Year 11 CAS Semester Two Exam 2006

8/3/2019 Year 11 CAS Semester Two Exam 2006

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CAS Mathematical Methods Unit 2 Semester Two Exam 2006

Year 11 CAS Semester Two Exam

Time Allowed:

Reading: 10 min

Writing: 1 hours

Student Name:_________________________________

Teacher: Mr P Sapiano Mrs K Marshall

Calculator Allowed


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Multiple choice section:

Q1 Solving forn in n P 2 = 34 yields n =8

a. 17b. 16

c. 15d. 14e. 13

Q2 A hospital committee of 5 is to be selected from 5 doctors and 8nurses. What is the probability the committee contains a majority ofnurses?

a. 322/429b. 320/429c. 5/13d. 5/8e. 1

Q3 The stationary point for the parabola with equationf(x) = 3x2 24x + 2

a. (0,2)b. (4,48)c. (-4,146)d. (2,-34)e. (4,-46)


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Q4 The equation of the parabola which passes through the point (1,10and has a gradient of 8x 1 for all values of x is

a. y = 4x2 x 2b. y = 4x 2 x 2c. y = 8x2 6 x 1d. y = 4x2 3xe. y = 8x2 x 6

Q5 If f(x) = (3x + 4)2 then f '(x) =

a. 12xb. 2(3x +4)c. 9xd. 18x + 24e. 18x

Q6 For the function with the rule f(x) = x3 - 3x + 3, the average rate ofchange of f(x) with respect to x between x = 2 and x = 3 is

a. 21b. 16c. 5d. 8e. 4

Q7 The exact value of cos( - 330 ) is

a. b. - 3c. - 3 / 2d. 3 / 2e. 3


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Q8 The solution to the equation 2 cosx 1 0ver the domain [ - , ] is

a. / 3 , / 3b. / 6 , / 6c. 5 / 6 ,5 / 6d. 2 / 3 , 2 / 3e. 2 / 3 , / 3

Q9 The period of the graph with equation y = 2 tan x is

a. 2b. 1c. 2 d. / 2e.

Q10. The log n( 1 / n4 ) equals

a. n / 4b. 4nc. 4d. n 4

e. 4

( 10 x 1 mark = 10 marks )


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Short Answer section:

Q1 A bacterial culture grows such that the number of bacteria N, after thours can be represented by: N = 1000 x 4 0.3t

a) Calculate how much is present after 5 hours.

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( 2 Marks )

b) How long does it take for the number to triple?

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( 4 marks )


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Q2 Find the equation of the tangent and the normal to the curve withequation f(x) = x3 + x2 - 3x + 6 at the point ( 1, 5 ).

Equation of tangent:

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

( 3 marks )

Equation of normal:__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

( 3 marks)


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Q 3 On the set of axes below :

(i) Sketch the graph of the trigonometric function y = (1/40)tan(x/2) for the domain [ 0 , ] include all coordinates

of axes intercepts and indicate asymptotes with a brokenline.

y

x

(ii) State the period of the function___________________________________________________________________________________________

( iii ) State the range of the function.

___________________________________________________________________________________________

( 3 + 1 + 1 = 5 marks )


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Q4 For the function y = 2log22x, state the:

(a) equation of the asymptote

________________________________________________________________________________________________(b) x intercept

________________________________________________________________________________________________

(c) domain________________________________________________________________________________________________

(d) range

________________________________________________________________________________________________

(1 + 1 + 1 + 1 = 4 marks )

Q5 Calculate the sum of the solutions to the equation 2cosx - 3 = 0over the domain [ 0, 2 ] in exact form.

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

( 3 marks)


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Analysis Section:

Q1 The flowerbed is to be L shaped, as shown in the diagram. Itsperimeter is 48m.

y m

3y m

a) Write down an expression for the area A m2 in terms of yand x.

___________________________________________________

____________________________________________________________________________________________________________________________________________________________________________________________________________

b) Find y in terms of x____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

x m

x m


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c) Write down an expression for A in terms of x______________________________________________________________________________________________________

____________________________________________________________________________________________________________________________________________________________________________________________________________

d) Find the values of x and y which give the maximum area.______________________________________________________________________________________________________

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

e) Find the maximum area._____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

( 5 x 2 = 10 marks )


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Q2 The temperature D C inside a house at t hours after 4 a.m. is given

By D = - 2cos (t/12) - 1 for 0 t 24.

a) Find the temperature inside the house at 8 p.m.

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

b) At what time / times is the inside temperature a maximum?

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

c) Sketch the graph of D for 0 t 24.D

t


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d) Determine the amount of time the inside temperature is above zerodegrees.______________________________________________________________________________________________________________________

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

( 4 x 2 = 8 marks )

Q3 Show, using first principles, the derivative of the function withequation f(x) = x2 8x + 15

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( 3 marks )


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Q4 Polonium is a radioactive substance. The decay of polonium isdescribed by the formula

M = Mo e kt

Where M is the mass of polonium left after tdays, and Moand kare constants. At time t = 0, M = 10 gram and at t= 140, M = 5 gram

a) Find the values of Mo and k.___________________________________________________________

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

b) What will be the mass of polonium after 70 days?

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

c) After how many days is the mass remaining 2 grams?

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

______________________________________________________________________________________________________________________


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( 2 + 2 + 2 = 6 marks )

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Year 11 CAS Semester Two Exam 2006