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Mathematics
WAEC / WASSCE 1998
Fractions, Decimals, Percentages & Approximations
Solution
Express as a single fraction: \(\frac{x}{x-2}-\frac{x+2}{x+3}\)
A
\(\frac{2x^2 - 3x - 4}{(x-2)(x+3)}\)
B
\(\frac{2x^2 + 3x - 4}{(x-2)(x+3)}\)
C
\(\frac{2}{(x-2)(x+3)}\)
D
\(\frac{ 3x + 4}{(x-2)(x+3)}\)
E
\(\frac{3x - 4}{(x-2)(x+3)}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{x}{x-2}-\frac{x+2}{x+3}\)
\(\frac{[x][x+3] - ([x+2][x-2])}{[x-2][x+3]}\)
= \(\frac{x^2 + 3x - (x^2 - 4)}{[x-2][x+3]}\)
= \(\frac{3x + 4}{[x-2][x+3]}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26341)
Mathematics
UTME / JAMB 1998
Sets, Logic & Venn Diagrams
Diagram
In the venn diagram, the shaded region is?
Attached Figure / Diagram
A
(P \(\cap\) Q) \(\cup\) R
B
(P \(\cap\) Q) \(\cap\) R
C
(P \(\cap\) Q1) \(\cap\) R
D
(P \(\cap\) Q1) \(\cup\) R
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: WAEC / JAMB / NECO Classroom Archive (Record #33074)
Mathematics
WAEC / WASSCE 1998
Linear, Simultaneous & Quadratic Equations
Solution
Find the equation whose roots are \(\frac{2}{3}and \frac{-1}{4}\)
A
\(12x^2-5x+2=0\)
B
\(12x^2-11x+2=0\)
C
\(x^2-\frac{11}{12}x+2=0\)
D
\(x^2+\frac{11}{12}x-2=0\)
E
\(12x^2+11x+2=0\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x\(^2\) - (sum of given roots)x + (product of given roots ) = 0
x\(^2\) - (\(\frac{2}{3} + \frac{-1}{4}\))x + (\(\frac{2}{3} * \frac{-1}{4}\)) = 0
x\(^2\) - (\(\frac{8 - 3}{12}\))x + (\(\frac{- 2}{12}\))
x\(^2\) - \(\frac{5}{12}\)x + \(\frac{- 2}{12}\)
multiply through by the LCM 12
12 * x\(^2\) - 12 * \(\frac{5}{12}\)x + 12 * \(\frac{- 2}{12}\)
12x\(^2\) - 5x - 2 = 0
Source: WAEC / JAMB / NECO Classroom Archive (Record #26334)
Mathematics
UTME / JAMB 1998
Linear, Simultaneous & Quadratic Equations
Solution
Factorize r2 - r(2p + q) + 2pq
A
(r - 2q)(2r - p)
B
(r - p)(r + p0
C
(r - q)(r - 2p)
D
(2r - q)(r + p)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
r2 - r(2p + q) + 2pq = r2 - 2pr -qr + 2pq
= r(r - 2p) - q(r - 2p)
= (r - q)(r - 2p)
Source: WAEC / JAMB / NECO Classroom Archive (Record #30673)
Mathematics
UTME / JAMB 1998
Algebraic Expressions, Polynomials & Factorisation
Solution
When the expression pm\(^2\) + qm + 1 is divided by (m - 1), it has a remainder is 2, and when divided by (m + 1), the remainder is 4. Find p and q respectively
A
2, -1
B
-1, 2
C
3, -2
D
-2, 3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
pm\(^2\) + qm + 1 = (m - 1) Q(x) + 2, where Q(x) = remainder.
