mcr3u june student -...

MCR3U: June 2004

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Ottawa-Carleton Catholic School Board Staff Development and Evaluation Department

System Wide Assessment in

MATHEMATICS

MCR3U

June 2004

Student's Name: _________________________________ Teacher's Name: _________________________________ School: ___________________________________ Date: _______________________________________

Good Luck!!

MCR3U: June 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. 7. A formula sheet is supplied at the end of this exam.

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:

16, -8, 4, -1, 4

1, …

____________________

2. State the general term of: -30, -24, -18, -12, … ____________________

3. Determine the amount of $4000 borrowed for 2 years at 10%/a compounded semi-annually.

____________________

4. Simplify ( )3

23

−

b

aba . ____________________

5. Evaluate

+

− 02

1

1 444 . ____________________

6. Solve 1255 13

=−x . ____________________

7. What is the range of the following? ____________________

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

b) Give a reason. ___________________

9. Write the following inequality in set notation. ___________________

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

10. For ( )53

2)( −= ttf , determine ).1(1

−−f ___________________

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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 i34 +− . ____________________ 13. Simplify ( )ii 425 +− . ____________________

14. State the maximum or minimum value of: ____________________

( ) ( ) 342

++= xxg

15. How many roots does the following equation have? ____________________

( ) 342)(2

+−−= xxf

16. Draw a sketch of a parabola that has no zeroes. ____________________

17. If 3

2cos −=θ , in what two quadrants will the terminal arms lie?

____________________

18. Given 2

3sin =x , ππ ≤≤− x , find the values of x. ____________________

19. Convert 3

4π to degrees. ____________________

20. Give the transformation of xy cos= that will double the period.

____________________

21. Solve for x to one tenth of a degree for 01cos4 =+x , oox 1800 ≤≤ .

____________________

22. The length between the vertices of an ellipse is called the: ____________________

23. State the asymptotes of the hyperbola defined by: ____________________

644 22

=− yx

24. What is the center and radius of the circle ( ) 254 22=+− yx ?

____________________

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PART B: Short Answer: SHOW ALL WORK! (48 marks) 1. For the arithmetic sequence with terms t12 52= and t16 80= , find a and d.

(3 marks)

2. Evaluate. (3 marks)

21

11

25

25−−

−−

+

−

3. Solve for x. (3 marks)

2

2

27

19

+

+

=

x

x

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4. For the following series 1 1

1 4 ......... 65536,16 4

+ + + + + ?

a) Find the number of terms in this series. (2 marks)

b) Find the sum of the series. (1 mark)

5. The graph of a relation is shown:

a) Graph 1( )y f x−= . (1 mark)

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

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6. Determine the vertex of the following parabola by completing the square. (3 marks)

( ) 532 2

++−= xxxf

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)

22

1

132

12

2

−

+÷

++

−

x

x

xx

x

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9. Sketch the graph of 12cos2

1−= θy within the domain of 0 4≤ ≤θ π .

(4 marks)

10. The monthly sales of lawn equipment can be modeled by the function

5.536

sin4.32)( +

= tts

π, where S is the monthly sales in thousands of units

and t is the time in months where 1=t corresponds to January.

a) When are the average monthly sales of the lawn equipment greatest? Least? (3 marks)

b) When do the sales reach 25 440 units? Show the algebraic solution. (2 mark)

11. Prove the following identity. (3 marks)

xx

xcos1

cos1

sin 2

+=−

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12. Find the equation of the circle with a center at )2,1(− and x-intercept is 3.

(2 marks)

13. For the following conic, 061541694 22

=++−+ yxyx ,

a) Determine the type of conic. (1 mark) _______________

b) Write the conic in standard form. (2 marks)

c) Depending on the type of conic state the major/minor axis OR

transverse/conjugate axis. (2 marks)

d) State the foci. (1 mark)

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e) Graph the conic. (2 marks)

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Part C: Longer solutions. Show all work in the space provided. (15 marks) 1. Sean has a part time job at Canadian Tire, and is saving money for a school

trip to Costa Rica in two years. He needs $3800 for the trip. He wants to deposit equal amounts at the end of every three months for two years (24 months) in a saving plan that pays 8%/a, compounded quarterly. a) How much money does he need to deposit at the end of every 3

months in order to save the $3800? (2 marks) b) If Sean deposits $500 instead of the amount found in (b) every 3

months, how much spending money will he have for his trip? (1 mark)

2. Two roads intersect at an angle of 12o. Two cars leave the intersection, each

on a different road. One car travels at 90km/h and the other at 120 km/h. After 20 minutes, a police helicopter 1000m directly above and between the cars, notes the angle of depression of the slower car is 14o. What is the horizontal distance from the helicopter to the car? (5 marks)

3. Solve for x in the following trigonometric quadratic equation. (5 marks)

xx 2cos12cos2 2−=− , oo

x 3600 ≤≤

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