2007 - WAEC Mathematics Past Questions and Answers - page 3
21
If p \(\alpha \frac{I}{Q}\) which of the following is true?
A
q \(\alpha p^2\)
B
q \(\alpha \frac{1}{p^2}\)
C
q \(\alpha \sqrt{p}\)
D
q \(\alpha \frac{1}{p}\)
correct option: d
p \(\alpha \frac{I}{Q}\); p \(\frac{k}{q}\) (where k is constant)
q = \(\frac{k}{p}\)
q \(\alpha \frac{1}{p}\)
Users' Answers & Commentsq = \(\frac{k}{p}\)
q \(\alpha \frac{1}{p}\)
22
Simplify 3\(\sqrt{45} - 12\sqrt{15} + 16\sqrt{20}\), leaving your answer in surd form
A
29\(\sqrt{5}\)
B
14\(\sqrt{15}\)
C
12\(\sqrt{15}\)
D
11\(\sqrt{15}\)
correct option: a
3 \(\sqrt{45} - 12\sqrt{5} + 16\sqrt{20}\)
= 3 x \(\sqrt{9 \times 5} - 12 \times \sqrt{5} + 16 \times \sqrt{4 \times 5}\)
= 3 x 3 x \(\sqrt{5} - 12 \times \sqrt{5} + 16 \times 2 \times \sqrt{5}\)
= 9\(\sqrt{5} - 2 \sqrt{5} + 32 \sqrt{5}\)
= 9\(\sqrt{5} + 32\sqrt{5} - 12\sqrt{5}\)
= 29\(\sqrt{5}\)
Users' Answers & Comments= 3 x \(\sqrt{9 \times 5} - 12 \times \sqrt{5} + 16 \times \sqrt{4 \times 5}\)
= 3 x 3 x \(\sqrt{5} - 12 \times \sqrt{5} + 16 \times 2 \times \sqrt{5}\)
= 9\(\sqrt{5} - 2 \sqrt{5} + 32 \sqrt{5}\)
= 9\(\sqrt{5} + 32\sqrt{5} - 12\sqrt{5}\)
= 29\(\sqrt{5}\)
23
Which of the following statement is true for the ste P = {-3.2 \(\leq\) x < 5} where x is an integer?
A
least value of x is -3.2
B
least value of x is -3
C
greatest value of x is 4.9
D
greatest value of x is 5
correct option: b
p = {-3.2.....4.9}; Since x is an integer
least value of x is -3
Users' Answers & Commentsleast value of x is -3
24
Simplify \(\frac{3x^3}{(3x)^3}\)
A
1
B
\(\frac{1}{3}\)
C
\(\frac{1}{9}\)
D
\(\frac{1}{27}\)
correct option: c
\(\frac{3x^3}{(3x)^3}\) = \(\frac{3 \times x^3}{3^3 \times x^3}\)
= \(\frac{3 \times x^3}{3 \times 3 \times 3 \times x^3}\)
= \(\frac{1}{3^2}\)
= \(\frac{1}{9}\)
Users' Answers & Comments= \(\frac{3 \times x^3}{3 \times 3 \times 3 \times x^3}\)
= \(\frac{1}{3^2}\)
= \(\frac{1}{9}\)
25
N140,000 is shared between Abu, Kayode and Uche. Abu has twice as much as Kayode and Kayode has twice as much as Uche. What is Kayode'sshare?
A
N80,000
B
N40,000
C
N2,000
D
10,000
correct option: b
Let Abu's share = 2x;
Kayode's = x
Uche's share = \(\frac{x}{2}\)
Total: 2x + x + \(\frac{x}{2}\) = N140,000
\(\frac{7x}{2}\) = N140,000
x = \(\frac{280,000}{7}\) = N40,000
Kayode's share = N40,000
Users' Answers & CommentsKayode's = x
Uche's share = \(\frac{x}{2}\)
Total: 2x + x + \(\frac{x}{2}\) = N140,000
\(\frac{7x}{2}\) = N140,000
x = \(\frac{280,000}{7}\) = N40,000
Kayode's share = N40,000
26
I am x years old and my brother is 3 years older. How old was my brother last year?
A
(x - 4)years
B
(x + 2) years
C
(3x - 10years
D
(3x + 1)years
correct option: b
I am x years old; My brother = 3 + x; My brother
last year = (3 + x) - 1 = x + 3 - 1
= (x + 2) years
Users' Answers & Commentslast year = (3 + x) - 1 = x + 3 - 1
= (x + 2) years
27
For what value of x is the expression \(\frac{2x - 1}{x + 3}\) not defined?
A
3
B
2
C
\(\frac{1}{2}\)
D
-3
28
If x = 3, Y = 2 and z = 4, what is the value of 3x2 - 2y + z?
A
17
B
27
C
35
D
71
correct option: b
x = 3, y = 2, z = 4
3x2 - 2y + z
= 3(3)2 - 2(2) + 4
3(9) - 4 + 4 = 27
Users' Answers & Comments3x2 - 2y + z
= 3(3)2 - 2(2) + 4
3(9) - 4 + 4 = 27
29
Solve the simultaneous equations x + y = 2 and 3x - 2y = 1
A
x = 2 and y = 1
B
x = 1 and y = 1
C
x = 1 and y = 2
D
x = -1 and y = 1
correct option: b
x + y = 2........... (i)
3x - 2y = 1......(ii)
From (i): x = 2 - y ..........(iii)
subt. (2 - y) for x in (ii)
3(2 - y) 2y = 1
6 - 3y - 2y = 1
-5y = 1 - 6 = -5
y = \(\frac{-5}{-5}\) = 1
subst. (i) for y in (iii)
x = 2 - 1 = 1
x = 1, y = 1
Users' Answers & Comments3x - 2y = 1......(ii)
From (i): x = 2 - y ..........(iii)
subt. (2 - y) for x in (ii)
3(2 - y) 2y = 1
6 - 3y - 2y = 1
-5y = 1 - 6 = -5
y = \(\frac{-5}{-5}\) = 1
subst. (i) for y in (iii)
x = 2 - 1 = 1
x = 1, y = 1
30
If 8x-1 = \(\frac{1}{4}\), find x
A
-\(\frac{-5}{3}\)
B
-1
C
-\(\frac{1}{3}\)
D
\(\frac{1}{3}\)
correct option: d
8x-1 = \(\frac{1}{4}\)
23(x - 1 = 2-2
3x - 3 = -2
3x = -2 + 3
3x = 1
x = \(\frac{1}{3}\)
Users' Answers & Comments23(x - 1 = 2-2
3x - 3 = -2
3x = -2 + 3
3x = 1
x = \(\frac{1}{3}\)