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Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
Given that \(81\times 2^{2n-2} = K, find \sqrt{K}\)
A
\(4.5\times 2^{n}\)
B
\(4.5\times 2^{2n}\)
C
\(9\times 2^{n-1}\)
D
\(9\times 2^{2n}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(K = 81 \times 2^{2n - 2}\)
\(\sqrt{K} = \sqrt{81 \times 2^{2n - 2}}\)
= \(9 \times 2^{n - 1}\)
Source: Myschool Past Questions Archive (Record #26396)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{4}{x+1}-\frac{3}{x-1}\)
A
\(\frac{x+7}{x^2 - 1}\)
B
\(\frac{x-7}{x^2 + 1}\)
C
\(\frac{x-7}{x^2 - 1}\)
D
\(\frac{x-11}{x^2 - 1}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{4}{x+1}-\frac{3}{x-1} \\
=\frac{4x - 4 - 3x - 3}{(x+1)(x-1)}=\frac{x-7}{x^2 - 1}\)
Source: Myschool Past Questions Archive (Record #26397)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
If \(tan x = \frac{1}{\sqrt{3}}\), find cos x - sin x such that \(0^o \leq x \leq 90^o\)
A
\(\frac{\sqrt{3}+1}{2}\)
B
\(\frac{2}{\sqrt{3}+1}\)
C
\(\frac{\sqrt{3}-1}{2}\)
D
\(\frac{2}{\sqrt{3}-1}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\cos x = \frac{\sqrt{3}}{2}\)
\(\sin x = \frac{1}{2}\)
\(\cos x - \sin x = \frac{\sqrt{3} - 1}{2}\)
Source: Myschool Past Questions Archive (Record #26399)
Mathematics
WAEC / WASSCE 1999
Trigonometry, Elevation & Bearings
Solution
From the top of a cliff 20m high, a boat can be sighted at sea 75m from the foot of the cliff. Calculate the angle of depression of the boat from the top of the cliff
A
14.9 o
B
15.5 o
C
74.5 o
D
75.1 o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
From the diagram above:
\(\tan \theta = \frac{20}{75} = 0.267\)
\(\theta = \tan^{-1} 0.267 = 14.93^\circ\)
\(\approxeq\) 14.9^\circ
Source: Myschool Past Questions Archive (Record #26400)
Mathematics
WAEC / WASSCE 1999
Trigonometry, Elevation & Bearings
Diagram
Solution
From the diagram above. ABC is a triangle inscribed in a circle center O. ∠ACB = 40º and |AB| = x cm. Calculate the radius of the circle.
Attached Figure / Diagram
A
\(\frac{x}{sin 40^o}\)
B
\(\frac{x}{cos 40^o}\)
C
\(\frac{x}{2 sin 40^o}\)
D
\(\frac{x}{2 cos 40^o}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
In the diagram given in the question, < ABC = 90º ( < in a semi-circle)
In triangle ABC, Sin 40º = \(\frac{x}{|AC|}\)
|AC| = \(\frac{x}{sin40º}\)
Since |AC| is a diameter, radius is half of |AC| = \(\frac{x}{2sin40º}\)
Source: Myschool Past Questions Archive (Record #26401)
Mathematics
WAEC / WASSCE 1999
Trigonometry, Elevation & Bearings
Diagram
Solution
The diagram shows the position of three ships A, B and C at sea. B is due north of C such that |AB| = |BC| and the bearing of B from A = 040^\circ. What is the bearing of A from C
Attached Figure / Diagram
A
040o
B
070o
C
110o
D
290o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
< ABC = 40^\circ (alternate angles)
\(\therefore\) < ACB = \(\frac{180^\circ - 40^\circ}{2}\)
= 70^\circ
\(\therefore\) Bearing of A from C = 360^\circ - 70^\circ
= 290^\circ
Source: Myschool Past Questions Archive (Record #26402)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
A pole of length L leans against a vertical wall so that it makes an angle of 60o with the horizontal ground. If the top of the pole is 8m above the ground, calculate L.
A
\(16\sqrt{3}m\)
B
\(4\sqrt{3}m\)
C
\(\frac{\sqrt{3}}{16}\)
D
\(\frac{16\sqrt{3}}{3}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(sin 60 = \frac{8}{L} = 8 \div \frac{\sqrt{3}}{2}; L = \frac{8}{sin 60}=\frac{16}{\sqrt{3}}\)
When we rationalize gives \(\frac{16\sqrt{3}}{3}\)
Source: Myschool Past Questions Archive (Record #26403)
Mathematics
WAEC / WASSCE 1999
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PQST and QRST are parallelograms. Calculate the area of the trapezium PRST.
