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Mathematics
WAEC / WASSCE 2010
Fractions, Decimals, Percentages & Approximations
Correct 0.002473 to 3 significant figure
A
0.002
B
0.0024
C
0.00247
D
0.0025
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
No expanded working has been attached for this question yet. The verified answer is Option C.
Source: Myschool Past Questions Archive (Record #36518)
Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify 1\(\frac{1}{2} + 2\frac{1}{3} \times \frac{3}{4} - \frac{1}{2}\)
A
-2\(\frac{1}{3}\)
B
-2\(\frac{1}{4}\)
C
2\(\frac{1}{8}\)
D
2\(\frac{3}{4}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
1\(\frac{1}{2} + 2\frac{1}{3} \times \frac{3}{4} - \frac{1}{2}\)
\(\frac{3}{2} + \frac{7}{3} \times \frac{3}{4} - \frac{1}{2} = \frac{3}{2} + \frac{7}{4} - \frac{1}{2}\)
= \(\frac{6 + 7 - 2}{4} = \frac{11}{4}\)
= 2\(\frac{3}{4}\)
Source: Myschool Past Questions Archive (Record #36519)
Mathematics
WAEC / WASSCE 2010
Linear, Simultaneous & Quadratic Equations
Solution
The sum of 2 consecutive whole numbers is \(\frac{5}{6}\) of their product, find the numbers
A
3, 4
B
1, 2
C
2, 3
D
0, 1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let the no. be x and x + 1
x + (x + 1) = \(\frac{5}{6}\) of x(x + 1)
2x + 1 = \(\frac{5}{6}\) x(x + 1)
6(2x + 1) = 5x2 + 5x
12x + 6 = 5x2 + 5x
5x2 + 5x - 12x - 6 = 0
5x2 - 7x - 6 = 0
5x2 - 10x + 3x - 6 = 0
5x(x - 2) + 3(x - 2) = 0
(5x + 3)(x - 2) = 0
(5x + 3)(x - 2) = 0
(5x + 3) = 0
x - 2 = 0
for (5x + 3) = 0
5x = -3
x = \(\frac{-3}{5}\) (Imposible since x is a whole number)
x - 2 = 0
x = 2
x = \(\frac{-3}{5}\)(Impossible since x is a whole number)
x - 2 = 0
x = 2
The numbers are x = 2
x + 1 = 2 + 1
= 3
Source: Myschool Past Questions Archive (Record #36520)
Mathematics
WAEC / WASSCE 2010
Fractions, Decimals, Percentages & Approximations
Solution
A casting is made up of Copper and Zinc. If 65% of the casting is Zinc and there are 147g of Copper. What is the mass of the casting?
A
320g
B
420g
C
520g
D
620g
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
%Zinc + %Copper = 100%
65% + %Copper = 100%
%Copper = 100% - 65% = 35%
%Copper = \(\frac{\text{Mass of % Copper}}{\text{Mass of Casting}}\) x 100%
Mass of Casting = \(\frac{147}{35}\) x 100%
= 420g
Source: Myschool Past Questions Archive (Record #36521)
Mathematics
WAEC / WASSCE 2010
Inequalities & Linear Programming
Solution
Given that P = {x : 1 \(\leq x \leq 6\)}, and Q = {x : 2 \(\leq x \leq 10\)} where x is an integer. Find n(P \(\cap\) Q)
A
5
B
6
C
8
D
10
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
P = {1, 2, 3, 4, 5, 6}; Q = {3, 4, 5, 6, 7, 8, 9}
P \(\cap\) Q) = {2, 3, 4, 5, 6}
n(P \(\cap\) Q) = 5
Source: Myschool Past Questions Archive (Record #36522)
Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
The sum of 6 and one-third of x is one more than twice x, find x
A
x = 7
B
x = 5
C
x = 3
D
x = 2
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
6 = \(\frac{1}{3}x\) = 1 + 2x
6 = 1 = \(\frac{2x}{1} - \frac{x}{3}\)
5 = \(\frac{6x - x}{3} = \frac{5x}{3}\)
5 = \(\frac{5x}{3}\)
3 x 5 = 5x
15 = 5x
x = \(\frac{15}{5}\)
= 3
Source: Myschool Past Questions Archive (Record #36523)
Mathematics
WAEC / WASSCE 2010
Inequalities & Linear Programming
Solution
Given that = {x: -2 < x \(\leq\) 9}, where x is an integer what is n(T)?
