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Mathematics
WAEC / WASSCE 2007
Permutations, Combinations & Probability
Solution
If the probability of an event occurring is x, what is the probability of the event not occurring?
A
1 - x
B
x - 1
C
0
D
\(\frac{1}{x}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
If p is the probability of an event happening(occurring) and the probability of an event not occurring is p1 then p + p1 = 1
p1 = 1 - p
x1 = 1 - x
Source: Myschool Past Questions Archive (Record #36275)
Mathematics
WAEC / WASSCE 2007
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The table shows the ages(in years) of twenty children chosen at random from a community. What is the mean age? \(\begin{array}{c|c} Age(years) & 1 & 2 & 3 & 4 & 5 \\ \hline {\text {Number of children}} & 2 & 3 & 5 & 6 & 4 \end{array}\)
A
4.46 years
B
3.35 years
C
3.30years
D
3.00 years
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
Mean(age) = \(\frac{(1 \times 2) + (2 \times 3) + (3 \times 5) + (4 \times 6) + (5 \times 4)}{2 + 3 + 5 + 6 + 4}\)
= \(\frac{2 + 6 + 15 + 24 + 20}{20}\)
= \(\frac{67}{20}\)
= 3.35yrs
Source: Myschool Past Questions Archive (Record #36276)
Mathematics
WAEC / WASSCE 2007
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The table shows the ages(in years) of twenty children chosen at random from a community. What is the median of the distribution? \(\begin{array}{c|c} Age(years) & 1 & 2 & 3 & 4 & 5 \\ \hline {\text {Number of children}} & 2 & 3 & 5 & 6 & 4 \end{array}\)
A
3.5 years
B
3.0 years
C
2.5 years
D
2.0 years
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Median = (\(\frac{n + 1}{2})^{th}\)
= \(\frac{20 + 1}{2} = \frac{21}{2}\)
= 10.5
= \(\frac{{\text{10th term and 11th term}}}{2}\)
= \(\frac{3 + 4}{2} = \frac{7}{2}\)
= 3.5yrs
Source: Myschool Past Questions Archive (Record #36277)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
Divide the sum of 8, 6, 7, 2, 0, 4, 7, 2, 3, by their mean
A
9
B
8
C
7
D
6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
Sum = 8 + 6 + 7 + 2 + 0 + 4 + 7 + 2 + 3 = 39
mean = \(\frac{39}{9}\) = 4.33
then \(\frac{sum}{mean}\) = \(\frac{39}{4.33}\)
= 9
Source: Myschool Past Questions Archive (Record #36279)
Mathematics
WAEC / WASSCE 2007
Trigonometry, Elevation & Bearings
Solution
Q is 32 km away from P on a bearing 042o and R is 25km from P on a bearing of 132o. Calculate the bearing of R from Q.
A
122o
B
184o
C
190o
D
226o
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
△PQR is a right-angle triangle
/QR/\(^2\) = 32\(^2\) + 25\(^2\) = 1024 + 625 = 1649
/QR/ = \(\sqrt{1649}\) = 40.6Km
Let < PQR = \theta
\(\frac{25}{sin \theta}\) = \(\frac{40.6}{sin 90}\)
Sin \theta = \(\frac{25 Sin 90}{40.6}\) = 38º
Bearing of R from Q = 270 - (48 + 38) = 184º
Source: Myschool Past Questions Archive (Record #36280)
Mathematics
WAEC / WASSCE 2007
Trigonometry, Elevation & Bearings
Solution
The bearing of a point P from another point Q is 310o. If |PQ| = 200m, how far west of Q is P?
A
128.6m
B
153.2m
C
167.8m
D
187.9m
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
cos 40 = \(\frac{x}{200}\)
x - 200 x cosx
= 200 x 0.7660
x = 153.2m
Source: Myschool Past Questions Archive (Record #36281)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
Find the value of a if log\(_{10}\) a + log\(_{10}\)a\(^2\) = 0.9030
A
4.0
B
2.0
C
1.6
D
0.0
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
log\(_{10}\) a + log\(_{10}\)a\(^2\) = 0.9030
log (a x a\(^2\)) = 0.9030
log a\(^3\) = 0.9030
a\(^3\) = 10^.9030(antilogarithm table)
a\(^3\) = 7.998
a = 3\(\sqrt{7.998}\)
a = 1.9998 ≈ 2.0
Source: Myschool Past Questions Archive (Record #36283)
Mathematics
WAEC / WASSCE 2007
Fractions, Decimals, Percentages & Approximations
Solution
A messenger was paid N2.50 an hour during the normal working hours and 4.00 n hour during overtime. If he received N31.00 for 10 hours work, how many hours are for overtime?
