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Mathematics
WAEC / WASSCE 2012
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
Given that the mean of the scores 15, 21, 17, 26, 18 and 29 is 21, calculate the standard deviation of the scores
A
\(\sqrt{10}\)
B
4
C
5
D
\(\sqrt{30}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
\(\begin{array}{c|c} x & x - x & (x - \bar{x})^2\\ \hline 15 & -6 & 36\\21 & 0 & 0\\17 & -4 & 16\\ 26 & 5 & 25 \\ 18 & -3 &9 \\ 29 & 8 & 64 \end{array}\)
\(E(x - \bar{x})^2\) = 150
N = 6
S.D = \(\sqrt{\frac{(x - x)^2}{N}}\)
S.D = \(\sqrt{\frac{150}{6}}\) = 5
Source: Myschool Past Questions Archive (Record #36775)
Mathematics
WAEC / WASSCE 2012
Permutations, Combinations & Probability
Solution
A bag contains 4 red and 6 black balls of the same size. If the balls are shuffled briskly and two balls are drawn one after the other without replacement, find the probability of picking balls of different colours
A
\(\frac{8}{15}\)
B
\(\frac{13}{25}\)
C
\(\frac{11}{15}\)
D
\(\frac{13}{15}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Prob(RB + BR) = Total balls = 4 + 6 = 10
= prob(\(\frac{4}{10} \times \frac{6}{9}\)) + prob(\(\frac{6}{10} \times \frac{4}{9}) = \frac{24}{90} + \frac{24}{90}\)
= \(\frac{48}{90} = \frac{16}{30} = \frac{8}{15}\)
Source: Myschool Past Questions Archive (Record #36780)
Mathematics
WAEC / WASSCE 2012
Indices, Logarithms & Surds
Solution
Which of these statements about y = \(\sqrt{8m}\) is correct?
A
log y = log 8 x log \(\sqrt{m}\)
B
log y = 3 log 2 x \(\frac{1}{2}\) log m
C
log y = 3 log 2 - \(\frac{1}{2}\) log m
D
log y = \(\frac{3}{2}\) log 2 + \(\frac{1}{2}\) log m
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y = \(\sqrt{8m}\); log y = log \(\sqrt{8m}\)
log y = log \(\sqrt{8}\) + log \(\sqrt{m}\)
log y = \(\frac{1}{2}\)log 2\(^3\) + log m\(\frac{1}{2}\)
log y = \(\frac{3}{2}\) log 2 + \(\frac{1}{2}\) log m
Source: Myschool Past Questions Archive (Record #36781)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Solution
If x + 0.4y = 3 and y = \(\frac{1}{2}\)x, find the value of (x + y)
A
1\(\frac{1}{4}\)
B
2\(\frac{1}{2}\)
C
3\(\frac{3}{4}\)
D
5
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
x + 0.4y = 3...(i)
y = \(\frac{1}{2}\)x
x = 2y
x - 2y = 0....(ii)
solve simultaneously; x + 0.4y
= 3 - x - 2y = 0
2.4 = 3
y = \(\frac{3 \times 10}{2.4 \times 10} \)
= \(\frac{30}{24} = \frac{5}{4}\)
x - 2(\(\frac{5}{4}\)) = 0
x - \(\frac{5}{2}\) = 0
x = \(\frac{5}{2}\)
x + y = \(\frac{5}{2} + \frac{5}{4}\)
\(\frac{10 + 5}{4} = \frac{15}{4}\)
= 3\(\frac{3}{4}\)
Source: Myschool Past Questions Archive (Record #36784)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Solution
Express 3 - [\(\frac{x - y}{y}\)] as a single fraction
A
\(\frac{3xy}{y}\)
B
\(\frac{x - 4y}{y}\)
C
\(\frac{4y - x}{y}\)
D
3 - \(\frac{x - y}{y}\)
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
(\(\frac{x -y}{y}\)); \(\frac{3}{1} - \frac{x y}{y}\)
= \(\frac{3y - (x - y)}{y}\)
= \(\frac{3y - x + y}{y}\)
= \(\frac{4y - x}{y}\)
Source: Myschool Past Questions Archive (Record #36787)
Mathematics
WAEC / WASSCE 2012
Sets, Logic & Venn Diagrams
Solution
If p = {prime factors of 210} and Q = {prime less than 10}, find p \(\cap\) Q
A
{1,2, 3}
B
{2, 3, 5}
C
{1, 3, 5,7}
D
{2,3,5,7}
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
prime factor of 210 = 2, 3, 5, 7
prime numbers less than 10 = 2, 3, 5 , 7
Source: Myschool Past Questions Archive (Record #36790)
Mathematics
WAEC / WASSCE 2012
Fractions, Decimals, Percentages & Approximations
Solution
Alfred spent \(\frac{1}{4}\) of his money on food, \(\frac{1}{3}\) on clothing and save the rest. If he saved N72000.00, how much did he spend on food?
