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Mathematics
WAEC / WASSCE 2009
Plane Geometry, Polygons & Circle Theorems
Solution
If \(\frac{3}{2x} - \frac{2}{3x} = 4\), solve for x
A
\(\frac{4}{5}\)
B
\(\frac{4}{13}\)
C
\(\frac{5}{24}\)
D
\(\frac{13}{24}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{3}{2x} - \frac{2}{3x} = 4\)
\(\frac{9 - 4}{6x}\); \(\frac{5}{6x}\) = 4
5 = 24x ; x = \(\frac{5}{24}\)
Source: Myschool Past Questions Archive (Record #36437)
Mathematics
WAEC / WASSCE 2009
Indices, Logarithms & Surds
Solution
If (2x + 3)3 = 125, find the value of x
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(2x + 3 )2 = 125
2n + 3 = 3\(\sqrt{125}\)
2x + 3 = 5
2x = 5 - 3
x = \(\frac{2}{2}\)
= 1
Source: Myschool Past Questions Archive (Record #36446)
Mathematics
WAEC / WASSCE 2009
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorize x2 - 2x - 3xy completely
A
(x - 2)(3x - y)
B
(x - 3y)(x - 2)
C
(x - 3y)(x - 3y)
D
(3x + y)(x - 2)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
x2 - 2x - 3xy + 6y = x(x - 2) -3y(x - 2)
= (x - 3y)(x - 2)
Source: Myschool Past Questions Archive (Record #36447)
Mathematics
WAEC / WASSCE 2009
Mensuration (Areas, Perimeters & Volumes)
Solution
The diameter of a bicycle wheel is 42cm. If the wheel makes 16 complete revolution, what will be the total distance covered by the wheel? [Take \(\pi \frac{22}{7}\)
A
672cm
B
1056cm
C
2112cm
D
4224cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
d = 42cm
Circumference = \(\pi d = \frac{22}{7} \times 42cm\)
= 22 x 6cm = 132cm
Total distance covered = circumference x number of revolutions
= 132cm x 16 = 2112cm
Source: Myschool Past Questions Archive (Record #36448)
Mathematics
WAEC / WASSCE 2009
Plane Geometry, Polygons & Circle Theorems
Solution
If M and N are two fixed points in a plane. Find the locus L = [P : PM = PN]
A
a line equal to MN
B
line parallel to MN
C
Perpendicular bisector of MN
D
A circle centre P, radius MN
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Locus L = (P : PM = Pn}
For M and N being two fixed points
Since PM = PN, P is equidistant from Mand N, So L must be the perpendicular bisector of the line MN
Source: Myschool Past Questions Archive (Record #36453)
Mathematics
WAEC / WASSCE 2009
Trigonometry, Elevation & Bearings
Solution
Given that sin 60o = \(\frac{\sqrt{3}}{2}\) and cos 60o = \(\frac{1}{2}\), evaluate \(\frac{1 - sin 60^o}{1 + cos 60^o}\)
A
\(\frac{2 + \sqrt{3}}{3}\)
B
\(\frac{1 - \sqrt{3}}{3}\)
C
\(\frac{1 + \sqrt{3}}{3}\)
D
\(\frac{2 - \sqrt{3}}{3}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
Sin 60 = \(\frac{\sqrt{3}}{2}\); cos 60o = \(\frac{1}{2}\)
= \(\frac{1 - \sin 60}{1 + \cos 60} = \frac{1 - \frac{\sqrt{3}}{2}}{1 + \frac{1}{2}}\)
= \(\frac{2 - \sqrt{3}}{3}{2}\div \frac{2 + 1}{2}\)
= \(\frac{2 - \sqrt{3}}{2} \times \frac{2}{3}\)
= \(\frac{2 - \sqrt{3}}{3}\)
Source: Myschool Past Questions Archive (Record #36455)
Mathematics
WAEC / WASSCE 2009
Fractions, Decimals, Percentages & Approximations
Solution
In an examination, Kofi scored x% in Physics, 50% in Chemistry and 70% in Biology. If his mean score for the three subjects was 55%, find x
A
40
B
45
C
55
D
60
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{x + 50 + 70}{3} = 55\)
x + 120 = 3(55)
x + 120 = 165
