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Mathematics
WAEC / WASSCE 2004
Indices, Logarithms & Surds
Solution
Find the next two terms of the sequence
1, 5, 14, 30, 55, ...
A
61,110
B
67,116
C
81,140
D
91, 140
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(1 + 2^2 = 5 + 3^2 = 14 + 4^2 = 30 + 5^2 = 55\)
\(55 + 6^2 = 91 + 7^2 = 140\).
91, 140 are the next two terms.
Source: Myschool Past Questions Archive (Record #26636)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Solution
Each interior angle of a regular polygon is 108^\circ. How many sides has it?
A
5
B
7
C
9
D
14
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
The exterior angle of the polygon = 180 – 108 = 72^\circ. The sum of exterior angle of the regular polygon = 360^\circ
The number of sides \(=\frac{360}{72}=5\)
Source: Myschool Past Questions Archive (Record #26637)
Mathematics
WAEC / WASSCE 2004
Linear, Simultaneous & Quadratic Equations
Solution
Solve the equation 10-3x-x2 = 0
A
x=2 or-5
B
x= -2 or 5
C
x = 1 or 10
D
x = 2 or 5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
10 – 3x - x2 = 0; 10 – 5x + 2x - x2 = 0
5(2 – x) + x(2 – x) = 0; (2 – x)(5 + x) = 0
2 – x = 0 or 5 + x = 0; x = 2 or x = -5
Source: Myschool Past Questions Archive (Record #26638)
Mathematics
WAEC / WASSCE 2004
Fractions, Decimals, Percentages & Approximations
Solution
Find, correct to two decimal places, the mean of 9, 13, 16, 17, 19, 23, 24.
A
23.00
B
17.29
C
16.50
D
16.33
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Mean \(= \frac{sum\hspace{1mm}of\hspace{1mm}all\hspace{1mm}the\hspace{1mm}numbers}{Total\hspace{1mm}Number}\\
\frac{9+13+16+17+19+23+24}{7}\\
\frac{121}{7}=17.2857=17.29\)
Source: Myschool Past Questions Archive (Record #26639)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, ∆XYZ is similar to ∆PRQ, |XY| = 5cm, |XZ| =3.5cm and |PR| = 8cm. Find |PQ|
Attached Figure / Diagram
A
5.6 cm
B
11.2cm
C
11.4cm
D
28.0cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{PQ}{PR}=\frac{XZ}{XY}; \frac{PQ}{8}=\frac{3.5}{5}\\
PQ=\frac{8\times 3.5}{5}=\frac{28}{5}=5.6cm\)
Source: Myschool Past Questions Archive (Record #26640)
Mathematics
WAEC / WASSCE 2004
Algebraic Expressions, Polynomials & Factorisation
Solution
Factorise 27p2x2 - 48y2.
A
9(3px - 4y)2
B
3(3px - 4y)(3px - 4y)
C
9(px - 4y)(3p x + 4y)
D
3(3px -4y)(3px +4y)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
27p2x2 - 48y2; 3(32 p2x2-42y2)
3[(3px) 2 - (4y) 2]; 3[(3px-4y)(3px+4y)]
Source: Myschool Past Questions Archive (Record #26641)
Mathematics
WAEC / WASSCE 2004
Mensuration (Areas, Perimeters & Volumes)
Solution
What is the volume of a solid cylinder of diameter 7cm and height 7cm? (Take \(\pi = \frac{22}{7}\))
A
38.5cm3
B
77cm3
C
269.5cm3
D
1078cm3
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Volume of a solid cylinder = Base area x height
Base area \(=\pi r^2\) =\(\frac{22}{7} \times \frac{7}{2}\times \frac{7}{2}\) = \(\frac{77}{2}\)
Volume of a solid cylinder = \(\frac{77}{2}\times \frac{7}{1}\) = \(\frac{539}{2}cm^3\)
=269.5cm\(^3\)
Source: Myschool Past Questions Archive (Record #26642)
Mathematics
WAEC / WASSCE 2004
Linear, Simultaneous & Quadratic Equations
Solution
Find the sum of the roots of the equation 2x2 + 3x - 9 = 0
A
-18
B
-6
C
\(-\frac{9}{2}\)
D
\(-\frac{3}{2}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
The general quadratic equation
x2 - (sum of roots) x + (product of root) = 0
Comparing with the given equation
