WAEC Mathematics Past Questions & Answers - Page 36

176.

Given that \(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\) 

= x + y\(\sqrt{15}\), find the value of (x + y) 

A.

1\(\frac{3}{5}\)

B.

1\(\frac{2}{5}\)

C.

1\(\frac{1}{5}\)

D.

\(\frac{1}{5}\)

Correct answer is C

\(\frac{\sqrt{3} + \sqrt{5}}{\sqrt{5}}\)  = x + y\(\sqrt{15}\)

cross multiply to have: \(\sqrt{3}\) + \(\sqrt{5}\) =  x\(\sqrt{5}\) + 5y\(\sqrt{3}\)

Collect like roots :   x\(\sqrt{5}\) =  \(\sqrt{5}\) → x = 1

                                5y\(\sqrt{3}\) =  \(\sqrt{3}\) → y = \(\frac{1}{5}\)

∴ ( x + y ) = 1 + \(\frac{1}{5}\)

= 1\(\frac{1}{5}\)

177.

An amount of N550,000.00 was realized when a principal, x was saved at 2% simple interest for 5 years. Find the value of x

A.

N470,000.00

B.

N480,000.00

C.

N490,000.00

D.

N500,000.00

Correct answer is D

S.I = \(\frac{x \times 2 \times 5}{100}\) = 0.1x

A = P + S.I

550,000 = x + 0.1x

\(\frac{550,000}{1.1} = \frac{1.1x}{1.1}\)

x = N500,000

178.

If 101\(_{\text{two}}\) + 12y = 3.3\(_{\text{five}}\). Find the value of y

A.

8

B.

7

C.

6

D.

5

Correct answer is C

012 + 01 = 01

101\(_2\) + 12\(_y\) = 2.3\(_5\)

1 x 2\(^o\) + 0 x 2\(^o\) + 1 x2\(^2\) + 1 x y\(^o\) + 2 x y\(^1\) = 3 x 5\(^o\) + 3 x 5\(^1\)

1 + 4 + 1 + 2y = 3 + 15

6 + 2y = 18 

2y = 18 - 6

\(\frac{2y}{2} = \frac{12}{2}\)

y = 6

179.

Express 1 + 2 log10\(^3\) in the form log10\(^9\) 

A.

log10\(^{90}\)

B.

log10\(^{19}\)

C.

log10\(^{9}\)

D.

log10\(^{6}\)

Correct answer is A

1 + 2log\(_{10}^3\)

= log\(_{10}^{10} + log_{10}^{3^2}\)

= log\(_{10}^{10} + log_{10}^{9}\)

= log\(_{10}^{10 \times 90}\) = log\(_{10}^{90}\)

180.

Simplify; [(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{4}}\)]\(^{\frac{1}{3}}\)

A.

\(\frac{3}{4}\)

B.

\(\frac{9}{16}\)

C.

\(\frac{3}{8}\)

D.

\(\frac{1}{4}\)

Correct answer is C

[(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{4}}\)]\(^{\frac{1}{3}}\)

= [(\(\frac{9}{16}\))]\(^{\frac{3}{2}}\) x [(\(\frac{1}{16}\))\(^{\frac{3}{4}}\)]\(^{\frac{1}{3}}\)

= [(\(\sqrt{\frac{9}{10}}\))\(^3\) x (4\(\sqrt{\frac{1}{16}})^3\)]\(^{\frac{1}{3}}\)

= [(\(\frac{3}{4})^3 \times (\frac{1}{2})^3\)]\(^\frac{1}{3}\)

(\(\frac{27}{64} \times \frac{1}{8}\))\(^\frac{1}{3}\) = \({3}\sqrt{\frac{27}{64} \times \frac{1}{8}}\)

= \(\frac{3}{4} \times \frac{1}{2}\) = \(\frac{3}{8}\)