2013 - WAEC Mathematics Past Questions and Answers - page 1
1
Multiply 2.7 x 10-4 by 6.3 x 106 and leave your answers in standard form
A
1.7 x 103
B
1.70 x 103
C
1.701 x 103
D
17.01 x 103
correct option: c
2.7 x 10-4 x 6.3 x 106
= 2.7 x 6.3 x 10-4 x 106
= 17.01 x 10-4 + 6
= 17.01 x 102
= 1.701 x 101 x 102
= 1.701 x 101 + 2
= 1.701 x 103
Users' Answers & Comments= 2.7 x 6.3 x 10-4 x 106
= 17.01 x 10-4 + 6
= 17.01 x 102
= 1.701 x 101 x 102
= 1.701 x 101 + 2
= 1.701 x 103
2
If 9(2 - x) = 3, find x
A
1
B
\(\frac{3}{2}\)
C
2
D
\(\frac{5}{2}\)
correct option: b
9(2 - x) = 3
32(2 - x) = 3
2(2 - x) = 1
4 - 2x = 1
-2x = 1 - 4
-2x = -3
x = \(\frac{-3}{-2}\)
x = \(\frac{3}{2}\)
Users' Answers & Comments32(2 - x) = 3
2(2 - x) = 1
4 - 2x = 1
-2x = 1 - 4
-2x = -3
x = \(\frac{-3}{-2}\)
x = \(\frac{3}{2}\)
3
In what number base is the addition 465 + 24 + 225 = 1050?
A
ten
B
nine
C
eight
D
seven
correct option: d
Users' Answers & Comments4
Simplify \(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)
A
9
B
4\(\frac{1}{2}\)
C
2
D
\(\frac{1}{2}\)
correct option: d
\(\frac{1\frac{7}{8} \times 2\frac{2}{5}}{6\frac{3}{4} \div \frac{3}{4}}\)
from numerator \(1 \frac{7}{8} \times 2 \frac{2}{5}\)
= \(\frac{15}{8} \times \frac{12}{5}\)
= \(\frac{3 \times 3}{2 \times 1} = \frac{9}{2}\)
from denominator \(6\frac{3}{4} \div \frac{3}{4}\)
= \(\frac{27}{4} \div \frac{3}{4}\)
= \(\frac{27}{4} \times \frac{4}{3}\)
= \(\frac{9 \times 1}{1 \times 1} = \frac{9}{1}\)
\(\frac{9}{2} \div \frac{9}{1} = \frac{9}{2} \times \frac{1}{9}\)
= \(\frac{1}{2}\)
Users' Answers & Commentsfrom numerator \(1 \frac{7}{8} \times 2 \frac{2}{5}\)
= \(\frac{15}{8} \times \frac{12}{5}\)
= \(\frac{3 \times 3}{2 \times 1} = \frac{9}{2}\)
from denominator \(6\frac{3}{4} \div \frac{3}{4}\)
= \(\frac{27}{4} \div \frac{3}{4}\)
= \(\frac{27}{4} \times \frac{4}{3}\)
= \(\frac{9 \times 1}{1 \times 1} = \frac{9}{1}\)
\(\frac{9}{2} \div \frac{9}{1} = \frac{9}{2} \times \frac{1}{9}\)
= \(\frac{1}{2}\)
5
If Un = n(n2 + 1), evaluate U5 - U4
A
18
B
56
C
62
D
80
correct option: 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
Users' Answers & CommentsU5 = 5(2 + 1)
= 5(25 + 1)
= 5(26) = 130
U4 = 4(42 + 1) = 4(16 + 1)
= 4(17) = 68
U5 - U4 = 130 - 68
= 62
6
If \(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\), find K
A
-2
B
-1
C
1
D
2
correct option: 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
Users' Answers & Comments\(\sqrt{50} - \frac{2}{\sqrt{2}}\) = 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
7
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 option: 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\(\frac{5}{9}\)%
Users' Answers & Commentserror = N72 - N68 = 4
actual value = N72
%error = \(\frac{4}{72} \times 100\)
= \(\frac{100}{18} = \frac{50}{9}\) = 5\(\frac{5}{9}\)%
8
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 option: 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)
Users' Answers & Comments24 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)
9
Simplify: \(\frac{x^2 - y^2}{(x + y)^2} + \frac{(x - y)^2}{(3x + 3y)}\)
A
\(\frac{x - y}{3}\)
B
x + y
C
\(\frac{3}{x - y}\)
D
x - y
correct option: c
\(\frac{x^2 - y^2}{(x + y)^2} + \frac{(x - y)^2}{(3x + 3y)}\)
\(\frac{(x + y)(x - y)}{(x + y)(x + y)} + \frac{(x - y)(x - y)}{3(x + y)}\)
= \(\frac{3}{x - y}\)
Users' Answers & Comments\(\frac{(x + y)(x - y)}{(x + y)(x + y)} + \frac{(x - y)(x - y)}{3(x + y)}\)
= \(\frac{3}{x - y}\)
10
Solve the inequality: \(\frac{2x - 5}{2} < (2 - x)\)
A
x > 0
B
x < \(\frac{1}{4}\)
C
x > 2\(\frac{1}{2}\)
D
x < 2\(\frac{1}{4}\)
correct option: d
\(\frac{2x - 5}{2} < \frac{(2 - x)}{1}\)
2x - 5 < 4 - 2x
2x + 2x < 4 + 5
4x < 9
x < \(\frac{9}{4}\)
x < 2\(\frac{1}{4}\)
Users' Answers & Comments2x - 5 < 4 - 2x
2x + 2x < 4 + 5
4x < 9
x < \(\frac{9}{4}\)
x < 2\(\frac{1}{4}\)