JAMB Mathematics Past Questions & Answers - Page 325

1,621.

If P is a set of all prime factors of 30 and Q is a set of all factors of 18 less than 10, find P \(\cap\) Q

A.

{3}

B.

{2,3}

C.

{2,3,5}

D.

{1,2}

Correct answer is B

P = {2,3,5}

Q = {2,3,6,9}

P \(\cap\) Q = {2,3}

1,622.

Simplify \((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)

A.

\(2\sqrt{6}\)

B.

\(4\sqrt{6}\)

C.

\(8\sqrt{6}\)

D.

\(16\sqrt{6}\)

Correct answer is C

\((\sqrt{6} + 2)^2 - (\sqrt{6} - 2)^2\)

= \([(\sqrt{6} + 2) + (\sqrt{6} - 2)][(\sqrt{6} + 2) - (\sqrt{6} - 2)]\)

= \((\sqrt{6} + 2 + \sqrt{6} - 2)(\sqrt{6} + 2 - \sqrt{6} + 2)]\)

= \((2\sqrt{6})(4)\)

= \(8\sqrt{6}\)

1,623.

If log3x2 = -8, what is x?

A.

\(\frac{1}{3}\)

B.

\(\frac{1}{9}\)

C.

\(\frac{1}{27}\)

D.

\(\frac{1}{81}\)

Correct answer is D

log3x2 = -8

x2 = 3-8

x = \(3^{-8 \times \frac{1}{2}}\)

x = 3-4

x = \(\frac{1}{3^4}\)

x = \(\frac{1}{81}\)

1,624.

If 27\(^{x + 2}\) \(\div\) 9\(^{x + 1}\) = 3\(^{2x}\), find x.

A.

3

B.

4

C.

5

D.

6

Correct answer is B

\(27^{x + 2} \div 9^{x + 1} = 3^{2x}\)

\(3^{3(x + 2)} \div 3^{2(x + 1)} = 3^{2x}\)

\(3^{3x + 6} \div 3^{2x + 2} = 3^{2x}\)

\(\therefore (3x + 6) - (2x + 2) = 2x\)

\(x + 4 = 2x \implies x = 4\)

1,625.

A man earns N3,500 per month out of which he spends 15% on his children's education. If he spends additional N1,950 on food, how much does he have left?

A.

N525

B.

N1,025

C.

N1,950

D.

N2,975

Correct answer is B

Amount spent on children = \(\frac{15}{100} \times 3500 = N525\)

Amount spent = Amount on children + Additional amount on food

Amount Spent = N525 + N1950 = N2475

Therefore amount left = N3,500 - N2,475 = N1,025