2x2 +3x2 - 9 = 0; \(x^2 + \frac{3}{2}x - \frac{9}{2} = 0\\
Sum \hspace{1mm} of \hspace{1mm}roots = -\frac{3}{2}\)
Source: Myschool Past Questions Archive (Record #26643)
Mathematics
WAEC / WASSCE 2004
Sets, Logic & Venn Diagrams
Solution
Given that ξ = {1, 2, 3, . . . . . . ,10}, P= (x : x is prime) and Q = {y : y is odd}, find P'∩Q
A
{2}
B
{1,9}
C
{315.7}
D
{4, 6, 8, 10}
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
ξ = {1, 2, 3, . . . . . . ,10}, P = (2, 3, 5, 7) and Q = {1, 3, 5, 7, 9},
P'∩Q = {1, 4, 6, 8, 9, 10}∩{1, 3, 5, 7, 9} = {1, 9}
Source: Myschool Past Questions Archive (Record #26644)
Mathematics
WAEC / WASSCE 2004
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the mean deviation of 6, 7, 8, 9, 10
A
1.2
B
1.5
C
2
D
8
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\begin{matrix}
x & x-m & |x-m| \\
6 & -2 & 2 \\
7 & -1 & 1 \\
8 & 0 & 0 \\
9 & 1 & 1 \\
10 & 2 & 2 \\
& & 6
\end{matrix}
\)
Mean deviation\(=\frac{\sum|x-m|}{n}=\frac{6}{5} = 1.2\)
Source: Myschool Past Questions Archive (Record #26646)
Mathematics
WAEC / WASSCE 2004
Trigonometry, Elevation & Bearings
Solution
A point X is on the bearing 342o from a point Y. What is the bearing of Y from X?
A
342o
B
252o
C
198o
D
162o
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
If x is the bearing 342ofrom a point y
= 360o - 342o = 18o;
The bearing of y from x = 180o - 18o = 162o
Source: Myschool Past Questions Archive (Record #26647)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, O is the centre of the circle where OS//QR and ∠SOR = 35º. Find the value of ∠QPR.
Attached Figure / Diagram
A
35o
B
45o
C
55o
D
70o
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
∠SOR = ∠ORQ alternate angle.
Also ∠OQR = ∠OQR (Base angle of isosceles)
∠QOR = 180 – 2(35º) = 180 - 70º = 110º, ∠QPR = 1/2QOR = 1/2(110º) ∠QPR = 55º (theorem angle at center is twice angle at circumference)
Source: Myschool Past Questions Archive (Record #26648)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Solution
Find the average of the first four prime numbers greater than10
A
20
B
19
C
17
D
15
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
First four prime numbers greater than 10 are 11, 13, 17, 19
The average \(= \frac{11+13+17+19}{4}=15\)
Source: Myschool Past Questions Archive (Record #26649)
Mathematics
WAEC / WASSCE 2004
Indices, Logarithms & Surds
Solution
Given that \(\sqrt{128}+\sqrt{18}-\sqrt{K} = 7\sqrt{2}\), find K,
A
8
B
16
C
32
D
48
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\sqrt{128} +\sqrt{18}-\sqrt{k}=7\sqrt{2}\\
\sqrt{2\times 64}+\sqrt{9\times 2} - \sqrt{k} = 7\sqrt{2}\\
8\sqrt{2} + 3\sqrt{2} - \sqrt{k} = 7\sqrt{2}; 11\sqrt{2} - \sqrt{k} = 7\sqrt{2}\\
-\sqrt{k}=7\sqrt{2}-11\sqrt{2}; -\sqrt{k} = -4\sqrt{2}; \sqrt{k}=4\sqrt{2}\\
=\sqrt{4^2\times 2} = \sqrt{16\times 2}; \sqrt{k}=\sqrt{32}; k = 32\)
Source: Myschool Past Questions Archive (Record #26650)
Mathematics
WAEC / WASSCE 2004
Plane Geometry, Polygons & Circle Theorems
Diagram
Solution
In the diagram, PQRW is a circle. Line PW and QR are produced to meet at M, where ∠WMR = 30o and |WM| = |MR| Find the value of x
Attached Figure / Diagram
A
10o
B
25o
C
35o
D
60o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
MPQ = PQM = 3x; ∆MPQ
MPQ + PQM + PMQ = 180o; 3x + 3x + 30o = 180o
6x \times 30o = 180o; 6x + 180o - 30o; 6x + 150o
\(x = \frac{150}{6} = 25^{\circ}\)
Source: Myschool Past Questions Archive (Record #26651)