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Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
The base diameter of a cone is 14cm, and its volume is 462 cm3. Find its height. [Taken \(\pi = \frac{22}{7}\)]
A
3.5cm
B
5cm
C
7cm
D
9cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
From \(V = \frac{1}{3}\pi r^2 h. \hspace{1mm} r =\frac{14}{2}\\
462 = \frac{1}{3} \times \frac{22}{7} \times 7^2 \times h \\
h = \frac{3 \times 462}{22 \times 7}\\ h = 9\)
Source: Myschool Past Questions Archive (Record #26544)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
A number is selected at random from the set Y = {18, 19, 20, . . . 28, 29}. Find the probability that the number is prime.
A
\(\frac{1}{4}\)
B
\(\frac{3}{11}\)
C
\(\frac{1}{2}\)
D
\(\frac{3}{4}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Y = {18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29}
Number of prime numbers = 3
Prob(picking a prime number) = \(\frac{3}{12}\)
= \(\frac{1}{4}\)
Source: Myschool Past Questions Archive (Record #26545)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Diagram
The range of the distribution is
Attached Figure / Diagram
A
50
B
30
C
25
D
15
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #26547)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Diagram
The upper quartile of the distribution is
Attached Figure / Diagram
A
30
B
27.5
C
25
D
17.75
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #26548)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
Simplify \(\frac{2^{\frac{1}{2}}\times 8^{\frac{1}{2}}}{4}\)
A
1
B
2
C
4
D
16
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{2^{\frac{1}{2}}\times 8^{\frac{1}{2}}}{4}\\=\frac{2^{\frac{1}{2}}\times 2^{\frac{3}{2}}}{2^2}\\=2^{\frac{1}{2}}+2^{\frac{3}{2}}-2=2^0 = 1\)
Source: Myschool Past Questions Archive (Record #26551)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Diagram
In the diagram, |SR| = |RQ| and ∠PRQ = 58o ∠VQT = 19o, PQT, SQV and PSR are straight lines. Find ∠QPS
Attached Figure / Diagram
A
42o
B
39o
C
38o
D
30o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #26552)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
The volume of a cylinder of radius 14cm is 210cm3. What is the curved surface area of the cylinder?
A
15cm2
B
30cm2
C
616cm2
D
1262cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(V = \pi r^2 h\)
210 = \(\frac{22}{7} \times 14^2 \times\) h
h = \(\frac{210}{22 \times 28}\)
Curved surface area = 2\(\pi\) rh
= 2 \(\times \frac{22}{7} \times 14 \times \frac{210}{22 \times 26} = 30cm^2\)
Source: Myschool Past Questions Archive (Record #26554)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
Simplify \(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
A
\(7\sqrt{3}\)
B
\(10\sqrt{3}\)
C
\(14\sqrt{3}\)
D
\(18\sqrt{3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(3\sqrt{12} + 10\sqrt{3} - \frac{6}{\sqrt{3}}\)
= \(3(\sqrt{4 \times 3}) + 10\sqrt{3} - (\frac{6}{\sqrt{3}})(\frac{\sqrt{3}}{\sqrt{3}})\)
= \(6\sqrt{3} + 10\sqrt{3} - 2\sqrt{3}\)
= \(14\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #26555)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
Factorize m(2a-b)-2n(b-2a)
A
(2a-b)(2n-m)
B
(2a+b)(m-2n)
C
(2a-b)(m+2n)
D
(2a-b)(m-2n)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
m(2a - b) - 2n(b - 2a)
= m(2a - b) - (-2n)(2a - b)
= m(2a - b) + 2n(2a - b)
= (m + 2n)(2a - b)
Source: Myschool Past Questions Archive (Record #26556)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
If q oranges are sold for t Naira, how many oranges can be bought for p naira?
A
\(\frac{p}{2}t\)
B
\(\frac{qt}{p}\)
C
\(\frac{q}{pt}\)
D
\(\frac{pq}{t}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
q oranges = t naira
1 naira = \(\frac{q}{t}\)
p naira = \(p(\frac{q}{t})\)
= \(\frac{pq}{t}\) oranges
Source: Myschool Past Questions Archive (Record #26557)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Diagram
In the diagram, \(\bar{PS}\hspace{1mm} and \hspace{1mm}\bar{QT}\) are two altitudes of ∆PQR. Which of the following is equal to ∠RQT?
Attached Figure / Diagram
A
∠PQT
B
∠SRP
C
∠PQR
D
∠SPR
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #26560)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
Calculate and correct to two significant figures, the percentage error in approximating 0.375 to 0.4
A
2.0
B
2.5
C
6.6
D
6.7
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Measured value = 0.375
Approximation = 0.4
Error = 0.4 - 0.375 = 0.025
Error% = \(\frac{0.025}{0.375}\) x 100% = 6.67% = 6.7%
Source: Myschool Past Questions Archive (Record #26562)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Solution
Given that \(p = x-\frac{1}{x} and\hspace{1mm}q = x^2 + \frac{1}{x^2}\) express q in terms of p.
A
(p2 + 2)
B
(p - 2) 2
C
(p + 2) 2
D
(p2 - 2)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Given \(p = x - \frac{1}{x}\); \(q = x^2 + \frac{1}{x^2}\).
\(p^2 = (x - \frac{1}{x})(x - \frac{1}{x})\)
\(p^2 = x^2 + \frac{1}{x^2} - 2\)
\(p^2 = q - 2 \implies q = p^2 + 2\)
Source: Myschool Past Questions Archive (Record #26566)
Mathematics
WAEC / WASSCE 2002
Number and Numeration
Which of the following is not a rational number?
A
-5
B
\(\sqrt{4}\)
C
\(3\frac{3}{4}\)
D
\(\sqrt{90}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option D.
Source: Myschool Past Questions Archive (Record #26568)
Mathematics
NECO SSCE 2002
Number and Numeration
Solution
Given that the universal set U={14,15,16,17,18,19,20}, J ={16,19,20} and K= {14,15,18}, find (J' ∩ K')1.
A
{17}
B
{16, 17, 19, 20}
C
{1, 4, 15, 17, 18}
D
{14, 15, 16, 18, 19, 20}
E
{14, 15, 16, 17, 18, 19, 20}
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
U = {14,15,16,17,18,19,20}
J' = {14,15,17,18}
K' = {16,17,19,20}
(J' \(\cap\) K') = {17}
(J' \(\cap\) K')' = {14,15,16,18.19,20}
Source: Myschool Past Questions Archive (Record #41976)