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Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
What is the length of a rectangular garden whose perimeter is 32cm and area 39cm2?
A
25cm
B
18cm
C
13cm
D
9cm
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
perimeter = 2(l + b) = 32
l + b = \(\frac{32}{2}\)
l + b = 16
b = 16 - 1.......(1)
Area = l + b = 39
lb = 39 .....(2)
put (1) into (2)
l(16 - 1) = 39
16l - l2 = 39
l2 = 13l - 3l + 39 = 0
l(l - 13) - 3(1 - 13) = 0
(l - 3)(l + 130 = 0
l - 3 = 0 or l - 13 = 0
l = 3cm or l = 13cm; The length in 13cm
Source: Myschool Past Questions Archive (Record #36551)
Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
Simplify \(\frac{2}{2 + x} + \frac{2}{2 - x}\)
A
\(\frac{4}{4 - x^3}\)
B
\(\frac{8}{4 - x^2}\)
C
\(\frac{4x}{4 - x^2}\)
D
\(\frac{8 - 4x}{4 - x^2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
\(\frac{2}{2 + x} + \frac{2}{2 - x}\)
\(\frac{2(2 - x) + 2(2 + x)}{(2 + x)(2 - x)} = \frac{4 - 2x + 4 + 2x}{4 - 2x + 2x - x^2}\)
= \(\frac{8}{4 - x62}\)
Source: Myschool Past Questions Archive (Record #36553)
Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
The sum of the exterior of an n-sided convex polygon is half the sum of its interior angle. find n
A
6
B
8
C
9
D
12
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
sum of exterior angles = 360o
Sum of interior angle = (n - 2) x 180
360 = \(\frac{1}{2}\) x(n - 2) x 180(90o)
360 = \(\frac{1}{2}\) x(n - 2) x 90o
\(\frac{360}{90}\) = a - 2
4 = n - 2
n = 4 + 2 = 6
Source: Myschool Past Questions Archive (Record #36554)
Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
If y = \(\frac{(2\sqrt{x^2 + m})}{3N}\), make x the subject of the formular
A
\(\frac{\sqrt{9y^2 N^2 - 2m}}{3}\)
B
\(\frac{\sqrt{9y^2 N^2 - 4m}}{2}\)
C
\(\frac{\sqrt{9y^2 N^2 - 3m}}{2}\)
D
\(\frac{\sqrt{9y^2 N - 3m}}{2}\)
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
y = \(\frac{(2\sqrt{x^2 + m})}{3N}\)
3yN = 2(\(\sqrt{x^2 + m})\)
\(\frac{3yN}{2} = \sqrt{x^2 + m}\)
(\(\frac{3yN}{2})^2 = ( \sqrt{x^2 + m})\)
\(\sqrt{\frac{9y^2N^2}{4} - \frac{m}{1}}\)
x = \(\frac{\sqrt{9Y^2N^2 - 4m}}{4}\)
x = \(\frac{\sqrt{9y^2N^2 - 4m}}{2}\)
Source: Myschool Past Questions Archive (Record #36558)
Mathematics
WAEC / WASSCE 2010
Sequences & Series (AP & GP)
Solution
The nth term of the sequence -2, 4, -8, 16.... is given by
A
Tn = 2n
B
Tn = (-2)n
C
Tn = (-2n)
D
Tn = n
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
sequence: -2, 4, -8, 16........{GP}
a = -2; r = \(\frac{4}{-2}\) = -2
nth term Tn = arn-1
Tn = (-2)(-2)^n-1
Tn = (-2)1 + n - 1
Tn = (-2)n
Source: Myschool Past Questions Archive (Record #36559)
Mathematics
WAEC / WASSCE 2010
Fractions, Decimals, Percentages & Approximations
Solution
How many times, correct to the nearest whole number, will a man run round circular track of diameter 100m to cover a distance of 1000m?
