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Mathematics
WAEC / WASSCE 2004
Statistics (Data Representation, Central Tendency & Dispersion)
Diagram
Solution
The table above gives the marks scored by a group of students in a test. Use the table to answer the Question below
What is the median mark?
Attached Figure / Diagram
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Median = 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5
Median mark = \(\frac{3+3}{2} = \frac{6}{2} = 3\)
Source: Myschool Past Questions Archive (Record #26653)
Mathematics
WAEC / WASSCE 2004
Permutations, Combinations & Probability
Diagram
Solution
The table above gives the marks scored by a group of students in a test Use the table to answer the Question below
What is the probability of selecting a student from the group that scored 2 or 3?
Attached Figure / Diagram
A
\(\frac{1}{11}\)
B
\(\frac{5}{22}\)
C
\(\frac{7}{22}\)
D
\(\frac{6}{11}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Prob (2 or 3) = prob(2) + prob(3)
Prob (mark 2) \(=\frac{7}{22}\) + Prob(mark 3) = \(\frac{5}{22}\)
Prob(2 or 3) \(=\frac{7}{22}+\frac{5}{22}=\frac{12}{22}=\frac{6}{11}\)
Source: Myschool Past Questions Archive (Record #26654)
Mathematics
WAEC / WASSCE 2004
Inequalities & Linear Programming
Solution
Find the range of values of x for which\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\)
A
x > 4
B
x > -4
C
x < 4
D
x < -4
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\frac{x+2}{4}-\frac{x+1}{3}>\frac{1}{2}\)
\(\frac{3(x+2)-4(x+1)>6}{12}\); 3x + 6 – 4x – 4 > 6
- x + 2 > 6; - x > 4; x < -4
Source: Myschool Past Questions Archive (Record #26655)
Mathematics
WAEC / WASSCE 2004
Linear, Simultaneous & Quadratic Equations
Solution
A boy walks 800m in 20 minutes. Calculate his average speed in km per hour
A
2.4
B
4
C
16
D
24
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(Average \hspace{1mm}speed = \frac{Distance}{Time\hspace{1mm} taken}\)
Distance = 800m = \(\frac{800}{1000}\)km = 0.8km
Time\(\hspace{1mm}taken = 20\hspace{1mm}minutes = \frac{20}{60}\)hr
= \(\frac{1}{3}hr\\Average \hspace{1mm} speed = \left(0.8\div \frac{1}{3}\right)\)km/hr
= (0.8\(\times\)3)km/hr =2.4km/hr
Source: Myschool Past Questions Archive (Record #26656)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{2}{a+b}-\frac{1}{a-b}\)
A
\(\frac{3}{a+b}\)
B
\(\frac{a-3b}{a^2-b^2}\)
C
\(\frac{3a-b}{a^2 – b^2}\)
D
\(\frac{a-3b}{a^2+b^2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Simplify \(\frac{2}{a+b}-\frac{1}{a-b}; \frac{2(a-b)-1(a+b)}{(a+b)(a-b)}\)
= \(\frac{2a-2b-a-b}{(a+b)(a-b)}\)
= \(\frac{a-3b}{a^2 - ab + ab - b^2}\)
= \(\frac{a-3b}{a^2-b^2}\)
Source: Myschool Past Questions Archive (Record #26657)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The diagram is a circle centre O. Find the value of x
Attached Figure / Diagram
A
30o
B
50o
C
61o
D
78o
E
65.5\(^{\circ}\)
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
∠PQR (Reflex) = 360^\circ – 68^\circ = 292^\circ
∠PQR = 2∠PQR
292^\circ = 4x + 30^\circ
4x = 292 – 30 = 262
\(x = \frac{262}{4}=65.5^\circ\)
Source: Myschool Past Questions Archive (Record #26658)
Mathematics
WAEC / WASSCE 2004
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
Use the graph to answer the Question below
What are the roots of the equation x2 + 3x - 4 = 0?
Attached Figure / Diagram
A
1, 4
B
-1, -4
C
-1, 4
D
-4, 1
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x2 + 3x – 4 = 0 has roots value at the curve makes touches with the x – axis. The curve contact is at x = -4 and +1.
