Revision Final MTH1022

7/27/2019 Revision Final MTH1022

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Revision Final MTH1022

APR 2013

1. State the degree, leading coefficient, constant term and type for the following polynomials:

a.

b.

c.

d.

e. f.

2. Given and . Calculate .

3. Given and . Calculate .

4. Given matrix . Find determinant of .

5. Given matrix . Find determinant of .

6. Given . Find .

7. Find if

[ ] 8. Find the derivative for the following functions:

a.

b.

c.

() (

)

9. Find the integral of ∫( ) and ∫( ) .

10. Skewness is a measure of data distribution. If , thecurve will distributed as :

A. SymmetricalB. Skewed to the left (Negative skewed)C. Skewed to the right (Positive skewed)D. Skewed both side

11. Which is the following is a Special Continuous Probability Distribution Function. A. Binomial Distribution Function.

B. Poisson Distribution Function.

C. Uniform Distribution Function.

D. Normal Distribution Function.

12. The set of all possible outcomes of the experiment is called:

A. Event

B. Experiment

C. Sample space

D. Outcomes

13. If S and T are two events and P(T) = 0.4, P(S n T) = 0.15 and P(S) = 0.5, find P(S U T).



14. Find the values of b, c, d and e in the following matrix equation:

15. The table below gives the number of cake sold by three programmes to raise

funds for their college.

ProgrammePlainCake

MarbleCake

CarrotCake Total

DVI 19

DVA 34

DMS 42

i. Express this information in the form of a matrix equation , where is a square matrix of

order 3 and both and are column matrices with ii. Find | | iii. Find

which are Plain Cake, Marble Cake and Carrot Cake by using Cramer’s rule.

16. HAMM, DHAS, and DEFTECT will produce three productions. The table 1 below

shows the number of production by each of them.

Production

(thousand)

Production

(thousand)

Production

(thousand)

Total Profit (RM,

thousand)

HAMM 2 1 1 122

DHAS 1 1 1 87

DEFTECT 2 2 1 146

a. Table 1 represent the information above in the form of a matrix equation , where

is a square matrix of order 3 and both and are column matrices with

b. Find | | c. Find the profit per company for each of the production by using Cramer’s rule.

d. Determine how much ISUZU’s profit (in thousand) when it produced 2 of

Production X, 1 of Production Y, and 3 of Production Z.

17.

Find the area between the graph of: y = x² - x - 2 and the ‘x’ axis, from x = -2 to x = 3.



18.

Find the area between and the between the values .

19.

Calculate the AREA of the region bounded by the curve and line .

20. A manufacturer claims that the average life of their electric light bulbs is not more than 2000 hours. A

random sample of 64 bulbs is tested and the life, , in hours recorded. The results obtained for average

life of electric light in selected sample is 1997 hours and standard deviation is 12.31 hours. Is there

sufficient evidence, at 1% level, that the manufacturer is over estimating the length of the life of the light

bulbs?

a. State the null and alternative hypothesis.

b. Sketch the rejection region at .

c. From the hypothesis in (a), test the manufacturer’s claim using , level of

significance.

21. An article reports that the mean amount of working hours per week for HAMM is less than 48.A

researcher believes that this amount is suitable for automotive industry. However, the

researcher wants to find out if the mean amount of working hours per week is 45 and standard

deviation is 10 hours will affect the production.60 staff from one production are selected

randomly.

a. State the null and alternative hypothesis.

b. Sketch the rejection region at .

c. From the hypothesis in (a), test the researcher’s claim using , level of significance.

-3

2



22. The selling price of a certain used car is inversely or negatively related to the age of a car. That is as

the age increases, the selling price tends to decrease. The following table shows 10 cars of a certain

mode.

Selling price (Y) Age in years (X)

980 5

1760 3

1100 5

600 8

2100 2

1600 3

1400 4

710 7

800 6

1800 3

a. Plot the data on a scatter diagram. Interpret the result.

b. Calculate the correlation coefficient () between selling price and age in years. Interpret the result.

c. Find the regression equation of selling price on age of cars.

d. Estimate the selling price of a 1.5 years old car.

23. For a certain type of automobile, yearly repair cost in Ringgit Malaysia (Y) are

approximately linearly related to the age in years (X) of the car. The following

data show the sample of cars:

Repair

cost (Y) Age (X)

80 2

99 3

79 1

138 7

170 10

140 8

114 4

83 4

94 2

110 5

a. Plot the data on a scatter diagram. Interpret the result.

b. Calculate the correlation coefficient (r) between repair cost and age of the car. Interpret the result.

c. Obtain the linear regression of Y on X.

d. Estimate the repair cost of 6 years old and 3 years old.

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