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Mathematics
WAEC / WASSCE 1995
Indices, Logarithms & Surds
Solution
If \(y \propto \frac{1}{x^2}\) and x = 3 when y = 4, find y when x = 2.
A
1
B
3
C
9
D
18
E
21
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(y \propto \frac{1}{x^2}\)
\(y = \frac{k}{x^2}\)
\(4 = \frac{k}{3^2}\)
\(k = 4 \times 3^2 = 36\)
\(y = \frac{36}{x^2}\)
When x = 2,
\(y = \frac{36}{2^2} = 9\)
Source: Myschool Past Questions Archive (Record #23709)
Mathematics
WAEC / WASSCE 1995
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation 3x\(^2\) + 25x -18 = 0
A
-3,2
B
-2,3
C
-2,9
D
-9,2/3
E
2/3, 9.
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
3x\(^2\) + 25x - 18 = 0
3x\(^2\) + 27x - 2x - 18 = 0
3x(x + 9) - 2(x + 9) = 0
(3x - 2)(x + 9) = 0
x = \(\frac{2}{3}\) or x = -9.
Source: Myschool Past Questions Archive (Record #23710)
Mathematics
WAEC / WASSCE 1995
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation (x +2)(x - 7) = 0
A
x = 1 or 8
B
x = -2 or 7
C
x = -4 or 5
D
x = -3 or 6
E
x= -5 or -2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(x + 2)(x - 7) = 0
x + 2 = 0 \(\implies\) x = -2
x - 7 = 0 \(\implies\) x = 7
x = -2 or 7
Source: Myschool Past Questions Archive (Record #23711)
Mathematics
WAEC / WASSCE 1995
Linear, Simultaneous & Quadratic Equations
Solution
Solve the following simultaneous equations: x+ y = 3/2; x - y = 5/2 and use your result to find the value of 2y + x
A
-2
B
-1
C
1/2
D
1
E
31/2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x + y = \(\frac{3}{2}\) ... (i)
x - y = \(\frac{5}{2}\) ... (ii)
(i) - (ii):
2y = \(\frac{-2}{2}\) = -1
y = \(-\frac{1}{2}\)
x + y = \(\frac{3}{2}\)
x - \(\frac{1}{2}\) = \(\frac{3}{2}\)
x = \(\frac{3}{2} + \frac{1}{2}\)
= \(\frac{4}{2}\)
x = 2
\(\therefore\) 2y + x = 2(\(-\frac{1}{2}\)) + 2
= -1 + 2 = 1.
Source: Myschool Past Questions Archive (Record #23728)
Mathematics
WAEC / WASSCE 1995
Differentiation & Applications
Diagram
Use the graph of y = 3x\(^2\) + x - 7 above to answer the question
What is the minimum value of y?
Attached Figure / Diagram
A
-10
B
-7
C
-4
D
-1
E
2
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 #23730)
Mathematics
WAEC / WASSCE 1995
Linear, Simultaneous & Quadratic Equations
Diagram
Use the graph of y = 3x\(^2\) + x - 7 above to answer the question
Find the roots of the equation y=3x\(^2\) + x - 7
Attached Figure / Diagram
A
1.0 And -1.2
B
1.1and-1.3
C
1.4and-1.7
D
2.0 and -1.9
E
2.4 and -2.0
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 #23732)
Mathematics
WAEC / WASSCE 1995
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram above. |AB| = 12cm, |AE| = 8cm, |DCl = 9cm and AB||DC. Calculate |EC|
Attached Figure / Diagram
A
10cm
B
9cm
C
8cm
D
7cm
E
6cm
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
|AB| = 12 cm; |DC| = 9 cm; |AE| = 8 cm.
\(\Delta\) ABE and \(\Delta\) EDC are similar triangles. Hence,
\(\frac{|AB|}{|DC|} = \frac{|AE|}{|EC|}\)
\(\frac{12}{9} = \frac{8}{|EC|}\)
\(\therefore |EC| = \frac{9 \times 8}{12}\)
= 6 cm
Source: Myschool Past Questions Archive (Record #23734)
Mathematics
WAEC / WASSCE 1995
Plane Geometry, Polygons & Circle Theorems
Solution
The diagonals AC and BD of a rhombus ABCD are 16cm and 12cm long respectively. Calculate the area of the rhombus.
A
24cm2
B
36cm2
C
48cm2
D
60cm2
E
96cm2
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
Area of rhombus = \(\frac{pq}{2}\)
where p and q are the diagonals of the rhombus.
