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Mathematics
WAEC / WASSCE 2001
Number and Numeration
Solution
Three observation posts P,Q and R are such that Q is due east of P and R is due north of Q. If |PQ| = 5km and |PR| = 10km, find |QR|
A
5.0km
B
7.5km
C
7.6km
D
8.7km
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\((PR)^2 = (PQ)^2 + (QR)^2\)
\(10^2 = 5^2 + (QR)^2\)
\((QR)^2 = 100 - 25\)
\(QR = \sqrt{75}\)
= \(8.660\)
\(\approxeq\) 8.7 km
Source: Myschool Past Questions Archive (Record #26499)
Mathematics
WAEC / WASSCE 2001
Number and Numeration
Solution
Express 25^\circ 45' in decimal (Hint: 1^\circ = 60')
A
25.75o
B
25.55o
C
25.45o
D
25.15o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
25^\circ 45' = 25^\circ + \(\frac{45}{60}\)^\circ
= 25^\circ + 0.75^\circ
= 25.75^\circ
Source: Myschool Past Questions Archive (Record #26500)
Mathematics
WAEC / WASSCE 2001
Number and Numeration
Diagram
Solution
What is the range of their age?
Attached Figure / Diagram
A
14 years
B
20 years
C
30.5 years
D
31 years
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Range = 30.5 - 10.5
= 20 years
Source: Myschool Past Questions Archive (Record #26504)
Mathematics
WAEC / WASSCE 2001
Number and Numeration
Diagram
Solution
In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of ∆LMN is 18cm2, find the area of the quadrilateral MPQN
Attached Figure / Diagram
A
3cm2
B
6cm2
C
14cm2
D
24cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{LM}{LP} = \frac{3}{4}\)
\(\frac{Area of LMN}{Area of LPQ} = \frac{3^2}{4^2}\)
Area of LPQ = \(\frac{16}{9}\times 18 = 32 cm^2\)
Area of quadrilateral MPQN = 32 – 18 = \(14 cm^2\)
Source: Myschool Past Questions Archive (Record #26516)
Mathematics
WAEC / WASSCE 2001
Number and Numeration
Diagram
Solution
The diagram shows a triangular prism of length 7cm. The right - angled triangle PQR is a cross section of the prism |PR| = 5cm and |RQ| = 3cm. What is the area of the cross-section?
Attached Figure / Diagram
A
4 cm2
B
6cm2
C
15cm2
D
20cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
In \(\Delta\) RQP, QR\(^2\) + QP\(^2\) = RP\(^2\)
3\(^2\) + QP\(^2\) = 5\(^2\)
QP\(^2\) = 5\(^2\) - 3\(^2\)
QP = \(\sqrt{16}\)
= 4 cm
\(\therefore\) Area = \(\frac{1}{2} \times base \times height\)
= \(\frac{1}{2} \times 3 \times 4\)
= 6 cm\(^2\)
Source: Myschool Past Questions Archive (Record #26517)
Mathematics
WAEC / WASSCE 2001
Number and Numeration
Diagram
Solution
The diagram shows a triangular prism of length 7cm. The right - angled triangle PQR is a cross section of the prism |PR| = 5cm and |RQ| = 3cm. What is the volume of the prism?
Attached Figure / Diagram
A
28cm2
B
42cm2
C
70cm2
D
84cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Volume of prism = Area x height
In \(\Delta\) RQP, QR\(^2\) + QP\(^2\) = RP\(^2\)
3\(^2\) + QP\(^2\) = 5\(^2\)
QP\(^2\) = 5\(^2\) - 3\(^2\)
QP = \(\sqrt{16}\)
= 4 cm
\(\therefore\) Area = \(\frac{1}{2} \times base \times height\)
= \(\frac{1}{2} \times 3 \times 4\)
= 6 cm\(^2\)
Volume = 6 x 7
= 42 cm\(^3\)
Source: Myschool Past Questions Archive (Record #26518)
Mathematics
WAEC / WASSCE 2001
Number and Numeration
Solution
A solid cylinder of radius 7cm is 10 cm long. Find its total surface area.