A
9
B
10
C
11
D
12
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
T = {-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
n(T) = 11
Source: Myschool Past Questions Archive (Record #36524)
Mathematics
WAEC / WASSCE 2010
Inequalities & Linear Programming
Solution
Solve the inequality: 3(x + 1) \(\leq\) 5(x + 2) + 15
A
x \(\geq\) -14
B
x \(\leq\) - 14
C
x \(\geq\) -11
D
x \(\leq\) - 11
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
3(x + 1) \(\leq\) 5(x + 2) + 15
3x + 3 \(\leq\) 5x + 10 + 15
3x - 5x \(\leq\) 10 + 15 - 3
-2x \(\leq\) 22
x \(\geq\) \(\frac{-22}{2}\)
x \(\geq\) -11
Source: Myschool Past Questions Archive (Record #36526)
Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
An empty rectangular tank is 250cm long and 120cm wide. If 180 litres of water is poured into the tank. Calculate the height of the water
A
6.0cm
B
5.5cm
C
5.0cm
D
4.5cm
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Volume of water in tank = l x b x h = 180 litres
but 1 litre = 1000cm2
250 x 120 x hw = 180 x 1000
hw = \(\frac{180 \times 1000}{250 \times 120}\)
= 6cm
Source: Myschool Past Questions Archive (Record #36528)
Mathematics
WAEC / WASSCE 2010
Indices, Logarithms & Surds
Solution
Given that \(\frac{5^{n +3}}{25^{2n -3}}\) = 5º, find n
A
n = 1
B
n = 2
C
n = 3
D
n = 5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\frac{5^{n +3}}{25^{2n -3}} = 5^0\)
\(\frac{5^{n + 3}}{5^{2(2n - 3)}} = 5^0\)
n + 3 - 4n + 6 = 0
-3n + 9 = 0
-3n = -9
n = \(\frac{-9}{-3}\)
n = 3
Source: Myschool Past Questions Archive (Record #36529)
Mathematics
WAEC / WASSCE 2010
Permutations, Combinations & Probability
Solution
\(\begin{array}{c|c} \text{No. of pets} & 0 & 1 & 2 & 3 & 4 \\ \hline \text{No. of students} & 8 & 4 & 5 & 10 & 3\end{array}\) The table shows the number of pets kept by 30 students in a class. If a student is picked at random ftom the class. What is the probability that he/she kept more than one pet?
A
\(\frac{1}{5}\)
B
\(\frac{2}{5}\)
C
\(\frac{3}{5}\)
D
\(\frac{4}{5}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
pr. (More than one pet)
= \(\frac{\text{No. of students with > 1 pet}}{\text{total no. of students}}\)
= \(\frac{5 + 10 + 3}{30}\)
= \(\frac{18}{30}\)
= \(\frac{3}{5}\)
Source: Myschool Past Questions Archive (Record #36530)
Mathematics
WAEC / WASSCE 2010
Indices, Logarithms & Surds
Solution
Simplify 2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)
A
1
B
\(\frac{1}{3}\sqrt{3}\)
C
2\(\sqrt{3} - 5\frac{2}{3}\)
D
6\(\sqrt{3}\) - 17
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
2\(\sqrt{3}\) - \(\frac{6}{\sqrt{3}} + \frac{3}{\sqrt{27}}\)
= 2\(\sqrt{3} - \frac{6}{\sqrt{3}} + \frac{3}{\sqrt{9 \times 3}}\)
= 2\(\sqrt{3} - \frac{6}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} + \frac{3}{3\sqrt{3}}\)
= 2\(\sqrt{3} = 6 \frac{\sqrt{3}}{3} + \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}\)
= 2\(\sqrt{3} - 2\sqrt{3} + \frac{\sqrt{3}}{3}\)
= \(\frac{\sqrt{3}}{3} = \frac{1}{3} \sqrt{3}\)
Source: Myschool Past Questions Archive (Record #36531)
Mathematics
WAEC / WASSCE 2010
Trigonometry, Elevation & Bearings
Solution
If sin 3y = cos 2y and 0o \(\leq\) 90o, find the value of y
A
18o
B
36o
C
54o
D
90o
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
sin 3y = cos 2y, but sin \(\theta\) = cos(90 - \(\theta\))
sin 3y = cos(90 - 3y)
cos(90 - 3y) = cos 2y
90 - 3y = 2y
5y = 90
y = \(\frac{90}{5}\)
y = 18o
Source: Myschool Past Questions Archive (Record #36541)
Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
A rectangle has length xcm and width (x - 1)cm. If the perimeter is 16cm. Find the value of x
A
3\(\frac{1}{2}\)cm
B
4cm
C
4\(\frac{1}{2}\)cm
D
5cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
l = x; b = x - 1
perimeter = 2(l + b) = 16
l + b = \(\frac{16}{2}\) = 8
l + b = 8
x + x - 1 = 8
2x = 8 + 1
2x = 9
x = \(\frac{9}{2}\)cm
x = 4\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #36545)
Mathematics
WAEC / WASSCE 2010
Indices, Logarithms & Surds
Solution
Given that tan x = 1, where 0o \(\geq\) x 90o, evaluate \(\frac{1 - \sin^2 x}{\cos x}\)
A
2\(\sqrt{2}\)
B
\(\sqrt{2}\)
C
\(\frac{\sqrt{2}}{2}\)
D
\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Given tan x = 1
x = tan-1(1)
x = 45o
Now, \(\frac{1 - ( \frac{1}{\sqrt{2} )^2}}{\frac{1}{\sqrt{2}}}\)
= \(\frac{1 - \frac{1}{2}}{\frac{1}{2}}\)
= \(\frac{1}{2} + \frac{1}{\sqrt{2}}\)
= \(\frac{1}{2} \times \frac{1}{\sqrt{2}}\)
= \(\frac{\sqrt{2}}{2}\)
Source: Myschool Past Questions Archive (Record #36548)