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Mathematics
WAEC / WASSCE 2010
Number and Numeration
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
Number and Numeration
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
Geometry and Trigonometry
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Number and Numeration
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
Algebra
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
Geometry and Trigonometry
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
Number and Numeration
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
Statistics and 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
Number and Numeration
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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
Geometry and Trigonometry
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)