preparation exercise for mathematics 2bio

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http://ordinaryguy92.wordpress.com Centre for Foundation Studies, IIUM

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PREPARATION EXERCISE FOR MATHEMATICS 2 (SHF1124)

1. Solve the equation2 o o

3cos sin 2 0 for 0 360x x x

Ans: 90o, 123.69

o, 270

o, 303.69

o

2. Given that yx tan2tan , show that12cos3

2sin3)tan(

y

yyx

3. Sketch the graph of xy 2sin for x0 .Ans:

4. Find the exact value for the following:(a)

60tan

300cos

120sin(b) 210cos30sec (c)

12

5sin

Ans: (a) 0 (b) ( c)

5. Prove that

22

2

tancotcos

tansin

6. 3 Calculators are chosen at random from 14 calculators of which 4 are defective. Find the probability

that:

(a) None of calculator is defective

(b) At least 2 are defective Ans: (a)91

30(b)

91

16

7. BagA contains 1 green pen, 2 red pens and 3 blue pens. Bag B contains 2 black erasers and 3 white

erasers. Bag Ccontains 6 gift cards labeled 1, 2, 3, 4, 5 and 6.

An item is picked randomly from each bag. Find the probability of getting a blue pen, a black eraser

and a gift card with a number less than 3. Ans:15

1

x

y

2

2

2

0.25

NAME: ... MATRIC NO: . PROGRAM:


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8. The probability that a patient is allergic to penicillin is 0.2. Suppose that this drug is given to 3

patients. Find the probability that:

(a) All 3 of them are allergic to it

(b) At least one of them is not allergic to it Ans: (a) 0.008 (b) 0.992

9. Table below shows the frequency distribution of the age of a group of tourists who visited a

National Museum.

Age Frequency

5 9 3

10 14 6

15 19 8

20 24 15

25 - 29 m

30 - 34 1

It is given that the first quartile age of the distribution is 15.125. Calculate the value ofm. Ans: m = 7

10. Table below shows the masses of 100 children in a kindergarten.

Mass(kg) Frequency

20-29 15

30-39 25

40-49 37

50-59 16

60-69 470-79 3

(a) Without using an ogive, estimate the median mass.

(b) Calculate the mean and standard deviation of the given distribution.

Ans: (a) m= 42.20 (b) 8.11,2.42

x

11. The mean and varience of six numbers are 6 and 8 respectively. When a new numberp is added, the

mean remains the same. Find the values ofp and the new varience.

Ans:p = 36, new varience = 6.8571

12. The probability that it will rain on a particular day is5

2. IfXis the number of rainy days in a week,

Find:

(a) the mean of the distribution ofX,

(b) the standard deviation of the distribution ofX.

Ans: (a) 2.8 (b) 1.296


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13. Diagram below shows a standardized normal distribution graph.

The probability represented by the area of the shaded region is 0.7286.

(a)Find the value ofk,(b)X is a continuous random variable which is normally distributed with a mean of

and a standard deviation of 8. Find the value of ifX= 70 when the z-score is k.

Ans: (a) k= 1.1 (b) = 61.2

14. In a certain school, 80% of the students have computers at home..

(a) If 6 students from that school are chosen at random, calculate the probability that at least 2students have computers at home.

(b) If the standard deviation of the distribution is 14, find the number of students in that school.Ans: (a)0.9984 (b)1225

15. The masses of students in a school have a normal distribution with a mean kg and a standard

deviation 12kg.

(a)A student is chosen at random from the school. The probability that the student has a mass less

than 45kg is 0.2266, find the value of .

(b) Hence,calculate the probability that a student chosen at random will have a mass between 42 kg

and 45 kg.

Ans: (a) 54 (b) 0.0679

BARAKALLAHU FIKUM ABADAN ABADA!

preparation exercise for mathematics 2bio

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