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Mathematics
WAEC / WASSCE 1996
Linear, Simultaneous & Quadratic Equations
Solution
Expand (2x - 5)(x - 3)
A
x2 - 1x -15
B
2x2 - 11x + 15
C
22 - 5x - 8
D
x2 - 5x - 15
E
2x2 - 6x + 15
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
(2x - 5)(x - 3)
2x\(^2\) - 5x - 6x + 15
2x\(^2\) - 11x + 15
Source: Myschool Past Questions Archive (Record #23798)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify: \(\frac{5}{x - y} - \frac{4}{y - x}\)
A
9/x - y
B
9/y - x
C
1/x - y
D
1/y - x
E
y - 9x/x - y
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{5}{x - y} - \frac{4}{y - x}\)
= \(\frac{5(y - x) - 4(x - y)}{(x - y)(y - x)}\)
= \(\frac{5y - 5x - 4x + 4y}{(x - y)(y - x)}\)
= \(\frac{9y - 9x}{(x - y)(y - x)}\)
= \(\frac{9(y - x)}{(x - y)(y - x)}\)
= \(\frac{9}{x - y}\)
Source: Myschool Past Questions Archive (Record #23799)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Solution
If 3p - q = 6 and 2p + 3q = 4, find q
A
o
B
1/2
C
2/3
D
1
E
33/7
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
3p - q = 6 ........ 1
2p + 3q = 4 ....... 2
Multiply eqn 1 by 3
9p - 3q = 18 ........ 3
2p - 3q = 4 ......... 2
Add eqn3 and eqn2
11p = 22 => p = 22/11 = 2
Substitute for p =2 in eqn1
3p - q = 6
3x2 - q = 6 => 6 - q = 6 => -q = 6 - 6
q = 0
Source: Myschool Past Questions Archive (Record #23800)
Mathematics
WAEC / WASSCE 1996
Variations
Solution
M varies directly as n and inversely as the square of p. If M = 3, when n = 2 and p = 1, find M in terms of n and p.
A
M = 2n/3p
B
M = 3n2/2p2
C
M = n2/2p
D
M = 3n/2p2
E
M = 2n/3p2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(M \propto \frac{n}{p^2}\)
\(M = \frac{kn}{p^2}\)
\(3 = \frac{k(2)}{1^2}\)
\(3 = 2k \implies k = \frac{3}{2}\)
\(M = \frac{3n}{2p^2}\)
Source: Myschool Past Questions Archive (Record #23801)
Mathematics
WAEC / WASSCE 1996
Inequalities & Linear Programming
Diagram
Solution
If x is a real number which of the following is more illustrated on the number line?
Attached Figure / Diagram
A
x < 4
B
x > -2
C
-2 < x ≤ 4
D
-3 ≤ x < 4
E
-2 ≤ x < 4
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
The number line illustrates the inequality: -2 \le x < 4
Source: Myschool Past Questions Archive (Record #23802)
Mathematics
WAEC / WASSCE 1996
Linear, Simultaneous & Quadratic Equations
Solve the equation 4/a + 1/5a = 3
A
21/5
B
12/5
C
11/3
D
14/15
E
1/3
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 #23803)
Mathematics
WAEC / WASSCE 1996
Algebraic Expressions, Polynomials & Factorisation
Solution
Make p the subject if formula y = \(\frac{a + p}{a - p}\)
A
\(p = \frac{a(y - 1)}{y + 1}\)
B
\(p = \frac{2a - y}{a + y}\)
C
\(p = \frac{ay}{y + 1}\)
D
\(p = \frac{2y - 1}{y - 1}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
To make \( p \) the subject of the formula \( y = \frac{a + p}{a - p} \):
Start with the equation:
\(y = \frac{a + p}{a - p}\)
Cross-multiply: \(y(a - p) = a + p\)
Distribute \( y \): \(ya - yp = a + p\)
Rearrange to isolate terms involving \( p \): \(ya - a = p + yp\)
Factor out \( p \) on the right side: \(ya - a = p(1 + y)\)
Finally, solve for \( p \): \(p = \frac{ya - a}{1 + y}\)
Thus, the formula with \( p \) as the subject is: \(p = \frac{a(y - 1)}{y + 1}\)
Source: Myschool Past Questions Archive (Record #23804)
Mathematics
WAEC / WASSCE 1996
Algebraic Expressions, Polynomials & Factorisation
Factorize 32x3 - 8xy2
A
4(4x + y)(2x - y)
B
(16x - y)(2x + y)
C
8x(2x - y)
D
8x(2x + y)(2x - y)
E
4(2x + y)(4x - y)
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 #23805)
Mathematics
WAEC / WASSCE 1996
Linear, Simultaneous & Quadratic Equations
Solution
The roots of a quadratic equation are -1/4 and 3. The quadratic equation is
A
4x2 - 13x - 3 = 0
B
4x2 - 11x - 3 = 0
C
4x2 + 11x - 3 = 0
D
3x2 - 11x - 3 = 0
E
3x2 - 11x + 3 = 0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The roots of a quadratic equation are -\(\frac{1}{4}\) and 3.