A
\(70\pi cm^2\)
B
\(189\pi cm^2\)
C
\(210\pi cm^2\)
D
\(238\pi cm^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
S = \(2\pi r^2 + 2\pi rh\)
= \(2\pi r(r + h)\)
= \(2\pi (7) (7 + 10)\)
= \(238\pi cm^2\)
Source: Myschool Past Questions Archive (Record #26519)
Mathematics
WAEC / WASSCE 2001
Number and Numeration
Diagram
Solution
PQRS is a trapezium in which |PS| = 9cm, |QR| = 15cm, |PQ| = \(2\sqrt{3}, \angle PQR = 90^o and \angle QRS = 30^o\). Calculate the area of the trapezium
Attached Figure / Diagram
A
\(24\sqrt{3} cm^2\)
B
\(36\sqrt{3} cm^2\)
C
\(42\sqrt{3} cm^2\)
D
\(72\sqrt{3} cm^2\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Area of trapezium = \(\frac{1}{2}\)( a + b) x h
a = 9cm, b = 15cm, c = (15 - 9) = 6cm since height was not given, so we calculate for it using trig . ratio
h = 2\(\sqrt{3}\)cm
Area of trapezium = \(\frac{1}{2}\)( a + b ) x h = \(\frac{1}{2}\)( 9 + 15 ) x 2\(\sqrt{3}\)
= 24 x \(\sqrt{3}\) = 24\(\sqrt{3}\)cm\(^2\)
Source: Myschool Past Questions Archive (Record #26520)
Mathematics
WAEC / WASSCE 2001
Number and Numeration
Solution
Given that P = {b, d, e, f} and Q = {a, c, f, g} are subsets of the universal set U = {a,b, c, d, e, f, g}. Find P' ∩ Q
A
{a,c}
B
{a, c, d, g}
C
{c, d, g}
D
{a, c, g}
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
U = {a, b, c, d, e, f, g}
P = {b, d, e, f}
Q = {a, c, f, g}
P' = {a, c, g}
P' \(\cap\) Q = {a, c, g}
Source: Myschool Past Questions Archive (Record #26524)
Mathematics
WAEC / WASSCE 2001
Number and Numeration
Diagram
Solution
What is the length of \(\bar{RP}\)?
Attached Figure / Diagram
A
6
B
5
C
3
D
2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\bar{RP} = 3 - (-2)\)
= 5
Source: Myschool Past Questions Archive (Record #26529)
Mathematics
UTME / JAMB 2001
Number and Numeration
Diagram
Solution
The bar chart shows different colours of cars passing a particular point of a certain street in two minutes. What fraction of the cars is yellow
Attached Figure / Diagram
A
\(\frac{1}{5}\)
B
\(\frac{2}{25}\)
C
\(\frac{4}{15}\)
D
\(\frac{3}{25}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} \text{colour of cars} & \text{Number (frequency)} \\ \hline yellow & 3 \\white & 4\\ red & 8\\ green & 2\\ blue & 6\\ black & 2\\ \hline & 25 \\ \hline\end{array}\)
Thus, the fraction of the total numbers that are yellow is \(\frac{3}{25}\)
Source: Myschool Past Questions Archive (Record #33098)
Mathematics
UTME / JAMB 2001
Number and Numeration
Diagram
Solution
The histogram shows the distribution of passengers in taxis at a certain motor park. How many taxis have more than 4 passengers?
Attached Figure / Diagram
A
17
B
16
C
15
D
14
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} \text{no. of passengers} & \text{Number of taxis}\\ \hline 0.5 - 2.5 & 3\\ 2.5 - 4.5 & 4 \\ 4.5 - 6.5 & 7\\ 6.5 - 8.5 & 5\\ 8.5 - 10.5 & 4 \\ 10.5 - 12.5 & 1\\ \hline \text{Total} & 24 \end{array}\)
Thus, the taxi with more than 4 passengers
= 7 + 5 + 4 + 1 = 17
Source: Myschool Past Questions Archive (Record #33100)
Mathematics
NECO SSCE 2001
Number and Numeration
Solution
If s = \(\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}\)what does y equal?
A
\(\sqrt{\frac{(b^2 - a^2)}{(s^2 - x^2)}}\)
B
\(\sqrt{\frac{(b^2 - a^2)}{(s^2 \times 2)}}\)
C
\(\sqrt{\frac{x^2 - a^2 - b^2}{s}}\)
D
\(\frac{x^2 - a^2 - b^2}{s}\)
E
\(\sqrt{\frac{(b^2 x^2)}{(a^2 - s^2 x^2)}}\)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
s = \(\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}\)
s\(^2\) = \(\frac{a^2}{x^2} - \frac{b^2}{y^2}\)
\(\frac{b^2}{y^2}\) = \(\frac{a^2}{x^2}\) - s\(^2\)
\(\frac{b^2}{y^2}\) = \(\frac{a^2 - s^2 x^2}{x^2}\)
\(\frac{1}{y^2}\) = \((\frac{a^2 - s^2 x^2}{x^2}) \times \frac{1}{b^2}\)
\(\frac{1}{y^2}\) = \(\frac{a^2 - s^2 x^2}{b^2 x^2}\)
\(\therefore\) y\(^2\) = \(\frac{b^2 x^2}{a^2 - s^2 x^2}\)
y = \(\sqrt{\frac{b^2 x^2}{a^2 - s^2 x^2}}\)
Source: Myschool Past Questions Archive (Record #41771)
Mathematics
NECO SSCE 2001
Number and Numeration
Solution
Mr Aborowa bought a car for N200,000.00 and later sold it for N170,000.00. What is the percentage loss?
A
11.60%
B
7.60%
C
15%
D
17.65%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Using these:
Loss = C.p - S.p
: Percentage Loss = ( Loss X 100) \div C.p
=15 %
Source: Myschool Past Questions Archive (Record #41773)
Mathematics
NECO SSCE 2001
Number and Numeration
Simplify 27\(^{-\frac{1}{3}}\) \(\times\) 64\(^{-\frac{1}{3}}\) \(\times\) 4\(^{\frac{1}{3}}\)
A
48
B
12
C
\(\frac{4}{3}\)
D
\(\frac{1}{12}\)
E
\(\frac{1}{48}\)
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 #41781)