AIOU

1. Course: Understanding of Mathematics and Statistics (9417)
Semester: Spring, 2021
1
ASSIGNMENT No. 1
Q. 1
(a) Mr. Usman bought a bike for Rs. 60,000. If he sells that bike at half price, calculate his profit or loss
percentage.
Cost Price = Rs. 60000
Selling Price = 60000 / 2 = 30000
Loss = Cost Price – Selling Price
= 60000 – 30000
Loss = Rs. 30000
(b) Calculate the leather required to manufacture a football of radius 6 inches.
Radius = 6 inch
Surface area = 4πr^2
Surface Area = 4 * 3.14 * 6 * 6
= 452.16
Volume = 4/3 πr^3
= 4/3 * 3.14 * 6 * 6 * 6
Total Leather = 904.2
Q. 2
(a) Three sides of an equilateral triangle are given by . Find the exact length
of each side.
2y+4x = 3x+2y-3
4x – 3x = -3
x = -3
3x-3y+15 = 3x+2y-3
-3y-2y = -3-15
-5y = -18
Y = 18 / 5
Side 1: 18/5 -6 = -12/5
Side 2: -3-18/5+5 = -15-18+25 / 5 = -8/5
Side 3: -9+36/5-3 = -45+36-15 / 5 = -24/5
So -12/5, -8/5, -24/5 are the sides.
(b) The product of two positive consecutive even numbers is given by 80. Find the numbers.
Let the integers be:
x and x+2

2. Course: Understanding of Mathematics and Statistics (9417)
Semester: Spring, 2021
2
►x(x+2) = 80
►x^2 + 2x = 80
►x^2 + 2x -80 = 0
(Factorize using splitting the middle term)
►x^2 + 10x - 8x – 80 = 0
►x(x+10)-8(x+10) = 0
► (x-8)(x+10) = 0
Therefore the two integers are 8 and 10 (you can check this also- 8 and 10 are consecutive even integers and
they multiply into 80).
Q. 3
(a) Solve the following system of linear equations by using Cramer’s rule.
2x – y + z = 5, 4x + 2y + 3z = 8, 3x – 4y – z = 3

3. Course: Understanding of Mathematics and Statistics (9417)
Semester: Spring, 2021
3
(b) If the 4th and 21st terms of an A.P is 29 and 182 respectively. Find the 14th term and the general
formula for this sequence?
Let first term & common difference of Arithmetic Progression be a and d respectively.
Nth term of A.P. is a + (n - 1) d
Therefore, 4th term & 21th terms are
T4 = a + (4 - 1) d = a + 3d
T21 = a + (21 - 1) d = a + 20d
Therefore, a + 3d = 29 ————- (1)
And, a + 20d = 182 ——————— (2)
Subtracting (1) from (2)
17d = 153 => d = 153/17 => d = 9
Substitute d = 5 in (1)
a + 3 * 5 = 29 => a + 15 = 29
=> a = 29 - 15 => a = 14

4. Course: Understanding of Mathematics and Statistics (9417)
Semester: Spring, 2021
4
14th term = a + (14 - 1) d
= 14 + (14 - 1)*9 = 14 + 117
= 131
Q. 4
(a) A line is divided into five parts making a geometric sequence. The length of the shortest and the
longest part is 2 and 162 respectively. Find the length of the whole line?
a1 = 2
a5 = 162
Total Length of whole line = First term + Last term
= 2 + 162 = 164
(b) Use principle of mathematical induction to prove the following:
for every positive integer n.
Q. 5

5. Course: Understanding of Mathematics and Statistics (9417)
Semester: Spring, 2021
5
(a) Find of the given implicit function

6. Course: Understanding of Mathematics and Statistics (9417)
Semester: Spring, 2021
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7. Course: Understanding of Mathematics and Statistics (9417)
Semester: Spring, 2021
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8. Course: Understanding of Mathematics and Statistics (9417)
Semester: Spring, 2021
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(b)

9. Course: Understanding of Mathematics and Statistics (9417)
Semester: Spring, 2021
9