\(\therefore A = \frac{16 \times 12}{2}\)
= 96 cm\(^2\)
Source: Myschool Past Questions Archive (Record #23736)
Mathematics
WAEC / WASSCE 1995
Plane Geometry, Polygons & Circle Theorems
Solution
A water tank of height \(\frac{1}{2}\) m has a square base of side \(1\frac{1}{2}\) m. lf it is filled with water from a water tanker holding 1500 litres, how many litres of water are left in the water tanker? [1000 litres = 1m\(^3\)]
A
37.5litres
B
375 litres
C
3750 litres
D
37500 litres
E
375000 litres
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Volume of water taken by the tank = \(\frac{3}{2} \times \frac{3}{2} \times \frac{1}{2}\)
= \(\frac{9}{8} m^3\)
= \(\frac{9}{8} \times 1000\)
= 1125 litres
\(\therefore\) Water left = (1500 - 1125) litres
= 375 litres.
Source: Myschool Past Questions Archive (Record #23738)
Mathematics
WAEC / WASSCE 1995
Mensuration (Areas, Perimeters & Volumes)
Solution
A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take \pi = 22/7]
Find the total surface area of the container
A
35cm3
B
154cm3
C
220cm2
D
528cm2
E
770cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
T.S.A of a cylinder = \(2\pi r^2 + 2\pi rh\)
= \(2\pi r(r + h)\)
= \(2 \times \frac{22}{7} \times 7 \times (7 + 5)\)
= \(44 \times 12\)
= \(528 cm^2\)
Source: Myschool Past Questions Archive (Record #23740)
Mathematics
WAEC / WASSCE 1995
Mensuration (Areas, Perimeters & Volumes)
Solution
A cylindrical container, closed at both ends, has a radius of 7cm and height 5cm [Take \pi = 22/7]
What is the volume of the container?
A
35cm3
B
154cm3
C
220cm3
D
528cm3
E
770cm3
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
\(V = \pi r^2 h\)
\(V = \frac{22}{7} \times 7 \times 7 \times 5\)
= 770 cm\(^3\)
Source: Myschool Past Questions Archive (Record #23741)
Mathematics
WAEC / WASSCE 1995
Mensuration (Areas, Perimeters & Volumes)
Solution
Find the total surface area of solid circular cone with base radius 3cm and slant height 4cm. [Take \pi = 22/7]
A
37 5/7cm2
B
66cm2
C
75 3/7cm2
D
78 2/7cm2
E
88cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
T.S.A of a cone = \(\pi r^2 + \pi rl\)
= \(\frac{22}{7} \times 3^2 + \frac{22}{7} \times 3 \times 4\)
= \(\frac{198}{7} + \frac{264}{7}\)
= \(\frac{462}{7}\)
= 66 cm\(^2\)
Source: Myschool Past Questions Archive (Record #23742)
Mathematics
WAEC / WASSCE 1995
Mensuration (Areas, Perimeters & Volumes)
Solution
A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere.
A
3cm
B
6cm
C
9cm
D
12cm
E
More information is needed
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(Volume = \frac{4}{3} \pi r^3 = k\) ...(i)
\(S.A = 4\pi r^2 = k\) ... (ii)
Divide (i) by (ii),
\(\frac{4}{3} \pi r^3 \div 4\pi r^2 = \frac{k}{k}\)
\(\frac{r}{3} = 1 \implies r = 3cm\)
Diameter = 2 x 3cm = 6cm
Source: Myschool Past Questions Archive (Record #23743)
Mathematics
WAEC / WASSCE 1995
Mensuration (Areas, Perimeters & Volumes)
Diagram
Solution
The diagram above shows a cone with the dimensions of its frustrum indicated. Calculate the height of the cone.
Attached Figure / Diagram
A
12cm
B
15cm
C
18cm
D
24cm
E
30cm
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Considering the smaller and larger triangle, these two are similar triangles. Hence,
If the height of the smaller triangle = h,
\(\therefore \frac{h}{6} = \frac{h + 12}{12}\)
\(12h = 6h + 72 \implies 6h = 72\)
\(h = 12 cm\)
\(\therefore\) The height of the cone = 12 + 12 = 24 cm
Source: Myschool Past Questions Archive (Record #23744)
Mathematics
WAEC / WASSCE 1995
Mensuration (Areas, Perimeters & Volumes)
Solution
The positions of two countries P and Q are (15^\circN, 12^\circE) and (65^\circN, 12^\circE) respectively. What is the difference in latitude?
A
104o
B
100o
C
80o
D
50o
E
24o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Latitudinal difference = 65^\circ - 15^\circ
= 50^\circ
Source: Myschool Past Questions Archive (Record #23745)