A
3
B
4
C
5
D
6
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
No. of times = \(\frac{\text{Total distance}}{\text{Circumference of circle}}\)
= \(\frac{\text{Total distance}}{\pi d}\)
= \(\frac{1000m}{\frac{22}{7} \times 100m}\)
= \(\frac{1000 \times 7}{2200} = 3.187\)
= 3(approx.) nearest whole no.
Source: Myschool Past Questions Archive (Record #36561)
Mathematics
WAEC / WASSCE 2010
Fractions, Decimals, Percentages & Approximations
Solution
Bola sold an article for N6,900.00 and made a profit of 15%. If he sold it for N6,600.00 he would make a
A
profit of 13%
B
loss of 12%
C
Profit of 10%
D
loss of 5%
medium Difficulty
Verified Correct Answer: Option C
Step-by-Step Mathematical Solution
s.p = N6900
%profit = 15%
%profit = \(\frac{s.p - c.p}{c.p}\) x 100%
15% = \(\frac{6900 - c.p}{c.p}\) x 100%
\(\frac{15}{100}\)c.p = N6900 - c.p
0.15 c.p = N6900 - c.p
1.15c.p + c.p = N6900
c.p = \(\frac{6900}{1.15}\)
= 6000.00
Now new S.P = N6600
profit = s.p - c.p = 6000 - 6600
= 600
%profit = \(\frac{600}{6600}\) x 100%
= 10%
Source: Myschool Past Questions Archive (Record #36563)
Mathematics
WAEC / WASSCE 2010
Statistics (Data Representation, Central Tendency & Dispersion)
Solution
The mean age of R men in a club is 50 years, Two men aged 55 and 63, left the club and the mean age reduced by 1 year. Find the value of R
A
18
B
20
C
22
D
28
medium Difficulty
Verified Correct Answer: Option B
Step-by-Step Mathematical Solution
mean age = \(\frac{\text{sum of ages}}{\text{no. of men}}\)
50 = \9\frac{sum}{R}\)
sum = 50R.....(1)
Sum of ages of the men that left = 55 + 63 = 188
remaining sum = 50R - 118
remaining no. of men = R - 2
now mean age = 50 - 1 = 49 years
49 = \(\frac{50R - 118}{R - 2}\)
49(R - 2) = 50R - 118
49R - 50R = -188 - 98
-R = -20
R = 20
Source: Myschool Past Questions Archive (Record #36564)
Mathematics
WAEC / WASSCE 2010
Coordinate Geometry
Solution
\(\begin{array}{c|c} x & 0 & 2 & 4 & 6\\ \hline y & 1 & 2 & 3 & 4\end{array}\).
The table is for the relation y = mx + c where m and c are constants. What is the equation of the line described in the tablet?
A
y = 2x
B
y = x + 1
C
y = x
D
y = \(\frac{1}{2}x + 1\)
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
y = mx + c; when x = 0; y = 1
1 = m(0) + c; 1 = 0 + c; c = 1
when x = 2; y = 2
2 = m(2) + c; 2 = 2m + c; but c = 1
2 = 2m + 1
2 - 1 = 2m
2m = 1
m = \(\frac{1}{2}\)
y = \(\frac{1}{2}\)x + 1
Source: Myschool Past Questions Archive (Record #36565)
Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
What is the value of x when y = 5?
y = \(\frac{1}{2}\) x + 1
A
8
B
9
C
10
D
11
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
when y = 5; x = ?; y = \(\frac{1}{2}\)x + 1
5 = \(\frac{1}{2}\)x + 1
5 - 1 = \(\frac{1}{2}\)x
4 = \(\frac{1}{2}\)x
x = 4 x 2
x = 8
Source: Myschool Past Questions Archive (Record #36584)
Mathematics
WAEC / WASSCE 2010
Number Bases & Modular Arithmetic
Solution
The subtraction below is in base seven. Find the missing number.
