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Mathematics
WAEC / WASSCE 2003
Indices, Logarithms & Surds
Solution
Evaluate \(\frac{log8}{log\left(\frac{1}{4}\right)}\)
A
-2
B
\(\frac{-3}{2}\)
C
\(\frac{1}{2}\)
D
4
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{log8}{log\frac{1}{4}}=\frac{log2^3}{log2^{-2}}=\frac{3log2}{-2log2}=-\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #26582)
Mathematics
WAEC / WASSCE 2003
Mensuration (Areas, Perimeters & Volumes)
Solution
A pyramid of volume 120cm3 has a rectangular base which measures 5cm by 6cm. Calculate the height of the pyramid
A
5cm
B
9cm
C
12cm
D
15cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of pyramid = 120 cm\(^3\)
Base area = 5 cm \times 6 cm = 30 cm\(^2\)
120 = (\(\frac{1}{3}\)) \times 30 \times h
h = 12 cm
Source: Myschool Past Questions Archive (Record #26583)
Mathematics
WAEC / WASSCE 2003
Plane Geometry, Polygons & Circle Theorems
Solution
PQRS is a cyclic quadrilateral. If ∠QPS = 75^\circ, what is the size of ∠QRS?
A
180o
B
150o
C
105o
D
75o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
< QPS = 75^\circ
< QRS = 180^\circ - 75^\circ = 105^\circ (opposite angles of a cyclic quadrilateral)
Source: Myschool Past Questions Archive (Record #26584)
Mathematics
WAEC / WASSCE 2003
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, ZM is a straight line. Calculate the value of x.
Attached Figure / Diagram
A
27o
B
30o
C
35o
D
37o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The sum of angles in a triangle is 180o
2xo + (2x -21)o + ∠ZYP = 180o
Also ∠ZYP = 180o - (3x+14)o
∴2xo + (2x-21)o + 180o - (3x+14)o = 180
x = 35o
Source: Myschool Past Questions Archive (Record #26585)
Mathematics
WAEC / WASSCE 2003
Linear, Simultaneous & Quadratic Equations
Solution
Find the value of x in the equation 3x\(^2\) - 8x - 3 = 0
A
\(\frac{1}{3},-3\)
B
\(-\frac{1}{3},-3\)
C
\(-\frac{1}{3},3\)
D
\(\frac{1}{3},3\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3x\(^2\) - 8x - 3 = 0
3x\(^2\) - 9x + x - 3 = 0
3x(x - 3) + 1(x - 3) = 0
(3x + 1)(x - 3) = 0
3x = -1 \(\implies\) x = \(-\frac{1}{3}\)
or x = 3.
Source: Myschool Past Questions Archive (Record #26586)
Mathematics
WAEC / WASSCE 2003
Trigonometry, Elevation & Bearings
Solution
In\( ∆ PQR, P\hat{Q}P = 84^°, |Q\hat{P}R |= 43^°\) and |PQ| = 5cm. Find /QR/ in cm, correct to 1 decimal place.
A
3.4
B
4.3
C
5.9
D
6.2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Using the sine rule
\(\frac{|QR|}{sinP}=\frac{|PQ|}{sinR}\\
\frac{x}{sin43^o}=\frac{5}{sin53^o}\\
x = \frac{5\times sin43^o}{sin53^o}\\
=\frac{5\times 0.6820}{0.7986}\\
=4.3\)
Source: Myschool Past Questions Archive (Record #26587)
Mathematics
WAEC / WASSCE 2003
Indices, Logarithms & Surds
Solution
Given, that \(4P4_5 = 119_{10}\), find the value of P
A
1
B
2
C
3
D
4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(4P4_5 = 119_{10}\)
\(4 \times 5^2 + P \times 5^1 + 4 \times 5^0 = 119\)
\(100 + 5P + 4 = 119\)
\(5P = 119 - 104 = 15\)
\(P = 3\)
Source: Myschool Past Questions Archive (Record #26588)
Mathematics
WAEC / WASSCE 2003
Trigonometry, Elevation & Bearings
Solution
A ladder, 6m long, leans against a vertical wall at an angle 53o to the horizontal. How high up the wall does the ladder reach?
