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Mathematics
WAEC / WASSCE 2005
Indices, Logarithms & Surds
Solution
If \(log_9x= 1.5\),find x
A
36
B
27
C
24.5
D
13.5
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(log_9x= 1.5\Rightarrow x = 9^{1.5} = 9^{\frac{3}{2}}=(3^2)^{\frac{3}{2}}=3^3=27\)
Source: Myschool Past Questions Archive (Record #26692)
Mathematics
WAEC / WASSCE 2005
Sequences & Series (AP & GP)
Solution
A sequence is given by \(2\frac{1}{2}, 5, 7\frac{1}{2}, .....\) if the nth term is 25, find n
A
9
B
10
C
12
D
15
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(a = 2\frac{1}{2}, nth = a + (n-1)d \Rightarrow 25 = 2\frac{1}{2} + (n-1)2\frac{1}{2}\\
25 = \frac{5}{2}+(n-1)\frac{5}{2} \Rightarrow 22\frac{1}{2} = \frac{5n-5}{2}\Rightarrow \frac{45}{2} = \frac{5n-5}{2}\\
45 = 5n - 5 \Rightarrow 5n = 50 \Rightarrow n = 10\)
Source: Myschool Past Questions Archive (Record #26693)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Solution
Given that the root of an the equation \(2x^2 + (k+2)x+k=0\) is 2, find the value of k
A
-4
B
-2
C
-1
D
\(-\frac{1}{4}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Substituting for x in the equation
\(2(2)^2 + (k+2)2+k = 0 \Rightarrow 8 +2k + 4 + k =0 \Rightarrow 3k =-12; k=-4\)
Source: Myschool Past Questions Archive (Record #26694)
Mathematics
WAEC / WASSCE 2005
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Find the mean of the numbers 1, 3, 4, 8, 8, 4 and 7
A
4
B
5
C
6
D
7
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
mean \(=\frac{1+3+4+8+8+4+7}{7}=\frac{35}{7}=5\)
Source: Myschool Past Questions Archive (Record #26695)
Mathematics
WAEC / WASSCE 2005
Mensuration (Areas, Perimeters & Volumes)
Solution
What is the total surface area of a closed cylinder of height 10cm and diameter 7cm? [Take \(\pi = \frac{22}{7}\)]
A
77cm2
B
227cm2
C
297cm2
D
374cm2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
T.S.A of s closed cylinder = \(2\pi r(r+h)\)
=\(\frac{2}{1}\times \frac{22}{7} \times \frac{7}{2}\left(\frac{7}{2}+\frac{10}{1}\right) = \frac{22}{1}\left(\frac{27}{2}\right) = 27 \times 11 =297cm^2\)
Source: Myschool Past Questions Archive (Record #26696)
Mathematics
WAEC / WASSCE 2005
Mensuration (Areas, Perimeters & Volumes)
Solution
An arc of a circle of radius 14cm subtends angle 300o at the center. Find the perimeter of the sector formed by the arc
A
14.67cm
B
42.67cm
C
101.33cm
D
543.33cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The perimeter of the sector \(=2r+\frac{\theta}{360}\times 2\pi r \\
\Rightarrow 28 + \frac{300}{360} \times \frac{2}{1} \times \frac{22}{7}\times \frac{14}{1} = \frac{220}{3}+28\\
73.133+28=101.33cm\)
Source: Myschool Past Questions Archive (Record #26697)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
which of the following statements describes the locus of a point R which moves in a plane such that its equidistant from two intersecting lines?
A
the bisector of the angle formed by the lines
B
the point of intersection of the two lines
C
A cone, with two intersecting lines as slant height
D
A circle, with the point of intersection of the two lines as the center
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 #26698)
Mathematics
WAEC / WASSCE 2005
Sets, Logic & Venn Diagrams
Solution
P = {3, 9, 11, 13} and Q = {3, 7, 9, 15} are subset of the universal set ξ = {1, 3, 7, 9, 11, 13, 15} find PI ∩ QI
A
{3, 9}
B
{5, 7, 9}
C
{1}
D
{1, 11}
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
PI = {1, 7, 15} ; QI = {1, 13, 11}
PI ∩ QI = {1}
Source: Myschool Past Questions Archive (Record #26699)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Solution
A train moving at a uniform speed covers 36km in 21 minutes. How long does it take to cover 60km?