Source: Myschool Past Questions Archive (Record #26659)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Diagram
The values of x when y = 3 are approximately
Attached Figure / Diagram
A
-4.7 and 1.4
B
-4.6 and 1.5
C
-3.6 and 0.4
D
-3.6 and 1.5
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 #26660)
Mathematics
WAEC / WASSCE 2004
Linear, Simultaneous & Quadratic Equations
Solution
Which of the following quadratic equations has \(-\frac{1}{2}\) and \(\frac{3}{4}\) as its roots?
A
8x2 + 11x - 3 = 0
B
8x2 -11x – 3 = 0
C
8x2 + 2x -3 = 0
D
8x2 - 2x – 3 = 0
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
X2 - (sum of the roots)x + (product of the roots) = 0
Sum of the roots \(= -\frac{1}{2}+\frac{3}{4} = \frac{-2+3}{2}=\frac{1}{4}\)
Product of the roots = \(-\frac{1}{2}\times \frac{3}{4}=\frac{-3}{8}\\
X^2-\left(\frac{1}{4}\right)x-\frac{3}{8} = 0. Taking \hspace{1mm}the\hspace{1mm} common\)
\(8x^2-2x-3=0\);
Source: Myschool Past Questions Archive (Record #26661)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
The locus of a point which moves in a plane such that it is equidistant from two fixed points X and Y is
A
the perpendicular bisector of the line segment X Y
B
a line parallel to the line segment XY
C
a circle with XY as diameter
D
the line perpendicular to the line segment XY
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 #26662)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Which of the following is/are true? In a plane, the locus of points I. Equidistant from a straight line is a circle radius d where d is the distance between the point and the straight line.
II Equidistant from two given points P and Q is a circle of radius |PQ|. III Equidistant from two points is the perpendicular bisector of the line joining the two points.
A
I only
B
II only
C
III only
D
I, II and III
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 #26664)
Mathematics
WAEC / WASSCE 2004
Fractions, Decimals, Percentages & Approximations
Solution
The sides of two cubes are in the ratio 2:5. What is the ratio of their volumes?
A
4:5
B
8: 15
C
6:125
D
8:125
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The ratio of the two cubes = 2:5
Volume of the two cubes = 2\(^3\) : 5\(^3\) = 8 : 125
Source: Myschool Past Questions Archive (Record #26665)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Solution
Given that p = 2, q = -5 and r = - 4, evaluate 3p2 - q2 - r3
A
101
B
77
C
51
D
-27
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3(2)2 - (-5)2 - (-4)3
3(4) – (25) – (-64); 12 – 25 + 64 = 51
Source: Myschool Past Questions Archive (Record #26666)
Mathematics
WAEC / WASSCE 2004
Fractions, Decimals, Percentages & Approximations
Solution
A Cooperative Society charges an interest of 5\(\frac{1}{2}\)% per annum on any amount borrowed by its members. If a member borrows N125,000, how much does he pay back after one year?
A
N136875
B
N131,875
C
N126750
D
N126250
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The rate of interest charge = 5\(\frac{1}{2}\)% p.a
The amount borrowed = N125, 000:00
Interest charge \(=\frac{11}{200} of N125,000\)
= 11 \(\times N625.00 = N6,875.00\)
The amount refunded by the member, with interest charged by the cooperative society
N125,000 + N6,875.00 = N131,875.00
Source: Myschool Past Questions Archive (Record #26667)
Mathematics
WAEC / WASSCE 2004
Permutations, Combinations & Probability
Solution
A bag contains 3 red and 2 white identical balls. lf 2 balls are picked at random from the bag, one after the other and with replacement, find the probability that they are of different colours
A
\(\frac{36}{625}\)
B
\(\frac{16}{625}\)
C
\(\frac{12}{25}\)
D
\(\frac{13}{25}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Prob(RW or WR) = Prob(RW) + Prob(WR)
\(Prob(R) = \frac{3}{5}:Prob(W) = \frac{2}{5}\\
Prob(RW\hspace{1mm}or\hspace{1mm}WR)=\frac{3}{5}\times\frac{2}{5}+\frac{2}{5}\times \frac{3}{5}\\
\frac{6}{25}+\frac{6}{25}=\frac{12}{25}\)
Source: Myschool Past Questions Archive (Record #26668)