A
3.611m
B
4.521m
C
4.792m
D
7.962m
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Sin 53 = \(\frac {h}{6} \)
h = 6 sin 53 = 6 x 0.7986
= 4.792m
Source: Myschool Past Questions Archive (Record #26589)
Mathematics
WAEC / WASSCE 2003
Trigonometry, Elevation & Bearings
Diagram
Solution
What is the size of angle x in the diagram
Attached Figure / Diagram
A
15o
B
30o
C
45o
D
60o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(Sin\theta^{\circ} = \frac{opp}{hyp}\\
Sin X^{\circ}=\frac{5}{10}=0.5000\\SinX^{\circ}\\
X^{\circ} = sin^{-1}0.5000\\
X^{\circ}=30^{\circ}\)
Source: Myschool Past Questions Archive (Record #26590)
Mathematics
WAEC / WASSCE 2003
Plane Geometry, Polygons & Circle Theorems
Solution
The four interior angles of a quadrilateral are (x + 20) o, (x+ 10) o (2x - 45) o and (x - 25) o. Find the value of x
A
60
B
80
C
100
D
360
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sum of interior angles in a quadrilateral is 360
(x + 20)o + (x+ 10)o + (2x - 45)o + (x - 25)o = 360o
5xo - 40o = 360o
x = 400/5 = 80o
Source: Myschool Past Questions Archive (Record #26591)
Mathematics
WAEC / WASSCE 2003
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
Calculate the value of y in the diagram
Attached Figure / Diagram
A
17
B
34
C
44
D
45
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Sum of interior angle of the diagram equals 360o
180o - 5yo + 136o + 180o + 180o - 3yo = 360o
-8yo + 136o = 0
-8yo = -136; y = 17
Source: Myschool Past Questions Archive (Record #26592)
Mathematics
WAEC / WASSCE 2003
Permutations, Combinations & Probability
Solution
Out of 60 members of an Association, 15 are Doctors and 9 are Lawyers. If a member is selected at random from the Association, what is the probability that the member is neither a Doctor Nor a Lawyer
A
\(\frac{3}{5}\)
B
\(\frac{9}{10}\)
C
\(\frac{3}{20}\)
D
\(\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Member that are neither doctors nor lawyers = 60-(15+9)=36
Probability (Not doctors ad not lawyers) \(=\frac{36}{60}\\
=\frac{6}{10}=\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #26593)
Mathematics
WAEC / WASSCE 2003
Linear, Simultaneous & Quadratic Equations
Solution
Find the values of x for which \( \frac{1}{2x^2 - 13x +15} \) is not defined,
A
5 or \( \frac{3}{2} \)
B
1 or \( \frac{15}{13} \)
C
2 or 15
D
13 or 15
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The fraction is undefined when the denominator is equal to zero
\(2x^2 - 13x + 15 = 0\\
2x^2 - 3x - 10x + 15\\
x(2x-3)-5(2x-3) = 0\\
(2x-3)(x-5)=0\\
x = \frac{3}{2} or x = 5\)
Source: Myschool Past Questions Archive (Record #26594)
Mathematics
WAEC / WASSCE 2003
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, \(P\hat{Q}S = 65^o, R\hat{P}S = 40^o\hspace{1mm}and\hspace{1mm}Q\hat{S}R=20^o\hspace{1mm} Find P\hat{S}Q\)
Attached Figure / Diagram
A
85o
B
60o
C
55o
D
45o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
< QPS = < PRS = 65^\circ (angles in the same segment)
< PSR + 40^\circ + 65^\circ = 180^\circ
< PSR + 105^\circ = 180^\circ
< PSR = 75^\circ
< PSR = < PSQ + < QSR
75^\circ = < PSQ + 20^\circ \(\implies\) < PSQ = 75^\circ - 20^\circ = 55^\circ
Source: Myschool Past Questions Archive (Record #26595)
Mathematics
WAEC / WASSCE 2003
Algebraic Expressions, Polynomials & Factorisation
Solution
Evaluate \((111_{two})^2 - (101_{two})^2\)
A
10two
B
100two
C
1100two
D
11000two
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\((111_{2})^2 - (101_{2})^2\)
Difference of two squares
\((111 - 101)(111 + 101)\)
= \((10)(1100)\)
= \(11000_{2}\)
Source: Myschool Past Questions Archive (Record #26596)