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Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Solution
Which of the following is not a factors of 2p\(^2\) - 2?
A
2
B
p - 1
C
p + 1
D
2p - 2
E
2p + 1
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
2p\(^2\) - 2
2(p\(^2\) - 1)
= 2(p + 1)(p - 1)
Source: Myschool Past Questions Archive (Record #23497)
Mathematics
WAEC / WASSCE 1994
Linear, Simultaneous & Quadratic Equations
Solution
Find the quadratic equation whose roots are 3 and \(\frac{2}{3}\).
A
x2 - 11 / 3x + 6 = 0
B
x2 - 11x + 6 = O
C
3x2 - 11x + 2 = O
D
3X2 - 11x – 2 = 0
E
3x2 - 11x + 6 = 0
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
x = 3; x = \(\frac{2}{3}\).
(x - 3)(x - \(\frac{2}{3}\)) = 0
\(x^2 - \frac{2x}{3} - 3x + 2 = 0\)
\(x^2 - \frac{11x}{3} + 2 = 0\)
\(3x^2 - 11x + 6 = 0\)
Source: Myschool Past Questions Archive (Record #23498)
Mathematics
WAEC / WASSCE 1994
Linear, Simultaneous & Quadratic Equations
Solution
Which of the following is a root of the equation x\(^2\) +6x = 0?
A
0
B
1
C
2
D
3
E
It does not have any root.
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(x^2 + 6x = 0\)
\(x(x + 6) = 0\)
\(x = 0\) or \(x = -6\)
Source: Myschool Past Questions Archive (Record #23500)
Mathematics
WAEC / WASSCE 1994
Linear, Simultaneous & Quadratic Equations
Solution
Factorise: 6x\(^2\) + 7xy - 5y\(^2\)
A
(6x + 5y)(x - y)
B
(2x + 5y)(3x - y)
C
(3x + y)(2x - 5y)
D
(3x + 5y)(2x - y)
E
(2x + y)(3x - 5y)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(6x^2 + 7xy - 5y^2\)
= \(6x^2 + 10xy - 3xy - 5y^2\)
= \(2x(3x + 5y) - y(3x + 5y)\)
= \((2x - y)(3x + 5y)\)
Source: Myschool Past Questions Archive (Record #23504)
Mathematics
WAEC / WASSCE 1994
Indices, Logarithms & Surds
Solution
Solve the equation log8x - 4log8x = 2
A
1/4
B
1/2
C
1
D
2
E
4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
log\(_8\)x - 4log\(_8\)x = 2; log\(_8\)x - log\(_8\)x\(^4\) = 2
log\(_8\)(\(\frac{\text{x}}{x^4}\)) = 2
\(\frac{\text{x}}{x^4}\) = 8\(^2\) = \(\frac{1}{x^3}\) = 64
x\(^3\) = (\(\frac{1}{4}\))\(^3\);
x = \(\frac{1}{4}\)
Source: Myschool Past Questions Archive (Record #23505)
Mathematics
WAEC / WASSCE 1994
Indices, Logarithms & Surds
Solution
The angle subtended at the centre by a chord of a circle radius 6cm is 120^\circ. Find the length of the chord.