= 165 - 120
x = 45%
Source: Myschool Past Questions Archive (Record #36456)
Mathematics
WAEC / WASSCE 2009
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
What is the median of the following scores: 22 35 41 63 74 82
A
82
B
52
C
49
D
22
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
22 35 41 63 74 82
Median = \(\frac{41 + 63}{2} = \frac{104}{2}\)
= 52
Source: Myschool Past Questions Archive (Record #36458)
Mathematics
WAEC / WASSCE 2009
Fractions, Decimals, Percentages & Approximations
Solution
Express 2.7864 x 10-3 to 2 significant figures
A
0.28
B
0.27
C
0.0028
D
0.0027
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2.7864 x 10-3 = 0.0027864
= 0.0028(approx. 2 s.f)
Source: Myschool Past Questions Archive (Record #36459)
Mathematics
WAEC / WASSCE 2009
Indices, Logarithms & Surds
Solution
If 92x = \(\frac{1}{3}\)(27x), find x
A
2
B
1
C
-1
D
-2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
92x = \(\frac{1}{3}\)(27x)
(22)2x = \(\frac{(3^{3x})}{3}\)
(34x) = 33x - 1
4x = 3x - 1
4x - 3x = -1
x = -1
Source: Myschool Past Questions Archive (Record #36460)
Mathematics
WAEC / WASSCE 2009
Fractions, Decimals, Percentages & Approximations
Solution
If 85% of x is N3230, what is the value of x?
A
N2745.50
B
N3714.50
C
N3800.00
D
N4845.00
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
85% of x = 3230
\(\frac{85}{100} \times x\) = N3230
x = \(\frac{100}{85}\) x N3230
x = N3800.00
Source: Myschool Past Questions Archive (Record #36462)
Mathematics
WAEC / WASSCE 2009
Number Bases & Modular Arithmetic
Solution
The capacity of a water tank is 1,800 litres. If the tank is in form of a cuboid with base 600cm by 150 cm. Find the height of the tank
A
2cm
B
20cm
C
200cm
D
2000cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
1 litre = 1000cm3
1800 litre = 1800 x 1000cm3
l x b x h = capacity
600 x 150 x h = 1800000
h = \(\frac{1800000}{600 \times 150}\)cm
h = 20cm
Source: Myschool Past Questions Archive (Record #36463)
Mathematics
WAEC / WASSCE 2009
Plane Geometry, Polygons & Circle Theorems
Solution
An arc of a circle subtends an angle of 60o at the centre. If the radius of the circle is 3cm, find , in terms of \(\pi\), the length of the arc
A
\(\pi\)cm
B
2\(\pi\)cm
C
3\(\pi\)cm
D
6\(\pi\)cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Length of arc = \(\frac{\theta}{360} \times 2\pi r\)
= \(\frac{60}{360} \times 2\pi \times 3cm\)
= \(\pi\)cm
Source: Myschool Past Questions Archive (Record #36465)
Mathematics
WAEC / WASSCE 2009
Plane Geometry, Polygons & Circle Theorems
Solution
solve \(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0
A
1
B
\(\frac{1}{5}\)
C
-\(\frac{1}{5}\)
D
-1
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{2x + 1}{6} - \frac{3x - 1}{4}\) = 0
\(\frac{4(2n + 1) - 6(3x - 1)}{24}\) = 0
-10x + 10 = 0
-10x = -10
x = \(\frac{-10}{-10}\)
x = 1
Source: Myschool Past Questions Archive (Record #36466)
Mathematics
WAEC / WASSCE 2009
Inequalities & Linear Programming
Solution
If a positive integer, list the values of x which satisfy the equation 3x - 4 0
A
{1, 2, 3}
B
{2, 3}
C
{2, 3, 4}
D
{2, 3, 4, 5}
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
3x - 4 1 = 1< x; since x is an integer, and 1 < x3.33
x = {2, 3}
Source: Myschool Past Questions Archive (Record #36467)