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Mathematics
WAEC / WASSCE 2005
Number and Numeration
Solution
Simplify the expression \(log_{10}18 - log_{10}2.88+log_{10}16\)
A
31.12
B
3.112
C
2
D
1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(log_{10}18 - log_{10}2.88+log_{10}16\\
=log_{10}18 - log_{10}\left(\frac{288}{100}\right)+log_{10}16 = log_{10}\left(\frac{18\times 16}{1}\times \frac{100}{288}\right)\\
=log_{10}\left(\frac{288\times 100}{288}\right)=log_{10}100=log_{10}10^2=2log_{10}10=2\)
Source: Myschool Past Questions Archive (Record #26673)
Mathematics
WAEC / WASSCE 2005
Number and Numeration
Diagram
Solution
In the diagram, KL//MN, ∠LKP = 30o and ∠NMP = 45o. Find the size of the reflex ∠KPM.
Attached Figure / Diagram
A
285o
B
255o
C
225o
D
210o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
∠KPM = 360o - (30 + 45)o
= 360o - 75o = 285o
Source: Myschool Past Questions Archive (Record #26678)
Mathematics
WAEC / WASSCE 2005
Number and Numeration
Solution
Convert 101101two to a number in base ten
A
61
B
46
C
45
D
44
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
1011012 = 1 x 25 + 0 x 24 + 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20 = 32 + 0 + 8 + 4 + 0 + 1 = 4510
Source: Myschool Past Questions Archive (Record #26680)
Mathematics
WAEC / WASSCE 2005
Number and Numeration
Solution
expand (2x-3y)(x-5y)
A
\(2x^2 + 13xy - 15y^2\)
B
\(2x^2 - 13xy - 15y^2\)
C
\(2x^2 + 13xy + 15y^2\)
D
\(2x^2 - 13xy + 15y^2\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\((2x-3y)(x-5y)=2x^2 - 10xy - 3xy + 15y^2\\
=2x^2 - 13xy + 15y^2\)
Source: Myschool Past Questions Archive (Record #26682)
Mathematics
WAEC / WASSCE 2005
Number and Numeration
Solution
Make f the subject of the relation \(v = u + ft\)
A
\(\frac{v-u}{t}\)
B
\(\frac{u-v}{t}\)
C
\(t(v+u\)
D
\(\frac{v}{u}-t\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(v=u+ft \Rightarrow v-u=ft\Rightarrow f=\frac{v-u}{t}\)
Source: Myschool Past Questions Archive (Record #26683)
Mathematics
WAEC / WASSCE 2005
Number and Numeration
Diagram
Solution
In the diagram PQ and MN are straight lines. Find the value of x
Attached Figure / Diagram
A
13o
B
17o
C
28o
D
30o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
The straight line MN = 180 = 2(x+30o) + 86o =>
180 = 2x + 60o + 86o => 180o = 2x + 146o => 2x = 180 - 46 = 34o => x = 34/2 = 17o
Source: Myschool Past Questions Archive (Record #26686)
Mathematics
WAEC / WASSCE 2005
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
Solution
If y \(\alpha\) x\(^2\) and y = 1\(\frac{1}{4}\) when x = 4, find the value of y when x = \(\frac{1}{2}\)
A
\(2\frac{1}{2}\)
B
5
C
10
D
80
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y \(\propto x^2\), y = 1\(\frac{1}{4}\), x = 4
y = \(\frac{\text{k}}{x^2}\)
k = y x\(^2\) = \(\frac{5}{4}\) x 4\(^2\) = 20
y = \(\frac{20}{x^2}\) = \(\frac{20}{x^2}\) = \(\frac{20}{(\frac{1}{2})^2}\)
= \(\frac{20}{\frac{1}{4}}\) = 20 x 4 = 80
Source: Myschool Past Questions Archive (Record #26712)
Mathematics
WAEC / WASSCE 2005
Number and Numeration
Solution
The monthly salary of a man increased from N2,700 to N3,200. Find the percentage increase
A
10%
B
15%
C
15.6%
D
18.5%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
\(\% increase = \frac{Increase}{initial\hspace{1mm} salary}\times 100\%\)
Increase = N3,200 - N2,700 = N500
Initial \(\hspace{1mm} salary = N2,700.00 = \frac{N500}{N2,700}\times 100\% = 18.5\%\)
Source: Myschool Past Questions Archive (Record #26714)
Mathematics
NECO SSCE 2005
Number and Numeration
Mohammed is 8 years older than Joy now. In five years’ time he will be twice as old as Joy. How old is Joy now?
A
1\(\frac{1}{2}\)years
B
3years
C
4\(\frac{1}{2}\)years
D
6 years
E
8 years
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option B.
Source: Myschool Past Questions Archive (Record #42354)