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Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
If \(\left(\frac{1}{4}\right)^{(2-y)} = 1\), find y.
A
-2
B
\(-\frac{1}{2}\).
C
\(\frac{1}{2}\)
D
2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(2^{-2(2-y)}-x=2^{0}; -4 + 2y = 0\\
2y = 4; y = 2\)
Source: Myschool Past Questions Archive (Record #26630)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm
A
1920cm2
B
592cm2
C
296cm2
D
148cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Total surfaced area of a cupboard = 2(lb + lh + bh)
l = length h = height b = base
l = 12cm h = 10cm b = 8cm
T.S.A = 2(\(12 \times 8 \times + 12 \times 10 + 8 \times 10\))
= 2\((96 + 120 + 80)cm^2 = 592cm^2\)
Source: Myschool Past Questions Archive (Record #26631)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
If \(\frac{x}{a+1}+\frac{y}{b}\) 1. Make y the subject of the relation
A
\(\frac{b(a-x+1)}{a+1}\)
B
\(\frac{a+1}{b(a-x+1)}\)
C
\(\frac{a(b-x+1)}{b+1}\)
D
\(\frac{b}{a(b-x+1)}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
If \(\frac{bx+y(a+1)}{b(a+1)}=1\\
bx + ya + y = ba + b; y(a+1) = ba+b-bx\\
y(a+1)=b(a+1-x); y = \frac{b(1+a-x}{a+1}\)
Source: Myschool Past Questions Archive (Record #26634)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
lf \(log_q p= r\), express p in terms of q and r
A
p =qr
B
p =rq
C
\(p = \frac{r}{q}\)
D
p=qr
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
If \(log_q p\) = r convert from logarithm to indices
P = q\(^r\)
Source: Myschool Past Questions Archive (Record #26635)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Diagram
Solution
In the diagram, ∆XYZ is similar to ∆PRQ, |XY| = 5cm, |XZ| =3.5cm and |PR| = 8cm. Find |PQ|
Attached Figure / Diagram
A
5.6 cm
B
11.2cm
C
11.4cm
D
28.0cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{PQ}{PR}=\frac{XZ}{XY}; \frac{PQ}{8}=\frac{3.5}{5}\\
PQ=\frac{8\times 3.5}{5}=\frac{28}{5}=5.6cm\)
Source: Myschool Past Questions Archive (Record #26640)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
Factorise 27p2x2 - 48y2.
A
9(3px - 4y)2
B
3(3px - 4y)(3px - 4y)
C
9(px - 4y)(3p x + 4y)
D
3(3px -4y)(3px +4y)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
27p2x2 - 48y2; 3(32 p2x2-42y2)
3[(3px) 2 - (4y) 2]; 3[(3px-4y)(3px+4y)]
Source: Myschool Past Questions Archive (Record #26641)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
What is the volume of a solid cylinder of diameter 7cm and height 7cm? (Take \(\pi = \frac{22}{7}\))
A
38.5cm3
B
77cm3
C
269.5cm3
D
1078cm3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of a solid cylinder = Base area x height
Base area \(=\pi r^2\) =\(\frac{22}{7} \times \frac{7}{2}\times \frac{7}{2}\) = \(\frac{77}{2}\)
Volume of a solid cylinder = \(\frac{77}{2}\times \frac{7}{1}\) = \(\frac{539}{2}cm^3\)
=269.5cm\(^3\)
Source: Myschool Past Questions Archive (Record #26642)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
Given that ξ = {1, 2, 3, . . . . . . ,10}, P= (x : x is prime) and Q = {y : y is odd}, find P'∩Q
A
{2}
B
{1,9}
C
{315.7}
D
{4, 6, 8, 10}
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
ξ = {1, 2, 3, . . . . . . ,10}, P = (2, 3, 5, 7) and Q = {1, 3, 5, 7, 9},
P'∩Q = {1, 4, 6, 8, 9, 10}∩{1, 3, 5, 7, 9} = {1, 9}
Source: Myschool Past Questions Archive (Record #26644)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Diagram
Solution
In the diagram, O is the centre of the circle where OS//QR and ∠SOR = 35º. Find the value of ∠QPR.
Attached Figure / Diagram
A
35o
B
45o
C
55o
D
70o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
∠SOR = ∠ORQ alternate angle.
Also ∠OQR = ∠OQR (Base angle of isosceles)
∠QOR = 180 – 2(35º) = 180 - 70º = 110º, ∠QPR = 1/2QOR = 1/2(110º) ∠QPR = 55º (theorem angle at center is twice angle at circumference)
Source: Myschool Past Questions Archive (Record #26648)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
Find the average of the first four prime numbers greater than10
A
20
B
19
C
17
D
15
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
First four prime numbers greater than 10 are 11, 13, 17, 19
The average \(= \frac{11+13+17+19}{4}=15\)
Source: Myschool Past Questions Archive (Record #26649)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
Given that \(\sqrt{128}+\sqrt{18}-\sqrt{K} = 7\sqrt{2}\), find K,
A
8
B
16
C
32
D
48
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\sqrt{128} +\sqrt{18}-\sqrt{k}=7\sqrt{2}\\
\sqrt{2\times 64}+\sqrt{9\times 2} - \sqrt{k} = 7\sqrt{2}\\
8\sqrt{2} + 3\sqrt{2} - \sqrt{k} = 7\sqrt{2}; 11\sqrt{2} - \sqrt{k} = 7\sqrt{2}\\
-\sqrt{k}=7\sqrt{2}-11\sqrt{2}; -\sqrt{k} = -4\sqrt{2}; \sqrt{k}=4\sqrt{2}\\
=\sqrt{4^2\times 2} = \sqrt{16\times 2}; \sqrt{k}=\sqrt{32}; k = 32\)
Source: Myschool Past Questions Archive (Record #26650)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
Find the range of values of x for which\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\)
A
x > 4
B
x > -4
C
x < 4
D
x < -4
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\)
\(\frac{3(x+2)-4(x+1)>6}{12}\); 3x + 6 – 4x – 4 > 6
- x + 2 > 6; - x > 4; x < -4
Source: Myschool Past Questions Archive (Record #26655)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
Simplify \(\frac{2}{a+b}-\frac{1}{a-b}\)
A
\(\frac{3}{a+b}\)
B
\(\frac{a-3b}{a^2-b^2}\)
C
\(\frac{3a-b}{a^2 – b^2}\)
D
\(\frac{a-3b}{a^2+b^2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Simplify \(\frac{2}{a+b}-\frac{1}{a-b}; \frac{2(a-b)-1(a+b)}{(a+b)(a-b)}\)
= \(\frac{2a-2b-a-b}{(a+b)(a-b)}\)
= \(\frac{a-3b}{a^2 - ab + ab - b^2}\)
= \(\frac{a-3b}{a^2-b^2}\)
Source: Myschool Past Questions Archive (Record #26657)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Diagram
The values of x when y = 3 are approximately
Attached Figure / Diagram
A
-4.7 and 1.4
B
-4.6 and 1.5
C
-3.6 and 0.4
D
-3.6 and 1.5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #26660)
Mathematics
WAEC / WASSCE 2004
Number and Numeration
Solution
The sides of two cubes are in the ratio 2:5. What is the ratio of their volumes?
A
4:5
B
8: 15
C
6:125
D
8:125
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The ratio of the two cubes = 2:5
Volume of the two cubes = 2\(^3\) : 5\(^3\) = 8 : 125
Source: Myschool Past Questions Archive (Record #26665)