The quadratic equation in x
x = -\(\frac{1}{4}\) or 3
(x + \(\frac{1}{4}\)) = 0 or (x - 3) = 0
(x + \(\frac{1}{4}\))(x - 3) = 0
x\(^2\) - 3x + \(\frac{x}{4}\) - 3(\(\frac{1}{4}\)) = 0
x\(^2\) - \(\frac{11x}{4}\) - \(\frac{3}{4}\) = 0
multiply thru by 4
4x\(^2\) - 11x - 3 = 0
Source: Myschool Past Questions Archive (Record #23806)
Mathematics
WAEC / WASSCE 1996
Linear, Simultaneous & Quadratic Equations
The graph of 2y = 5x2 - 3x2 - 2 cuts the y axis at the point
A
(1,0)
B
(-2/5, 0)
C
(0, -1)
D
(0, -2)
E
(0, 1)
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 #23807)
Mathematics
WAEC / WASSCE 1996
Plane Geometry, Polygons & Circle Theorems
Diagram
In the diagram above, O is the center of the circle of radius 3.5cm, ∠POQ = 60o
Use the information to answer the question below [Take \pi = 22/7]
What is the length of the arc PXQ?
Attached Figure / Diagram
A
22cm
B
181/3cm
C
\(\frac{11}{3}\)cm
D
91/6cm
E
71/3cm
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 #23808)
Mathematics
WAEC / WASSCE 1996
Fractions, Decimals, Percentages & Approximations
Solution
Find, correct to 1 decimal place, the volume of cylinder of height 8cm and base radius 3cm. [Take π = 3.142]
A
503.0cm3
B
300.0cm3
C
250.0cm3
D
226.2cm3
E
150.9cm3
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Volume =\(\pi\)r2h = 3.142 x 3 x 3 x 8
=72 x 3.142 = 226.2cm3
Source: Myschool Past Questions Archive (Record #23811)
Mathematics
WAEC / WASSCE 1996
Indices, Logarithms & Surds
Solution
One side of a rectangle is 8cm and the diagonal is 10cm. What is the area of the rectangle?
A
80cm2
B
48cm2
C
40cm2
D
36cm2
E
24cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
From the diagram above, using Pythagoras' theorem
y = \(\sqrt{10^2 - 8^2}\) = \(\sqrt{36}\) = 6 cm
Area of Rectangle = length x breath = 6 x 8 = 48 cm\(^2\)
Source: Myschool Past Questions Archive (Record #23812)
Mathematics
WAEC / WASSCE 1996
Mensuration (Areas, Perimeters & Volumes)
two towns X and Y both on latitude 60oS have longitude 27oE and 33oW respectively. Find to the nearest kilometers, the distance between X and Y measured along the parallel of latitude. [Take 2πR = 4 x 104km, where R is the Radius of the earth]
A
28850km
B
16667km
C
8333km
D
6667km
E
3333km
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 #23813)
Mathematics
WAEC / WASSCE 1996
Mensuration (Areas, Perimeters & Volumes)
The angle of a sector of a circle of radius 35cm is 288o. Find the perimeter of the sector. [Take π = 22/7]
A
246cm
B
211cm
C
141cm
D
114cm
E
44cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option A.
Source: Myschool Past Questions Archive (Record #23814)