2015 - WAEC Mathematics Past Questions and Answers - page 1
1
If {X: 2 d- x d- 19; X integer} and 7 + x = 4 (mod 9), find the highest value of x
A
2
B
5
C
15
D
18
correct option: c
Users' Answers & Comments2
The sum 110112, 11112 and 10m10n02. Find the value of m and n.
A
m = 0, n = 0
B
m = 1, n = 0
C
m = 0, n = 1
D
m = 1, n = 1
correct option: c
Users' Answers & Comments3
A trader bought an engine for $15,000.00 outside Nigeria. If the exchange rate is $0.075 to N1.00, how much did the engine cost in Naira?
A
N250,000.00
B
N200,000.00
C
N150,000.00
D
N100,000.00
correct option: b
N1.00 = $0.075
N X = $15,000
X = \(\frac{1.00 \times 15000}{0.075}\)
= N200,000.00
4
If \(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\), find the value of x.
A
1
B
\(\frac{1}{2}\)
C
-\(\frac{1}{2}\)
D
-1
correct option: b
\(\frac{27^x \times 3^{1 - x}}{9^{2x}} = 1\)
\(\frac{3^{3x} \times 3^{1 - x}}{3^{2(2 - x)}} = 3^0\)
\(3^{3x} \times 3^{1 - x} \div 3^{4x} = 3^0\)
\(3^{(3x + 1 - x - 4x)} = 3^0\)
\(3^{(1 - 2x)} = 3^0\)
since the bases are equal,
1 - 2x = 0
- 2x = -1
x = \(\frac{1}{2}\)
Users' Answers & Comments\(\frac{3^{3x} \times 3^{1 - x}}{3^{2(2 - x)}} = 3^0\)
\(3^{3x} \times 3^{1 - x} \div 3^{4x} = 3^0\)
\(3^{(3x + 1 - x - 4x)} = 3^0\)
\(3^{(1 - 2x)} = 3^0\)
since the bases are equal,
1 - 2x = 0
- 2x = -1
x = \(\frac{1}{2}\)
5
Find the 7th term of the sequence: 2, 5, 10, 17, 6,...
A
37
B
48
C
50
D
63
correct option: c
Users' Answers & Comments6
Given that logx 64 = 3, evaluate x log8
A
6
B
9
C
12
D
24
correct option: c
If logx 64 = 3, then 64 = x3
43 = x3
Since the indices are equal,
x = 4
Hence, x log28 = log28x
= log284
= log2(23)4
= log2212
= 1 log2 = 1(1)
= 12
Users' Answers & Comments43 = x3
Since the indices are equal,
x = 4
Hence, x log28 = log28x
= log284
= log2(23)4
= log2212
= 1 log2 = 1(1)
= 12
7
If 2n = y, Find 2\(^{(2 + \frac{n}{3})}\)
A
4y\(^\frac{1}{3}\)
B
4y\(^-3\)
C
2y\(^\frac{1}{3}\)
D
2y\(^-3\)
correct option: a
If 2n = y,
then, 2\(^{(2 + \frac{n}{3})}\) = 22 x 2\(^\frac{n}{3}\)
= 4 x (2n)\(^{\frac{1}{3}}\)
But y = 2n, hence
2\(^{(2 + \frac{n}{3})}\) = 4 x y\(^{\frac{1}{3}}\)
= 4y\(^\frac{1}{3}\)
Users' Answers & Commentsthen, 2\(^{(2 + \frac{n}{3})}\) = 22 x 2\(^\frac{n}{3}\)
= 4 x (2n)\(^{\frac{1}{3}}\)
But y = 2n, hence
2\(^{(2 + \frac{n}{3})}\) = 4 x y\(^{\frac{1}{3}}\)
= 4y\(^\frac{1}{3}\)
8
Factorize completely: 6ax - 12by - 9ay + 8bx
A
(2a - 3b)(4x + 3y)
B
(3a + 4b)(2x - 3y)
C
(3a - 4b)(2x + 3y)
D
(2a + 3b)(4x -3y)
correct option: b
6ax - 12by - 9ay + 8bx
= 6ax - 9ay + 8bx - 12by
= 3a(2x - 3y) + 4b(2x - 3y)
= (3a + 4b)(2x - 3y)
Users' Answers & Comments= 6ax - 9ay + 8bx - 12by
= 3a(2x - 3y) + 4b(2x - 3y)
= (3a + 4b)(2x - 3y)
9
Find the equation whose roots are \(\frac{3}{4}\) and -4
A
4x2 - 13x + 12 = 0
B
4x2 - 13x - 12 = 0
C
4x2 + 13x - 12 = 0
D
4x2 + 13x + 12 = 0
correct option: c
Let x = \(\frac{3}{4}\) or x = -4
i.e. 4x = 3 or x = -4
(4x - 3)(x + 4) = 0
therefore, 4x2 + 13x - 12 = 0
Users' Answers & Commentsi.e. 4x = 3 or x = -4
(4x - 3)(x + 4) = 0
therefore, 4x2 + 13x - 12 = 0
10
If m = 4, n = 9 and r = 16., evaluate \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)
A
1\(\frac{5}{16}\)
B
1\(\frac{1}{16}\)
C
\(\frac{5}{16}\)
D
- 1\(\frac{37}{48}\)
correct option: d
If m = 4, n = 9, r = 16,
then \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)
= \(\frac{4}{9}\) - \(\frac{16}{9}\) + \(\frac{9}{16}\)
= \(\frac{64 - 258 + 81}{144}\)
= \(\frac{-111}{144}\)
= - 1\(\frac{37}{48}\)
Users' Answers & Commentsthen \(\frac{m}{n}\) - 1\(\frac{7}{9}\) + \(\frac{n}{r}\)
= \(\frac{4}{9}\) - \(\frac{16}{9}\) + \(\frac{9}{16}\)
= \(\frac{64 - 258 + 81}{144}\)
= \(\frac{-111}{144}\)
= - 1\(\frac{37}{48}\)