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Mathematics
WAEC / WASSCE 1995
Sets, Logic & Venn Diagrams
Solution
If R = [2, 4, 6, 7] and S = [1, 2, 4, 8], then R∪S equal
A
[1,2,4,6,7,8]
B
[1,2,4,7,8]
C
[1,4.7,8]
D
[2.6.7]
E
[2.4]
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
R = {2, 4, 6, 7}; S = {1, 2, 4, 8}
R \(\cup\) S = {1, 2, 4, 6, 7, 8}
Source: Myschool Past Questions Archive (Record #23699)
Mathematics
WAEC / WASSCE 1995
Linear, Simultaneous & Quadratic Equations
Solution
Find the value(s) of x for which the expression is undefined: \(\frac{6x - 1}{x^2 + 4x - 5}\)
A
+4 or+1
B
-5 or +1
C
-5 or -1
D
+5 or -1
E
\(\frac{1}{6}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{6x - 1}{x^2 + 4x - 5}\)
The expression is undefined when \(x^2 + 4x - 5 = 0\)
\(x^2 + 5x - x - 5 = 0\)
\(x(x + 5) - 1(x + 5) = 0\)
\((x - 1)(x + 5) = 0\)
The expression is undefined when x = 1 or -5.
Source: Myschool Past Questions Archive (Record #23702)
Mathematics
WAEC / WASSCE 1995
Inequalities & Linear Programming
Diagram
Solution
Which of the following could be the inequality illustrated in the sketch graph above?
Attached Figure / Diagram
A
y≥2x+3
B
y≤-3x+3
C
y < 3x+2
D
y≤x +3
E
y≥3x+2.
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Gradient of the line = \(\frac{3 - 0}{0 - 1}\)
= -3
y = -3x + b.
Using (1,0), we have
0 = -3(1) + b
0 = -3 + b
b = 3
y = -3x + 3
\(\therefore\) The graph illustrates y \(\leq\) -3x + 3.
Source: Myschool Past Questions Archive (Record #23705)
Mathematics
WAEC / WASSCE 1995
Inequalities & Linear Programming
Solution
Solve the inequality: \(\frac{1}{3}(2x - 1) < 5\)
A
x < - 5
B
X<-6
C
X<7
D
x <8
E
x < 16
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{1}{3}(2x - 1) < 5\)
\(2x - 1 < 15\)
\(2x < 16\)
\(x < 8\)
Source: Myschool Past Questions Archive (Record #23706)
Mathematics
WAEC / WASSCE 1995
Linear, Simultaneous & Quadratic Equations
Solution
What is the smaller value of x for which x\(^2\) - 3x + 2= 0?
A
1
B
2
C
3
D
4
E
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x\(^2\) - 3x + 2 = 0
x\(^2\) - 2x - x + 2 = 0
x(x - 2) - 1(x - 2) = 0
(x - 2)(x - 1) = 0
x = 1 or 2. The smaller value of x = 1.
Source: Myschool Past Questions Archive (Record #23707)
Mathematics
WAEC / WASSCE 1995
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize the expression x(a - c) + y(c - a)
A
(a - c)(y - x)
B
(a - c)(x - y)
C
(a + c)(x - y)
D
(a + c)(x + y)
E
(a - c)(x + y)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x(a - c) + y(c - a)
= x(a - c) - y(a - c)
= (x - y)(a - c)
Source: Myschool Past Questions Archive (Record #23708)
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)