A
35 mins
B
40 mins
C
45 mins
D
90 mins
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Since 36km in 21 minutes
1km in \(\frac{21}{36}\)minutes
60km in \(\left(\frac{21}{36}\times 60\right)\)minutes = \(\frac{70}{2}\)min
= 35 mins
Source: Myschool Past Questions Archive (Record #26700)
Mathematics
WAEC / WASSCE 2005
Fractions, Decimals, Percentages & Approximations
Solution
The salary of a man was increased in the ratio 40:47. calculate the percentage increase in the salary
A
85.1%
B
58.5%
C
17.5%
D
14.9%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\%Increase = \frac{Actual \hspace{1mm}increase}{initial \hspace{1mm}ratio}\times 100\%\)
Actual increase = 7; Initial ratio = 40
\(=\left(\frac{7}{40} \times 100\%\right)=\frac{35}{2}=17.5\%\)
Source: Myschool Past Questions Archive (Record #26701)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Solution
A regular polygon has 9 sides. What is the size of one of its exterior angles?
A
20o
B
40o
C
90o
D
140o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Exterior angle \(=\frac{360}{n}\) where n = no of sides
\(=\frac{360}{9}=40^{\circ}\)
Source: Myschool Past Questions Archive (Record #26702)
Mathematics
WAEC / WASSCE 2005
Mensuration (Areas, Perimeters & Volumes)
Solution
The total surface area of the walls of a room 7m long, 5m wide and xm high is 96m2. Find the value of x
A
\(\frac{2}{3}\)
B
2
C
4
D
8
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Area of lengthwise 2 walls = \(2( L\times H ) = 2 \times 7 \times x = 14xcm^2\)
Area of breadthwise 2 walls = \(2( B \times H) = 2 \times 5 \times x = 10xcm^2\)
T.S.A of the room( walls only) = \(14xcm^2 + 10xcm^2 = 96cm^2\)
x = \(\frac{ 96}{14} = 4cm^2\)
Source: Myschool Past Questions Archive (Record #26704)
Mathematics
WAEC / WASSCE 2005
Plane Geometry, Polygons & Circle Theorems
Solution
For what values of y is the expression \(\frac{6y-1}{y^2 - y-6}\) not defined?
A
\(\frac{1}{6}, \frac{1}{4}\)
B
3, -2
C
-3, 2
D
0,1
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The expression is not defines when \(y^2\) - y - 6 = 0
=> \(y^2\) - 3y + 2y - 6 = 0 => (y-3)(y+2) = 0 => y
-3 = 0 or y + 2 = 0 => y = 3 or -2
Source: Myschool Past Questions Archive (Record #26705)
Mathematics
WAEC / WASSCE 2005
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
What are the roots of the equation?
Attached Figure / Diagram
A
-1 and 1
B
4 and 1
C
1 and 4
D
4 and 4
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The two points of contact of the curve with the x-axis are x = 1 and x = 4. The roots of the equation are x = 1 and x = 4
Source: Myschool Past Questions Archive (Record #26706)
Mathematics
WAEC / WASSCE 2005
Linear, Simultaneous & Quadratic Equations
Diagram
Solution
What is the equation of the curve?
Attached Figure / Diagram
A
\(y=x^2+6x+4\)
B
\(y=x^2-5x-4\)
C
\(y=x^2-5x+4\)
D
\(y=x^2+5x-4\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
The factor for the curve are (x-1)(x-4). The product off the curves gives \(=x^2-5x+4=y\)
Source: Myschool Past Questions Archive (Record #26707)