# FPMA 0901 CCHS Quadratic Function & Weight of A Radioactive Substance Problem

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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 𝑓: 𝑅 → 𝑅 and 𝑔: 𝑅 → 𝑅 defined by 𝑓(𝑥) = 3𝑥 − 2 and 𝑔(𝑥) = 𝑥+4.
Then find 𝑓 −1 (−2), (𝑓 ∘ 𝑔)(−1).
(2 marks)
b. Let 𝑓: 𝑅 → 𝑅 be the quadratic function defined by 𝑓(𝑥) = (𝑥 + 1)2 − 4. Then find
the x-intercept, axis, vertex, maximum/minimum and the graph.
(3 marks)
2. The height 𝑔 meters of a ball hit vertically upwards t seconds after it is given by
𝑔(𝑡) = 6𝑡 − 3𝑡 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 : 25𝑥+3 = 125𝑥
(1 mark)
ii. Rewrite the following using the logarithmic rule
3.
𝑥 𝑦
ℓ𝑜𝑔 ( 𝑧√4 )
(1 marks)
b. The weight of a radioactive substance is given by 𝑤(𝑡) = 150(0.998)𝑡 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: 300°
ii. Convert the radian into degree:
−5𝜋
3
(2 marks)
b. For a triangle shown above, find
sin𝜃, cos𝜃, tan𝜃, sin∅, cos∅, tan∅?
(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 – 10
3
10 – 20
3
20 – 30
10
30 – 40
7
40 – 50
4
50 – 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 𝑓: 𝑅 → 𝑅 and 𝑔: 𝑅 → 𝑅 defined by 𝑓(𝑥) = 2𝑥 − 3 and 𝑔(𝑥) = 𝑥−4.
Then find 𝑓 −1 (−2), (𝑓 ∘ 𝑔)(−1).
(2 marks)
b. Let 𝑓: 𝑅 → 𝑅 be the quadratic function defined by 𝑓(𝑥) = (𝑥 − 1)2 − 4. Then find the
x-intercept, axis, vertex, maximum/minimum and the graph.
(3 marks)
2. The height 𝑔 meters of a ball hit vertically upwards t seconds after it is given by
𝑔(𝑡) = 18𝑡 − 3𝑡 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 : 125𝑥+3 = 25𝑥
(1 mark)
√𝑥 𝑦
ii. Rewrite the following using the logarithmic rule log ( 𝑧 −2 )
(1 marks)
b. The weight of a radioactive substance is given by 𝑤(𝑡) = 100(0.998)𝑡 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: −150°.
ii. Convert the radian into degree:
3𝜋
4
.
(2 marks)
b. For a triangle shown above, find
sin𝜃, cos𝜃, tan𝜃, sin∅, cos∅, tan∅?
(3 marks)
𝜃
3
𝜑
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 – 10
2
10 – 15
3
15 – 20
5
20 – 25
6
25 – 30
7
30 – 35
5
35 – 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 𝑓: 𝑅 → 𝑅 and 𝑔: 𝑅 → 𝑅 defined by 𝑓(𝑥) = 5𝑥 − 3 and 𝑔(𝑥) = 2𝑥−1.
Then find 𝑓 −1 (−2), (𝑓 ∘ 𝑔)(−1).
(2 marks)
b. Let 𝑓: 𝑅 → 𝑅 be the quadratic function defined by 𝑓(𝑥) = (𝑥 + 2)2 − 9. Then find the
x-intercept, axis, vertex, maximum/minimum and the graph.
(3 marks)
2. The height 𝑔 meters of a ball hit vertically upwards t seconds after it is given by
𝑔(𝑡) = 16𝑡 − 2𝑡 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 : 49𝑥+3 = 2401𝑥
(1 mark)
3
√𝑥𝑦
ii. Rewrite the following using the logarithmic rule log ( 𝑧 −1 )
(1 marks)
b. The weight of a radioactive substance is given by 𝑤(𝑡) = 50(0.998)𝑡 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: 900° .
−7𝜋
ii. Convert the radian into degree: 4
(3 marks)
(2 marks)
4
b. For a triangle shown above, find
sin𝜃, cos𝜃, tan𝜃, sin∅, cos∅, tan∅?
(3 marks)
𝜃
𝜑
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 – 40
3
40 – 50
3
50 – 60
10
60 – 70
7
70 – 80
4
80 – 90
1
90 – 100
2
Find the mean and the standard deviation.
(5 marks)
*****######*****

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