mcr3u january student - · pdf filemcr3u: january 2004 ... formula sheet. 7. a formula sheet...

MCR3U: January 2004

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Ottawa-Carleton Catholic School Board Staff Development and Evaluation Department

System Wide Assessment in

MATHEMATICS

MCR3U

January 2004

Student's Name: ________________________________ Teacher's Name: ________________________________ School: __________________________________ Date: __________________________________

Good Luck!!

MCR3U: January 2004

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GRADE 11 MATHEMATICS MCR 3U

FINAL EXAMINATION

INSTRUCTIONS: 1. Read all questions carefully. 2. All questions are to be answered in the space provided. 3. Non-programmable calculators are permitted but cannot be shared. 4. Programmable calculators are NOT permitted. 5. Anyone caught cheating or prepared to cheat will receive a mark of zero on

the examination. 6. There are 12 pages to this examination including this page, but excluding the

formula sheet. 7. A formula sheet is supplied at the end of this exam. You may remove it.

EVALUATION:

Part A: Answers only 28 marks Part B: Short answers 48 marks Part C: Full solutions 15 marks

Technical and presentation marks 9 marks

TOTAL 100

Student Name: ___________________

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Part A: Answers only required in the space provided. (28 marks, 1 mark each)

1. Identify the type of sequence represented by: 2, 6, 10, 14, 18, … ____________________

2. State the general term of: 16, -8, 4, -2, 1,… ____________________

3. Determine the amount of an investment worth $5000 in 3 years at a rate of 4%/a compounded annually.

____________________

4. Simplify ( )

yx

xy2

322. ____________________

5. Evaluate 4

3

16−

. ____________________ 6. Solve 8132

=x . ____________________

7. What is the domain of the following? ____________________

8. a) State whether the following is a function. ___________________

b) Give a reason. ___________________

9. Write the following inequality in set notation. ___________________

úúúú

-5 -4 -3 -2 -1 0 1 2 3 4 5

10. For 23)( −= ttg , determine ).2(1−g ____________________

MCR3U: January 2004

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11. Given a function )(xfy = , what type of transformation

has been applied in the following: a) )(xafy = ____________________

b) )(kxfy = ____________________

c) )( pxfy += ____________________

d) qxfy += )( ____________________

12. State the complex conjugate for .23 i−− ____________________ 13. Simplify ( )( )ii 8435 −+ . ____________________

14. State the maximum or minimum value of: ____________________

( ) ( ) 4322

−+−= xxf

15. How many zeroes does the following equation have? ____________________ 353)( 2

−+−= xxxg

16. Draw a sketch of a parabola that has one root. ____________________

17. If 3

1sin =θ , in what two quadrants will the terminal arms lie?

____________________

18. Given 2

1cos −=x , π20 ≤≤ x , find the values of x. ____________________

19. Convert o120 to radians. ____________________

20. Give the transformation of xy sin= that will double the amplitude.

____________________

21. Solve for x to one tenth of a degree for 53sin10 =−x , oo

x 1800 ≤≤ .

____________________

22. The line segment A1A2 of a hyperbola is called the: ____________________ 23. State the center of the ellipse defined by: ____________________

( ) ( ) 1612422

=++− yx

24. What is the equation of the circle with the center (0,3) and radius 8 units?

____________________

MCR3U: January 2004

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PART B: Short Answer: SHOW ALL WORK! (48 marks) 1. For the geometric sequence with terms t2 8= , and t4 32= , find a and r.

(3 marks)

2. Evaluate. (3 marks)

4 3

3 2

2 1

2 3

− −

− −

+

+

3. Solve for x. (3 marks)

31

27

2 20

3

x

x

+=

MCR3U: January 2004

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4. For the following series − − − − +77 70 63 252.... , a) Find the number of terms in this series. (2 marks) b) Find the sum of the series. (1mark)

5. The graph of a relation is shown:

a) Graph ( )y f x=−1 . (2 marks)

b) State the domain and range of ( )f x−1 . (2 marks)

MCR3U: January 2004

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6. Determine the vertex of the following parabola by completing the square. (3 marks) f x x x( ) = − − −4 7 22

7. Sketch the reciprocal function of the given function on the axis below.

(3 marks)

8. Simplify the following and state the restrictions. (3 marks)

x x x

x

x3 22 15

12 9

3

6

− −

−÷

+

9. Sketch the graph of y = +

2

1

2sin θ π within the domain of πθ 40 ≤≤ .

(4 marks)

MCR3U: January 2004

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10. The average monthly maximum temperature of Ottawa can be modeled by

T t t( ) . cos= − +14 96

13π

, where T is the temperature in Celsius and t = 0

represents January1, t =1 represents February 1, and so on. a) When is the average monthly maximum temperature highest? Lowest?

(3 marks)

b) Use the model to predict when the temperature is 0° . (2 mark) 11. Prove the following identity. (3marks)

tantan sin cos

xx x x

+ =1 1

12. Find the equation of the circle whose diameter with end points A( , )− 2 4 and

B( , )2 8 . (2 marks)

MCR3U: January 2004

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13. For the conic 9 16 36 96 36 02 2x y x y− − + + = ,

a) Determine the type of conic. (1 mark) b) Write the conic in standard form. (2 marks)

c) State the asymptotes. (2 marks)

d) State the foci. (1 mark) e) Graph the conic. (2 marks)

MCR3U: January 2004

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MCR3U: January 2004

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Part C: Longer solutions. Show all work in the space provided. (15 marks) 1. Kelly has a part time job at Toys ‘R Us, and is saving money for a school

trip to Costa Rica next year. She deposits $500 at the end of every month for one year (12 months) in a saving plan that pays 6%/a, compounded monthly. a) How much money will she have in the account when the last $500 is

deposited? (2 marks)

b) How much interest has Kelly earned on her account? (2 marks)

2. Solve for x, to one decimal place, in the following trigonometric quadratic equation. (4 marks)

xx2cos12sin138 =+ , oo

x 18090 ≤≤

mcr3u january student - · pdf filemcr3u: january 2004 ... formula sheet. 7. a formula sheet...

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