5 1 6 2seven
-2 6 4 4seven
--------
2 * 1 5
--------
A
2
B
3
C
4
D
5
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
5 1 6 2seven
-2 6 4 4seven
--------
2 2 1 5
--------
the missing number is 2
Source: Myschool Past Questions Archive (Record #36585)
Mathematics
WAEC / WASSCE 2010
Linear, Simultaneous & Quadratic Equations
Solution
If the sum of the roots of the equation (x - p)(2x + 1) = 0 is 1, find the value of x
A
1\(\frac{1}{2}\)
B
\(\frac{1}{2}\)
C
-\(\frac{3}{2}\)
D
-1\(\frac{1}{2}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
(x - p)(2x + 1) = 0
2x2 + x - 2px - p = 0
2x2 + x (1 - 2p) - p = 0
2x2 - (2p - 1)x - p = 0
divide through by 2
x2 - \(\frac{(2p - 1)}{2}\)x - \(\frac{p}{2}\) = 0
compare to x2 - (sum of roots)x + product of roots = 0
sum of roots = \(\frac{2p - 1}{2}\)
But sum of roots = 1
Given; \(\frac{2p - 1}{2}\) = 1
2p - 1 = 2 x 1
2p - 1 = 2
2p = 2 + 1 = 3
p = \(\frac{3}{2}\)
p = 1\(\frac{1}{2}\)
Source: Myschool Past Questions Archive (Record #36587)
Mathematics
WAEC / WASSCE 2010
Linear, Simultaneous & Quadratic Equations
Solution
If x2 + kx + \(\frac{16}{9}\) is a perfect square, find the value of k
A
\(\frac{8}{3}\)
B
\(\frac{7}{3}\)
C
\(\frac{5}{3}\)
D
\(\frac{2}{3}\)
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
x2 + kx + \(\frac{16}{9}\); Perfect square
But, b2 - 4ac = 0, for a perfect square
where a - 1; b = k; c = \(\frac{16}{9}\)
k2 - 4(1) x \(\frac{16}{9}\) = 0
k2 - \(\frac{64}{9}\) = 0
k2 = \(\frac{64}{9}\)
k = \(\sqrt{\frac{64}{9}}\)
k = \(\frac{8}{3}\)
Source: Myschool Past Questions Archive (Record #36591)
Mathematics
WAEC / WASSCE 2010
Plane Geometry, Polygons & Circle Theorems
Solution
If x km/h = y m/s, then y =
A
\(\frac{7}{18}\)x
B
\(\frac{11}{20}\)x
C
\(\frac{4}{15}\)x
D
\(\frac{5}{18}\)x
medium Difficulty
Verified Correct Answer: Option D
Step-by-Step Mathematical Solution
x kmh-1 = y ms-1
\(\frac{x km}{1 hr}\) = y ms-1
\(x \times \frac{1km}{1hr}\) = y ms-1
\(x \times \frac{1000m}{60 \times 60s}\) = y ms-1
\(x \times \frac{1000}{3600} \frac{m}{s}\) = y ms-1
\(x \times \frac{5}{18} ms^{-1}\)
\(x \times \frac{5}{18} ms^{-1}\) = y ms-1
y = \(\frac{5}{18}\)x
Source: Myschool Past Questions Archive (Record #36592)
Mathematics
WAEC / WASSCE 2010
Inequalities & Linear Programming
Solution
The mean of the numbers 2, 5, 2x and 7 is less than or equal to 5. Find the range of the values of x
A
x \(\leq\) 3
B
x \(\geq\) 3
C
x < 3
D
x > 3
medium Difficulty
Verified Correct Answer: Option A
Step-by-Step Mathematical Solution
mean \(\leq\) 5; \(\frac{2 + 5 + 2x + 7}{4}\) \(\leq\) 5
= \(\frac{14 + 2x}{4} \leq 5\)
= 14 + 2x \(\leq\) 5 x 4
14 + 2x \(\leq\) 20 ; 2x \(\leq\) 20 - 14
2x \(\leq\) 20 - 14
2x \(\leq\) 6
x \(\leq\) \(\frac{6}{2}\)
x \(\leq\) 3
Source: Myschool Past Questions Archive (Record #36594)