482?

A.

223

B.

2228

C.

2.235

D.

22.37

E.

0.2229

Correct answer is A

\(\begin{array}{c|c} Nos. & log \\ \hline 222.9 & 2.3482\end{array}\)

N : b Look for the antilog of .3482 which gives 222.9

1,762.

If x\(^2\) + 4 = 0, then x ?

A.

4

B.

-4

C.

2

D.

-2

E.

None of the above

Correct answer is E

x\(^2\)  + 4 = 0

x\(^2\)  = -4

You can't apply a square root to a negative number. So the answer is None of the above.

1,763.

Find the square root of 170 - 20\(\sqrt{30}\)

A.

2 \(\sqrt{10}\) - 5\(\sqrt{3}\)

B.

2 \(\sqrt{5}\) - 5\(\sqrt{6}\)

C.

5 \(\sqrt{10}\) - 2\(\sqrt{3}\)

D.

3 \(\sqrt{5}\) - 8\(\sqrt{6}\)

Correct answer is B

\(\sqrt{170 - 20 \sqrt{30}} = \sqrt{a} - \sqrt{b}\)

Squaring both sides,

\(170 - 20\sqrt{30} = a + b - 2\sqrt{ab}\)

Equating the rational and irrational parts, we have

\(a + b = 170 ... (1)\)

\(2 \sqrt{ab} = 20 \sqrt{30}\)

\(2 \sqrt{ab} = 2 \sqrt{30 \times 100} = 2 \sqrt{3000} \)

\(ab = 3000 ... (2)\)

From (2), \(b = \frac{3000}{a}\)

\(a + \frac{3000}{a} = 170 \implies a^{2} + 3000 = 170a\)

\(a^{2} - 170a + 3000 = 0\)

\(a^{2} - 20a - 150a + 3000 = 0\)

\(a(a - 20) - 150(a - 20) = 0\)

\(\text{a = 20 or a = 150}\)

\(\therefore b = \frac{3000}{20} = 150 ; b = \frac{3000}{150} = 20\)

\(\sqrt{170 - 20\sqrt{30}} = \sqrt{20} - \sqrt{150}\) or \(\sqrt{150} - \sqrt{20}\)

= \(2\sqrt{5} - 5\sqrt{6}\) or \(5\sqrt{6} - 2\sqrt{5}\)

1,764.

The number of telephone calls N between two cities A and B varies directly as the population P\(_{A}\), P\(_B\) respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation?

A.

N = \(\frac{kp_A}{D^2} + {cp_B}{D^2}\)

B.

N = \(\frac{k P_{A} P_{B} }{D^2}\)

C.

N = \(\frac{kD_AP_D}{B^2}\)

D.

N = \(\frac{kD^2_AP_D}{B}\)

Correct answer is B

\(N \propto P_{A}\); \(N \propto P_{B}\); \(N \propto \frac{1}{D^{2}}\)

\(\therefore N \propto \frac{P_{A} P_{B}}{D^{2}}\)

\(N = \frac{k P_{A} P_{B}}{D^{2}}\)

1,765.

The sum of the progression is 1 + x + x2 + x3 + ......

A.

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

B.

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

C.

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

D.

\(\frac{1}{x}\)

Correct answer is A

Sum of n terms of Geometric progression is \(S_{n} = \frac{a(1 - r^n)}{1 - r}\)

In the given series, a (the first term) = 1 and r (the common ratio) = x.

\(S_{n} = \frac{1(1 - x^{n})}{1 - x}\)

a = 1, and as n tends to infinity

\(S_{n} = \frac{1}{1 - x}\)