A
2
B
3
C
4
D
6
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
Let normal working hour = x
let overtime = y
after 10 hours = N31.00
1 x 2.50x + 4y = 31
4 x x + y = 10
2.50x + 4y = 31
- 4x + 4y = 30
----------------
-1.5x = -9
x = 6; x + y = 10
6 + y = 10
y = 10 - 4
y = 4hrs for over time
Source: Myschool Past Questions Archive (Record #36284)
Mathematics
WAEC / WASSCE 2007
Fractions, Decimals, Percentages & Approximations
Solution
At what rate per cent per annum will N520.00 yield a simple interest of N39.00 in three years?
A
4%
B
3\(\frac{1}{2}\)%
C
3%
D
2\(\frac{1}{2}\)%
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
SI = \(\frac{PRT}{100}\)
39 = \(\frac{520 \times R \times 3}{100}\)
1560R = 3900
R = \(\frac{3900}{1560}\)
= 2.5%
R = 2\(\frac{1}{2}\)%
Source: Myschool Past Questions Archive (Record #36286)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
PQR is an equilateral triangle with sides 2\(\sqrt{3cm}\). calculate its height
A
1.7cm
B
3.0cm
C
3.2cm
D
3.9cm
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
By Pythagoras theorem
h2 = (2\(\sqrt{3})^2 - (\sqrt{3})^2\)
= 22(\(\sqrt{3})^2 - 3\)
4(3) - 3 = 112 - 3
h2 = 9
h = \(\sqrt{9}\)
= 3cm
Source: Myschool Past Questions Archive (Record #36287)
Mathematics
WAEC / WASSCE 2007
Plane Geometry, Polygons & Circle Theorems
Solution
Which of the following is a factor of 2 - x - x2?
A
1 - x
B
1 + x
C
x - 1
D
2 - x
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
2 - x - x2; (2 - 2x) + (x - x2)
= 2(1 - x) + x(1 - x)
= (1 - x)(2 + x)
= 1 - x
Source: Myschool Past Questions Archive (Record #36288)
Mathematics
WAEC / WASSCE 2007
Algebraic Expressions, Polynomials & Factorisation
Solution
make w the subject of the relation \(\frac{a + bc}{wd + f}\) = g
A
\(\frac{a + bc - fg}{dg}\)
B
\(\frac{a - bc + fg}{dg}\)
C
\(\frac{a + bc - f}{dg}\)
D
\(\frac{a + bc - dg}{dg}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
\(\frac{a + bc}{wd + f}\) = g(cross multiply)
a = bc + wdg + fg
wdg = a + bc - fg
w = \(\frac{a + bc - fg}{dg}\)
Source: Myschool Past Questions Archive (Record #36289)
Mathematics
WAEC / WASSCE 2007
Inequalities & Linear Programming
Solution
For what range of values of x is 4x - 3(2x - 1) > 1?
A
x > -1
B
x > 1
C
x < 1
D
x < -1
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
4x - 3(2x - 1) > 1
4x - 6x + 3 > 1
-2x > 1 - 3; 2x > -2
x < \(\frac{-2}{-2}\)
= x < 1
Source: Myschool Past Questions Archive (Record #36290)
Mathematics
WAEC / WASSCE 2007
Indices, Logarithms & Surds
Solution
Find the smallest value of k such that 2\(^2\) x 3\(^3\) x 5 x k is a perfect square.
A
3
B
5
C
15
D
30
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
2\(^2\) x 3\(^3\) x 5\(^1\) x k;
2\(^2\) x 3\(^2\) x 3 x 5 x k
2\(^2\) x 3\(^2\) x 15 x k
smallest value for k
2\(^2\) x 3\(^2\) x 15 = 2\(^2\) x 3\(^2\) x 15\(^2\)
k = 15
Source: Myschool Past Questions Archive (Record #36291)
Mathematics
WAEC / WASSCE 2007
Algebraic Expressions, Polynomials & Factorisation
Solution
Expand the expression(3a - xy)(3a + xy)
A
9a2 - x2y2
B
9a2 + x2y2
C
9a2 - xy
D
9a2 + x2y
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(3a - xy)(3a + xy); (3a)2 - (xy)2
difference of two sqs; 9a2 - x2y2
Source: Myschool Past Questions Archive (Record #36292)