Attached Figure / Diagram
A
60cm2
B
50cm2
C
40cm2
D
30cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
PR = 4 + 4 = 8 cm
Area of trapezium = \(\frac{1}{2} (a + b) h\)
= \(\frac{1}{2} (4 + 8) \times 5\)
= 30 cm\(^2\)
Source: Myschool Past Questions Archive (Record #26404)
Mathematics
WAEC / WASSCE 1999
Mensuration (Areas, Perimeters & Volumes)
Solution
The height of a pyramid on square base is 15cm. If the volume is 80cm\(^3\), find the length of the side of the base
A
3.3cm
B
5.3cm
C
4.0cm
D
8.0cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume = \(\frac{1}{3} b^2 h\)
\(\therefore b = \sqrt{\frac{3v}{h}}\)
\(b = \sqrt{\frac{3(80)}{15}} \)
\(b = \sqrt{16} = 4.0 cm\)
Source: Myschool Past Questions Archive (Record #26405)
Mathematics
WAEC / WASSCE 1999
Indices, Logarithms & Surds
Solution
Simplify 3.72 x 0.025 and express your answer in the standard form
A
\(9.3\times 10^3\)
B
\(9.3\times 10^2\)
C
\(9.3\times 10^{-2}\)
D
\(9.3\times 10^{-3}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(3.72 \times 0.025 = 0.093 = 9.3\times 10^{-2}\)
Source: Myschool Past Questions Archive (Record #26406)
Mathematics
WAEC / WASSCE 1999
Number Bases & Modular Arithmetic
Solution
Two numbers 2\(4_x\) and 31\(_y\) are equal in value when converted to base ten. Find the equation connecting x and y
A
2x = 3(y - 1)
B
4x - y = 1
C
3y + 2x = 3
D
3y = 2 (x + 3)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
24\(_x\) = 31\(_y\)
\(2 \times x^1 + 4 \times x^0 = 3 \times y^1 + 1 \times y^0\)
\(2x + 4 = 3y + 1 \implies 2x = 3y + 1 - 4\)
\(2x = 3y - 3 = 3(y - 1)\)
Source: Myschool Past Questions Archive (Record #26407)
Mathematics
WAEC / WASSCE 1999
Linear, Simultaneous & Quadratic Equations
Solution
A car travel at x km per hour for 1 hour and at y km per hour for 2 hours. Find its average speed
A
\(\frac{2x + 2y}{3}kmh^{-1}\)
B
\(\frac{x + y}{3}kmh^{-1}\)
C
\(\frac{x + 2y}{3}kmh^{-1}\)
D
\(\frac{2x + y}{3}kmh^{-1}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Travelled x km/h for 1 hour \(\therefore\) traveled x km in the first hour.
Traveled y km/h for 2 hours \(\therefore\) traveled 2y km in the next 2 hours.
Average speed = \(\frac{x + 2y}{1 + 2}\)
= \(\frac{x + 2y}{3} kmh^{-1}\)
Source: Myschool Past Questions Archive (Record #26408)
Mathematics
WAEC / WASSCE 1999
Fractions, Decimals, Percentages & Approximations
Solution
The height and base of a triangle are in ratio 1:3 respectively. If the area of the triangle is 216 cm\(^2\), find the length of the base.
A
24cm
B
36cm
C
72cm
D
144cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area = \(\frac{1}{2} \times base \times height\)
\(height : base = 1 : 3\)
\(\implies base = 3 \times height\)
Let height = h;
Area = \(\frac{1}{2} \times 3h \times h = 216\)
\(3h^2 = 216 \times 2 = 432\)
\(h^2 = \frac{432}{3} = 144\)
\(h = \sqrt{144} = 12.0 cm\)
\(\therefore base = 3 \times 12 = 36 cm\)
Source: Myschool Past Questions Archive (Record #26409)
Mathematics
WAEC / WASSCE 1999
Mensuration (Areas, Perimeters & Volumes)
Solution
Water flows from a tap into cylindrical container at the rate 5\picm\(^3\) per second. If the radius of the container is 3cm, calculate the level of water in the container at the end of 9 seconds.
A
2cm
B
5cm
C
8cm
D
15cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Volume of water after 9 seconds = \(5\pi \times 9 = 45\pi cm^3\)
Volume of cylinder = \(\pi r^2 h\)
\(\therefore \pi r^2 h = 45\pi\)
\(\pi \times 3^2 \times h = 45\pi\)
\(\implies 9h = 45 \)
\(h = 5 cm\)
(where h = height of the water after 9 secs)
Source: Myschool Past Questions Archive (Record #26410)
Mathematics
WAEC / WASSCE 1999
Inequalities & Linear Programming
Solution
Amina had m mangoes. She ate 3 and shared the remainder equally with her brother Uche. Each had at least 10. Which of the following inequalities represents the statements above.
A
\(\frac{m}{2}-3\le 10\)
B
\(\frac{m}{2}-3\ge 10\)
C
\(\frac{m-3}{2}\ge10\)
D
\(\frac{m-3}{2}\le10\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Total number of mangoes = m
Amina ate 3 mangoes \(\implies\) Remainder = m - 3
Shared equally with Uche \(\implies \frac{m - 3}{2}\)
\(\frac{m - 3}{2} \geq 10\)
Source: Myschool Past Questions Archive (Record #26411)