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Mathematics
WAEC / WASSCE 1998
Permutations, Combinations & Probability
Solution
A die with faces numbered 1 to 6 is rolled once. What is the probability of obtaining 4?
A
\(\frac{1}{36}\)
B
\(\frac{1}{6}\)
C
\(\frac{1}{3}\)
D
\(\frac{1}{2}\)
E
\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
When the die is rolled, occasion of getting 4
P(obtaining a 4) = \(\frac{1}{6}\)
= \(\frac{1}{6}\)
Source: Myschool Past Questions Archive (Record #26343)
Mathematics
WAEC / WASSCE 1998
Mensuration (Areas, Perimeters & Volumes)
Diagram
Solution
In the diagram above, the area of triangle ABC is 35cm\(^2\). Find the value of y
Attached Figure / Diagram
A
5cm
B
10cm
C
17.5cm
D
28cm
E
70cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Area of triangle ABC = 35cm\(^2\).
Area of triangle ABC = \(\frac{1}{2}\) x B x H
= 0.5 x y x 7 = 35
= 3.5y = 35
y = \(\frac{35}{3.5}\) = 10 cm.
Source: Myschool Past Questions Archive (Record #26344)
Mathematics
WAEC / WASSCE 1998
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
The graph is that of the quadratic expression
Attached Figure / Diagram
A
\(y=x^2 + x - 2\)
B
\(y=x^2 - x + 2\)
C
\(y=x^2 - x - 2\)
D
\(y=x + x + 2\)
E
\(y=x^2 - 2 x - 2\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The curve cuts the x-axis at x = -1 and x = 2
(x + 1)(x - 2) = 0
x\(^2\) - 2x + x - 2 = 0
x\(^2\) - x - 2 = 0
Source: Myschool Past Questions Archive (Record #26345)
Mathematics
WAEC / WASSCE 1998
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
The values of x when y = -1 are approximately
Attached Figure / Diagram
A
-10 and 2.0
B
-1.3 and 2.3
C
-0.6 and 2.6
D
-0.6 and 1.6
E
1.6 and 1.6
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Draw a straight line from y = -1 to meet the curve on both sides. From the point where the straight line touches the curve, draw a line from there to meet the x-axis, then read off the values.
So when y = -1, x = - 0.6 or 1.6
Source: Myschool Past Questions Archive (Record #26346)
Mathematics
WAEC / WASSCE 1998
Permutations, Combinations & Probability
Solution
A box contain 2 white and 3 blue identical balls. If two balls are picked at random, one after the other, without replacement, what is the probability of picking two balls of different colours?
A
\(\frac{5}{25}\)
B
\(\frac{7}{20}\)
C
\(\frac{3}{5}\)
D
\(\frac{2}{3}\)
E
\(\frac{5}{6}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Balls were picked without replacement
n( white balls) = 2, n( black balls ) = 3
Total Balls = 2 + 3 = 5 balls
Pr( two balls of different colours ) = WB OR BW
= \(\frac{2}{5} \times \frac{3}{4} + \frac{3}{5} \times \frac{2}{4}\)
= \(\frac{6}{20} + \frac{6}{20}\) = \(\frac{12}{20}\) = \(\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #26347)
Mathematics
WAEC / WASSCE 1998
Trigonometry, Elevation & Bearings
Diagram
Solution
In ∆PQR. ∠PQR is a right angle. |QR| = 2cm and ∠PRQ = 60o. Find |PR|
Attached Figure / Diagram
A
4√3cm
B
4cm
C
2√3cm
D
\(\frac{4}{3}cm\)
E
1cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
cos60 = \(\frac{adj}{hyp}\)
cos60 = \(\frac{2}{x}\)
x = \(\frac{2}{cs60}\) = 2 x \(\frac{2}{1}\) = 4cm
Source: Myschool Past Questions Archive (Record #26348)
Mathematics
WAEC / WASSCE 1998
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PQ||SR. Find the value of Z
Attached Figure / Diagram
A
30o
B
40o
C
45o
D
90o
E
120o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
In the diagram above:
x = x\(_1\) alternate angles
y = y\(_1\) same reason
(x\(_1\) + y\(_1\)) + x + y = 180º
(x + y) + x + y = 2 x 90º
2(x + y) = 2 x 90º
⇒ x + y = 90º
but Z = (x\(_1\) + y\(_1\)) = 90º
Source: Myschool Past Questions Archive (Record #26349)
Mathematics
WAEC / WASSCE 1998
Trigonometry, Elevation & Bearings
Solution
In \(sin(X+30)^o=cos40^o\),find X
A
10o
B
20o
C
50o
D
60o
E
90o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Using Sin \theta = Cos(90 - \theta)
Given that Sin(x - 30)º = Cos 40º
Cos 40º = Cos(90 - (x + 30º)
Cos cancels out Cos
40º = 90º - 30º - x
40º = 60º - x
40º - 60º = - x
-20º = - x
Therefore, x = 20º
Source: Myschool Past Questions Archive (Record #26350)
Mathematics
WAEC / WASSCE 1998
Inequalities & Linear Programming
Find the value of X if \(cos x = \frac{5}{8}\) for \(0^o\le X\le 180^o\)
A
141.3o
B
128.7o
C
51.3o
D
48.7o
E
38.7o
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 #26351)
Mathematics
WAEC / WASSCE 1998
Plane Geometry, Polygons & Circle Theorems
A chord of circle of radius 26cm is 10cm from the center of the circle. calculate the length of the chord
A
16cm
B
27.86cm
C
32cm
D
48cm
E
55.72cm
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 #26353)
Mathematics
WAEC / WASSCE 1998
Plane Geometry, Polygons & Circle Theorems
Two chords PQ and RS of a circle intersected at right angles at a point inside the circle. If ∠QPR = 35o,find ∠PQS
A
35o
B
45o
C
55o
D
70o
E
90o
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 #26354)
Mathematics
WAEC / WASSCE 1998
Plane Geometry, Polygons & Circle Theorems
Diagram
In the diagram, O is the center of the circle and the reflex angle ROS is 264o. Find ∠RTS
Attached Figure / Diagram
A
48o
B
53o
C
66o
D
132o
E
192o
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 #26355)
Mathematics
WAEC / WASSCE 1998
Plane Geometry, Polygons & Circle Theorems
If the exterior angles of quadrilateral are yo, (y + 5)o, (y + 10)o and (y + 25)o, find y
A
10o
B
20o
C
40o
D
60o
E
80o
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 #26356)
Mathematics
WAEC / WASSCE 1998
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram PQ is a diameter of circle PMQN center O, if ∠PQM = 63o, find ∠MNQ
Attached Figure / Diagram
A
58.5o
B
44o
C
35o
D
31.5o
E
27o
medium Difficulty
Verified Correct Answer: Option E
Step-by-Step Mathematical Solution
In the given diagram,
< PMQ = 90º (< in a semi-circle)
Source: Myschool Past Questions Archive (Record #26357)
Mathematics
WAEC / WASSCE 1998
Fractions, Decimals, Percentages & Approximations
Diagram
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 one decimal place, the length of arc PQ.
Attached Figure / Diagram
A
175.0cm
B
157.1cm
C
37.7cm
D
11.0cm
E
3.1cm
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 #26358)