WAEC Mathematics Past Questions & Answers - Page 45

221.

If m : n = 2 : 1, evaluate \(\frac{3m^2 - 2n^2}{m^2 + mn}\)

A.

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

B.

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

C.

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

D.

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

Correct answer is B

m = 2, n = 1

\(\frac{3m^2 - 2n^2}{m^2 _ mn}\)

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

= \(\frac{12 - 2}{4 + 2} = \frac{10}{6}\)

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

222.

Evaluate: 2\(\sqrt{28} - 3\sqrt{50} + \sqrt{72}\)  

A.

4\(\sqrt{7} - 21 \sqrt{2}\)

B.

4\(\sqrt{7} - 11 \sqrt{2}\)

C.

4\(\sqrt{7} - 9 \sqrt{2}\)

D.

4\(\sqrt{7} + \sqrt{2}\)

Correct answer is C

2\(\sqrt{28} - 3\sqrt{50} + \sqrt{22}\)

4\(\sqrt{7} - 15\sqrt{2} + 6\sqrt{2}\)

6\(\sqrt{7} - 9\sqrt{2}\)

223.

If 6, P, and 14 are consecutive terms in an Arithmetic Progression (AP), find the value of P.

A.

9

B.

10

C.

6

D.

8

Correct answer is B

6, p, 14

14 - p = p - 6 

14 + 6 = p - 6

14 + 6 = p + p

\(\frac{2p}{2}\)

= \(\frac{20}{2}\) 

p = 10

224.

If 23\(_y\) = 1111\(_{\text{two}}\), find the value of y

A.

4

B.

5

C.

6

D.

7

Correct answer is C

23\(_y\) = 1111\(_{\text{two}}\),

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

2y + 3 = 8 + 4 + 2 + 1 

2y + 3 = 15 

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

\(\frac{12}{2}\) 

y = 6

225.

Evaluate; \(\frac{\log_3 9 - \log_2 8}{\log_3 9}\) 

A.

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

B.

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

C.

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

D.

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

Correct answer is D

\(\frac{\log_3 9 - \log_2 8}{\log_3 9}\) 

= \(\frac{\log_3 3^2 - \log_2  2^3}{\log_3 3^2}\) 

= \(\frac{2 -3}{2}\)

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