WAEC Mathematics Past Questions & Answers - Page 103

511.

Simplify: \(\frac{x^2 - y^2}{(x + y)^2} \div \frac{(x - y)^2}{(3x + 3y)}\)

A.

\(\frac{x - y}{3}\)

B.

x + y

C.

\(\frac{3}{x - y}\)

D.

x - y

Correct answer is C

\(\frac{x^2 - y^2}{(x + y)^2} \div \frac{(x - y)^2}{(3x + 3y)}\)

\(\frac{(x + y)(x - y)}{(x + y)(x + y)}\div \frac{(x - y)(x - y)}{3(x + y)}\)

= \(\frac{3}{x - y}\)

512.

Four oranges sell for Nx and three mangoes sell for Ny. Olu bought 24 oranges and 12 mangoes. How much did he pay in terms of x and y?

A.

N94x + 6y)

B.

N(6x + 4y)

C.

N(24x + 12y)

D.

N(12x + 24y)

Correct answer is B

4 oranges sell for Nx, 1 orange will sell for \(\frac{Nx}{4}\)

24 oranges will sell for: \(\frac{Nx}{4} \times 24\) = n6x

3 mangoes sell for Ny, 1 mango will sell for \(\frac{Ny}{3}\)

12 mangoes will sell for \(\frac{Ny}{3} \times 12\) = 4Ny

total money pay N6x + N4y = N(6x + 4y)

513.

A sales boy gave a change of N68 instead of N72. Calculate his percentage error

A.

4%

B.

5\(\frac{5}{9}\)%

C.

5\(\frac{15}{17}\)%

D.

7%

Correct answer is B

% error = \(\frac{error}{\text{actual value}} \times 100\)

error = N72 - N68 = 4

actual value = N72

%error = \(\frac{4}{72} \times 100\)

= \(\frac{100}{18} = \frac{50}{9}\) = 5\(\frac{5}{9}\)%

514.

If \(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\), find K

A.

-2

B.

-1

C.

1

D.

2

Correct answer is D

\(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\)

\(\sqrt{50} - \frac{2}{\sqrt{2}}\) = K\(\sqrt{8}\)

= \(\sqrt{2} \times 25 - \frac{2}{\sqrt{2}}\)

= K \(\sqrt{4 \times 2}\)

\(\frac{5\sqrt{2}}{1} - \frac{2}{\sqrt{2}}\) = 2K\(\sqrt{2}\)

\(\frac{5\sqrt{4} - 2}{\sqrt{2}} = 2K\sqrt{2}\)

\(\frac{10 - 2}{\sqrt{2}} = 2K \sqrt{2}\)

\(\frac{8}{\sqrt{2}} = \frac{2K\sqrt{2}}{1}\)

= 2k\(\sqrt{2} \times \sqrt{2}\) = 8

2k \(\sqrt{4}\) = 8

2k x 2 = 8

4k = 8

k = \(\frac{8}{4}\)

k = 2

515.

If Un = n(n2 + 1), evaluate U5 - U4

A.

18

B.

56

C.

62

D.

80

Correct answer is C

Un = n(n2 + 1)

U5 = 5(2 + 1)

= 5(25 + 1)

= 5(26) = 130

U4 = 4(42 + 1) = 4(16 + 1)

= 4(17) = 68

U5 - U4 = 130 - 68

= 62