2010 - WAEC Mathematics Past Questions and Answers - page 3

21
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
correct option: a

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

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22
If y = \(\frac{y(2\sqrt{x^2 + m})}{3N}\), 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
\(\frac{\sqrt{9y^2 N - 3m}}{2}\)
correct option: b

y = (\frac{y(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})

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23
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
correct option: b

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

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24
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
correct option: a

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.

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25
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
loss of 10%
D
loss of 5%
correct option: c

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%

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26
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
correct option: b

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

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27
\(\begin{array}{c|c} x & 0 & 2 & 4 & 6\ \hline y & 1 & 2 & 3 & 4\end{array}\).
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 = \(\frac{1}{2}x + 1\)
correct option: d

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

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28
What is the value of x when y = 5?
A
8
B
9
C
10
D
11
correct option: a

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

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29
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
correct option: a

5 1 6 2seven
-2 6 4 4seven
--------
2 2 1 5
--------

the missing number is 2

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30
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\(\frac{1}{2}\)
correct option: a

(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})

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