A
N43,200.00
B
N43,000.00
C
N42,200.00
D
N40,000.00
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
let the total amount be Nx i.e (\(\frac{1}{4}\))x + (\(\frac{1}{3}\))x + 72,000 = x
\(\frac{x}{4} + \frac{x}{4} + 72,000 = x\)
\(\frac{3x + 4x + 86,400}{12} = x\)
cross multiply to clear fraction
12x = 3x + 4x + 86,400
12x - 7x = 86,400
5x = 86,400
x - \(\frac{86,400}{5}\) = 172,800
amount spent on food = \(\frac{1}{4} \times 172,800\)
= N43,200
Source: Myschool Past Questions Archive (Record #36792)
Mathematics
WAEC / WASSCE 2012
Indices, Logarithms & Surds
Solution
Solve (\(\frac{27}{125}\))-\(\frac{1}{3}\) x (\(\frac{4}{9}\))\(\frac{1}{2}\)
A
\(\frac{10}{9}\)
B
\(\frac{9}{10}\)
C
\(\frac{2}{5}\)
D
\(\frac{12}{125}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(\(\frac{27}{125}\))-\(\frac{1}{3}\) x (\(\frac{4}{9}\))\(\frac{1}{2}\)
= (\(\frac{3^3}{5^3}\))-\(\frac{1}{3}\)-\(\frac{1}{3}\) x (\(\frac{3^2}{3^2}\))\(\frac{1}{2}\) -\(\frac{1}{2}\)
= \(\frac{3^{-1}}{3^{-1}} \times \frac{2}{3}\)
= \(\frac{\frac{1}{3}}{\frac{1}{5}} \times \frac{2}{3}\)
\(\frac{1}{3} \times \frac{5}{1} \times {2}{3} = \frac{10}{9}\)
Source: Myschool Past Questions Archive (Record #36793)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Solution
The sum of the interior angles of regular polygon is 1800o. How many sides has the polygon?
A
16
B
12
C
10
D
8
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Sum = (n - 2)180
1800 = (n - 2)180
divide both sides by 180o
\(\frac{1800}{180}\) = (n - 2)\(\frac{180}{180}\)
10 = n - 2
10 + 2 = n
n = 12
Source: Myschool Past Questions Archive (Record #36794)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Solution
Find the coefficient of m in the expression of (\(\frac{m}{2} - 1 \frac{1}{2}\)) (m + \(\frac{2}{3}\))
A
-\(\frac{1}{6}\)
B
- \(\frac{1}{2}\)
C
-1
D
-1\(\frac{1}{6}\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
(\(\frac{m}{2} - 1\frac{1}{4}\))(m + \(\frac{2}{3}\))
(\(\frac{m}{2} - \frac{3}{2}\))(\(\frac{m}{1} + \frac{2}{3}\))
= \(\frac{m^2}{3} + \frac{3m}{6} - \frac{6}{6}\)
= \(\frac{2m - 9m}{6}\)
= \(\frac{-7m}{6}\)
= 1\(\frac{1}{6}\)
Source: Myschool Past Questions Archive (Record #36796)
Mathematics
WAEC / WASSCE 2012
Mensuration (Areas, Perimeters & Volumes)
Solution
The volume of a cuboid is 54cm3. If the length, width and height of the cuboid are in the ratio 2:1:1 respectively, find its total surface area
A
108cm2
B
90cm2
C
80cm2
D
72cm2
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
V = L x B x H
V = \(2x \times x \times x = 2x^3\)
= 54cm3
i.e. 2x3 = 54
x3 = \(\frac{54}{2}\) = 27
x = 3\(\sqrt{27}\)
x = 3
L = 2x i.e. 2 x 3 = 6cm
B = x i.e. x = 3cm
H = x i.e. x = 3cm
but A = 2(LB + LH + BH) = 2(6 x 3) + (6 x 3) + (3 x 3) = 2(18 + 18 + 9) = 2(45)
= 90cm2
Source: Myschool Past Questions Archive (Record #36799)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
Solution
A side and a diagonal of a rhombus are 10cm and 12cm respectively, Find its area
A
20cm2
B
24cm2
C
48cm2
D
96cm2
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
From the diagram above
B\(^2\) = 10\(^2\) - 6\(^2\) = 64
B = \(\sqrt{64}\) = 8 cm( B represent half the second diagonal not given)
So, the second diagonal not given = 8 + 8 = 16cm.
But, Area of a rhombus = \(\frac{1}{2}\) x both diagonals that is, \(\frac{1}{2}\) x d\(_1\) x d\(_2\)
Area of a rhombus = \(\frac{1}{2}\) x 12 x 16 = 6 x 16 = 96cm\(^2\)
Source: Myschool Past Questions Archive (Record #36800)
Mathematics
WAEC / WASSCE 2012
Algebraic Expressions, Polynomials & Factorisation
Factorise completely: 32x2y - 48x3y3
A
16x2y(2 - 3xy2)
B
8xy(4x - 6x2y2)
C
8x2y(4 - 6xy2)
D
16xy(2x - 3x2y2)
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 #36801)
Mathematics
WAEC / WASSCE 2012
Plane Geometry, Polygons & Circle Theorems
If x and y are variables and k is a constant, which of the following describes an inverse relationship between x and y?
A
y = kx
B
y = \(\frac{k}{x}\)
C
y = k\(\sqrt{x}\)
D
y = x + k
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 #36803)
Mathematics
WAEC / WASSCE 2012
Trigonometry, Elevation & Bearings
Diagram
Solution
In the diagram, |QR| = 10m, |SR| = 8m
o, o and |PS| = x, Find x
Attached Figure / Diagram
A
1.32m
B
6.32m
C
9.32m
D
17.32
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
In right angled \(\bigtriangleup\)QPR
tan 30o = \(\frac{10}{x + 8}\)
(x + 8) tan 30 = 10
x + 8 = \(\frac{10}{0.5773}\)
x +8 = 17.3
x = 17.3 - 8
x = 9.32
Source: Myschool Past Questions Archive (Record #36805)