p(1)\(^2\) + q(1) + 1 = 2
p + q + 1 = 2
p + q = 1.....(i)
pm\(^2\) + qm + 1 = (m - 1)Q(x) + 4
p(-1)\(^2\) + q(-1) + 1 = 4
p - q + 1 = 4
p - q = 3....(ii)
p + q = 1, p - q = 3
Using elimination method, add eqn i and ii
2p = 4, p = 2
from eqn ii
p - q = 3
2 - q = 3
-q = 3 - 2 = 1
q = - 1
Therefore, p = 2 and q = -1
q = 2
Source: WAEC / JAMB / NECO Classroom Archive (Record #30667)
Mathematics
WAEC / WASSCE 1998
Mensuration (Areas, Perimeters & Volumes)
Diagram
Solution
In the diagram O is the center of circle PRQ. The radius is 3.5cm and ∠POQ = 50o. Use the diagram to answer question below. (take π = 3.142)
Calculate, correct to three significant figures, the area of sector OPQ
Attached Figure / Diagram
A
3.403cm2
B
5.350cm2
C
10.99cm2
D
157.1cm2
E
175.0cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area of a sector = \(\frac{\theta}{360}\) x \(\pi\)r\(^2\)
Area of a sector = \(\frac{50}{360}\) x 3.142 x 3.5 x 3.5
= \(\frac{50 \times 3.142\times 3.5 \times 3.5}{360}\)
= \(\frac{1924.475}{360}\) ≈ 5.346cm\(^2\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26359)
Mathematics
WAEC / WASSCE 1998
Mensuration (Areas, Perimeters & Volumes)
Diagram
Solution
Calculate the perimeter of the trapezium PQRS
Attached Figure / Diagram
A
24cm
B
36cm
C
48cm
D
72cm
E
520cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Using Pythagora's rule for △PSM
Hyp\(^2\) = Opp\(^2\) + Adj\(^2\)
5\(^2\) = Opp\(^2\) + 4\(^2\)
→ Opp\(^2\) = 25 - 16
→ Opp = \sqrt9 = 3
base SR = 18 + 3 = 21
base PQ = 18
side PS = 5
side QR = 4
perimeter of the trapezium PQRS = 21 + 18 + 5 + 4 = 48cm
Source: WAEC / JAMB / NECO Classroom Archive (Record #26360)
Mathematics
WAEC / WASSCE 1998
Mensuration (Areas, Perimeters & Volumes)
Solution
The diagonal and one side of a square are x and y units respectively. Find an expression for y in terms of x
A
\(y=\frac{x}{2}\)
B
\(y\frac{x}{\sqrt{2}}\)
C
\(y=\sqrt{x}\)
D
\(y=\sqrt{\frac{x}{2}}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
diagonal of a square(x) = y\sqrt2
y in terms of x →
y = \(\frac{x}{\sqrt2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26368)
Mathematics
UTME / JAMB 1998
Mensuration (Areas, Perimeters & Volumes)
Solution
a cylindrical drum of diameter 56 cm contains 123.2 litres of oil when full. Find the height of the drum in centimeters
A
12.5
B
25.0
C
45.0
D
50.00
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
V = \(\pi r^2 h\)
= 123.2 x 1000
= \(\frac{22}{7}\) x 28 x 28 x h
= 123200 = 88 x 28h
= 2464h
∴ h = \(\frac{123200}{2464}\)
= 50cm
N.B: 1 litre = 1 dm3
= 1000cm3
Source: WAEC / JAMB / NECO Classroom Archive (Record #30721)
Mathematics
WAEC / WASSCE 1998
Trigonometry, Elevation & Bearings
Solution
A ladder 5cm long long rest against a wall such that its foot makes an angle 30o with the horizontal. How far is the foot of the ladder from the wall?
A
\(\frac{5\sqrt{2}}{3}m\)
B
\(2\frac{1}{2}m\)
C
\(\frac{5\sqrt{3}}{2}m\)
D
\(\frac{10\sqrt{3}}{3}m\)
E
\(10\sqrt{3}m\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
cos 30 = \(\frac{adj}{hyp}\)
cross multiply:
adj = cos 30 X 5
= 5 \(\frac{\sqrt3}{2}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26352)
Mathematics
WAEC / WASSCE 1998
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The pie chart above show the distribution of how students travelled to a certain school on a particular day. Use this information to answer the question below
If a hundred students travelled by bus, find the total number of students in the school
Attached Figure / Diagram
A
300
B
400
C
500
D
600
E
750
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
If X represent the total number of students
where the bus holds a right angle; 90º
\(\frac{90}{360}\times X=100\)(students traveling by bus)
\(X=\frac{100\times 360}{90}=400\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26362)
Mathematics
WAEC / WASSCE 1998
Number Bases & Modular Arithmetic
Convert 35 to a number in base two
A
1011two
B
10011two
C
100011two
D
110010two
E
110001two
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 #23993)
Mathematics
WAEC / WASSCE 1998
Sequences & Series (AP & GP)
Solution
The nth term of a sequence is represented by 3 x 2(2-n). Write down the first three terms of the sequence
A
3/2, 3, 6
B
6, 3, 3/2
C
3/2, 3, 1/3
D
2/3, 3, 8/3
E
3/2, 0, 6
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
When n = 1, n = 2, n = 3
3 x 22 - 1 = 6
3 x 22 - 2 = 3
3 x 22 - 3 = 3/2
Source: Myschool Past Questions Archive (Record #23996)
Mathematics
WAEC / WASSCE 1998
Number Bases & Modular Arithmetic
Find the number whose logarithm to base 10 is 2.6025
A
0.0004
B
4.004
C
40.04
D
400.4
E
4004
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 #24000)
Mathematics
WAEC / WASSCE 1998
Fractions, Decimals, Percentages & Approximations
A piece of cloth was measured as 6.10m. If the actual length of the cloth is 6.35, find the percentage error, correct to 2 decimal places
A
3.05%
B
3.95%
C
15.00%
D
25.00%
E
39.30%
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 #24002)