A
3cm
B
6cm
C
\(4\sqrt{2}\) cm
D
\(3\sqrt{3}\) cm
E
\(6\sqrt{3}\) cm
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(\frac{r}{6} = \sin 60 \)
\(r = 6 \sin 60\)
= \(6 \times \frac{\sqrt{3}}{2}\)
= \(3\sqrt{3}\)
Chord = 2r = \( 2 \times 3\sqrt{3}\)
= \(6\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #23506)
Mathematics
WAEC / WASSCE 1994
Mensuration (Areas, Perimeters & Volumes)
Solution
A cuboid of base 12.5cm by 20cm holds exactly 1 litre of water. What is the height of the cuboid? (1 litre =1000cm3)
A
2cm
B
4cm
C
5cm
D
8cm
E
10cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Volume of cuboid = length x breadth x height
12.5 x 20 x h = 1000
250h = 1000
h = 4 cm
Source: Myschool Past Questions Archive (Record #23507)
Mathematics
WAEC / WASSCE 1994
Fractions, Decimals, Percentages & Approximations
Solution
Two ships on the equator are on longitudes 45oW and 45oE respectively. How far are they apart along the equator, correct to 2 significant figures? (Take the radius of earth = 6400km and \pi = 22/7)
A
15,000km
B
10,000km
C
6,400km
D
5,000km
E
3,200km
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
D = \(\frac{\theta}{360}\) x 2\piR
45 + \(\frac{45}{360}\) x \(\frac{44}{7}\) x 6400
= 10057 ≅ 10000km
Source: Myschool Past Questions Archive (Record #23510)
Mathematics
WAEC / WASSCE 1994
Fractions, Decimals, Percentages & Approximations
Solution
Calculate, correct to 2 significant figures, the length of the arc of a circle of radius 3.5cm which subtends an angle of 75^\circ at the centre of the circle. [Take \pi = 22/7].
A
2.3cm
B
4.6cm
C
8cm
D
16cm
E
110cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Length of arc = \(\frac{\theta}{360} \times 2\pi r\)
= \(\frac{75}{360} \times 2 \times \frac{22}{7} \times 3.5\)
= \(4.583 cm\)
\(\approxeq\) 4.6 cm (to 2 sig. figs)
Source: Myschool Past Questions Archive (Record #23511)
Mathematics
WAEC / WASSCE 1994
Mensuration (Areas, Perimeters & Volumes)
Solution
A circle has radius x cm. What is the area of a sector of the circle with angle 135°, leaving the answer in terms of x and π?
A
\( \frac{\pi x^2}{8} \)
B
\( \frac{3\pi x^2}{8} \)
C
\( \frac{5\pi x^2}{8} \)
D
\( \frac{3\pi x}{8} \)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
A = θ 360 x πr2 = 135 360 x π x x2 = (3πx2)/8
Source: Myschool Past Questions Archive (Record #23513)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PQRS is a trapezium with PQ||SR. STR is a straight line, PSHQT, PTHQR. If |PQ| = 12cm and the height of the trapezium is 9cm, find its area.
Attached Figure / Diagram
A
96cm2
B
108cm2
C
135cm2
D
162cm2
E
216cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
A = 1/2(A + B)h = 1/2(24 + 12) x 9 = 162
Source: Myschool Past Questions Archive (Record #23515)
Mathematics
WAEC / WASSCE 1994
Fractions, Decimals, Percentages & Approximations
Solution
Two solid spheres have volumes 250cmo and 128cmo respectively. Find the ratio of their radii.
A
125:64
B
25:16
C
2:1
D
4:3
E
5:4
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
4/3πR3/4/3πr3 = 250/180 = (R/r)3 = 5:4
Source: Myschool Past Questions Archive (Record #23536)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Diagram
In the diagram ST and QR are parallel. |PS| = 6cm, |SQ| = 8cm and |PR] = 18 2/3. Find |PT|
Attached Figure / Diagram
A
7cm
B
8cm
C
8 2/3cm
D
10cm
E
10 2/3cm
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 #23537)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PQ||RS and angles are as shown. Find x
Attached Figure / Diagram
A
145o
B
150o
C
155o
D
160o
E
165o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Join PR to a pentagon
90 + 90 + 140 + 55 + x = 540o
x = 165o
Source: Myschool Past Questions Archive (Record #23538)
Mathematics
WAEC / WASSCE 1994
Plane Geometry, Polygons & Circle Theorems
IF the exterior angles of a quadilateral are yo, (2y + 5)o , (y + 15)o and (3y - 10)o, find yo
A
61.43
B
60
C
52.86
D
51.43
E
50
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option E.
Source: Myschool Past Questions Archive (Record #23540)