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SET A

UNIVERSITY OF TECHNOLOGY AND APPLIED SCIENCES, SALALAH

FPMA0901-APPLIED MATHS

21SP

ASSIGNMENT 25 Marks

Each questions carries 5 marks. Total 25 marks. (5 x 5 = 25marks)

1.

1

a. Let π: π
β π
and π: π
β π
defined by π(π₯) = 3π₯ β 2 and π(π₯) = π₯+4.

Then find π β1 (β2), (π β π)(β1).

(2 marks)

b. Let π: π
β π
be the quadratic function defined by π(π₯) = (π₯ + 1)2 β 4. Then find

the x-intercept, axis, vertex, maximum/minimum and the graph.

(3 marks)

2. The height π meters of a ball hit vertically upwards t seconds after it is given by

π(π‘) = 6π‘ β 3π‘ 2

a. How long does it take for the ball to reach its maximum height?

b. What is the maximum height of the ball?

c. How long does it take for the ball to hit the ground?

(5 marks)

3. a. i. Solve for x : 25π₯+3 = 125π₯

(1 mark)

ii. Rewrite the following using the logarithmic rule

3.

π₯ π¦

βππ ( π§β4 )

(1 marks)

b. The weight of a radioactive substance is given by π€(π‘) = 150(0.998)π‘ grams, where t

is the number of years.

(i) Find how much radioactive substance was put aside?

(ii) Find the weight after 100 years

(3 marks)

4. a. i. Convert the degree into radian: 300Β°

ii. Convert the radian into degree:

β5π

3

(2 marks)

b. For a triangle shown above, find

sinπ, cosπ, tanπ, sinβ
, cosβ
, tanβ
?

(3 marks)

5. The time in minutes for a sample of 30 students to get to school on a given day is

summarized in the following frequency table:

Time Interval

Frequency

0 β 10

3

10 β 20

3

20 β 30

10

30 β 40

7

40 β 50

4

50 β 60

1

60 – 70

2

Find the mean.

(5 marks)

*****######*****

SET B

UNIVERSITY OF TECHNOLOGY AND APPLIED SCIENCES, SALALAH

FPMA0901-APPLIED MATHS

21SP

ASSIGNMENT 25 Marks

Each questions carries 5 marks. Total 25 marks. (5 x 5 = 25marks)

1.

1

a. Let π: π
β π
and π: π
β π
defined by π(π₯) = 2π₯ β 3 and π(π₯) = π₯β4.

Then find π β1 (β2), (π β π)(β1).

(2 marks)

b. Let π: π
β π
be the quadratic function defined by π(π₯) = (π₯ β 1)2 β 4. Then find the

x-intercept, axis, vertex, maximum/minimum and the graph.

(3 marks)

2. The height π meters of a ball hit vertically upwards t seconds after it is given by

π(π‘) = 18π‘ β 3π‘ 2

d. How long does it take for the ball to reach its maximum height?

e. What is the maximum height of the ball?

f. How long does it take for the ball to hit the ground?

(5 marks)

3. a. i. Solve for x : 125π₯+3 = 25π₯

(1 mark)

βπ₯ π¦

ii. Rewrite the following using the logarithmic rule log ( π§ β2 )

(1 marks)

b. The weight of a radioactive substance is given by π€(π‘) = 100(0.998)π‘ grams, where

t is the number of years.

(i) Find how much radioactive substance was put aside?

(ii) Find the weight after (a) 100 years

(3 marks)

4. a.

i. Convert the degree into radian: β150Β°.

ii. Convert the radian into degree:

3π

4

.

(2 marks)

b. For a triangle shown above, find

sinπ, cosπ, tanπ, sinβ
, cosβ
, tanβ
?

(3 marks)

π

3

π

5

5. The time in minutes for a sample of 30 students to get to school on a given day is

summarized in the following frequency table:

Time Interval

Frequency

5 β 10

2

10 β 15

3

15 β 20

5

20 β 25

6

25 β 30

7

30 β 35

5

35 β 40

2

Find the mean.

(5 marks)

*****######*****

SETC

UNIVERSITY OF TECHNOLOGY AND APPLIED SCIENCES, SALALAH

FPMA0901-APPLIED MATHS

21SP

ASSIGNMENT 25 Marks

Each questions carries 5 marks. Total 25 marks. (5 x 5 = 25marks)

1

1. a. Let π: π
β π
and π: π
β π
defined by π(π₯) = 5π₯ β 3 and π(π₯) = 2π₯β1.

Then find π β1 (β2), (π β π)(β1).

(2 marks)

b. Let π: π
β π
be the quadratic function defined by π(π₯) = (π₯ + 2)2 β 9. Then find the

x-intercept, axis, vertex, maximum/minimum and the graph.

(3 marks)

2. The height π meters of a ball hit vertically upwards t seconds after it is given by

π(π‘) = 16π‘ β 2π‘ 2

a. How long does it take for the ball to reach its maximum height?

b. What is the maximum height of the ball?

c. How long does it take for the ball to hit the ground?

(5 marks)

3. a. i. Solve for x : 49π₯+3 = 2401π₯

(1 mark)

3

βπ₯π¦

ii. Rewrite the following using the logarithmic rule log ( π§ β1 )

(1 marks)

b. The weight of a radioactive substance is given by π€(π‘) = 50(0.998)π‘ grams, where t

is the number of years.

(ii)

Find how much radioactive substance was put aside?

(ii) Find the weight after (a) 100 years.

4. a.

i. Convert the degree into radian: 900Β° .

β7π

ii. Convert the radian into degree: 4

(3 marks)

(2 marks)

4

b. For a triangle shown above, find

sinπ, cosπ, tanπ, sinβ
, cosβ
, tanβ
?

(3 marks)

π

π

5

5. The time in minutes for a sample of 30 students to get to school on a given day is

summarized in the following frequency table:

Time Interval

Frequency

30 β 40

3

40 β 50

3

50 β 60

10

60 β 70

7

70 β 80

4

80 β 90

1

90 β 100

2

Find the mean and the standard deviation.

(5 marks)

*****######*****

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Tags:

Quadratic Function

maximum height

polynomial of degree 2

weight of a radioactive substance

degree into radian

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