Grade 11 Math Final Exam Review 2012

7/28/2019 Grade 11 Math Final Exam Review 2012

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M r.G a rd n e rsMCR3U Exam Review name _______________________

Mr.G a rd n e rs Definitive MCR3U Exam Review 2012

If you can get perfect on this review.you should be good to go!* Indicates that we will go over these questions in June.

Functions and Quadratic Functions, Rational Expressions and Algebra

1. For the function f(x) = 8 4x, evaluate(a) f(4) (b) x, iff(x) = -16 (c) f -1 (x) (d) f -1 (-5)

2. For the function g(x) = 2x2 8x+ 1, determine(a) g(-2) (b) x, ifg(x) = 11 (c) g -1 (x).

(d) Is g -1 (x) a function, or not? If not, what restriction on the domain willmake it a function?

(e) x, ifg -1 (x) = 1

3. What is the inverse function ofh(x) = -3x2 +6x+ 4, if the domain ofh(x) is x> 1?

* 4. Simplify each in exact form, using imaginary numbers where required.

(a) 32 (b) 121 (c) 48

(d) 2

124

(e) 3

273 (f)

4

246 +

5. Simplify each expression and State the restrictions.

(a) 152

932

+

xx

x

(b)2

2

4 4

65

2

93

x

xx

x

x ++

+

(c) 9

4

96

222

+

++

x

x

xx

x

Trigonometry

6. Complete the table. Express your answers in exact form.

Degrees 270o 450o

Radian measure4

7

6

11

Related Acute Angle

One more co terminal angle

7. If cos =10

3 , what are the possibilities for csc ? Hint: Use Pythagorean theorem!

8. Sketch each angle, state its related acute angle, and determine its exact ratios of each. (Hint: CAST rule!)

(a) sin 315o(b) cos

6

11 (c)

3

5tan

(d)

o135sec


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Mr. Gardners MCR3U Exam Review name _______________________Page 2

9. Solve the following equations for , where 0 < 360o, or 20


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15. What is the equation of each function, g and h, in the graph below? The angle is in degrees.

Exponential Functions

16. For the function ( ) ( ) 42 1 = xxf , determine the following

(a) The domain (b) The range (c) The y-intercept

(d) The horizontal asymptote (e) State the transformations which must be applied to ( ) xxf 2= to

obtain ( ) ( ) 42 1 = xxf .

(f) Sketch ( ) xxf 2= and ( ) ( ) 42 1 = xxf the function as accurately as you can.

17. Simplify the following

(a) (-5) -4 (b)3 27

(c)4

3

16

(d)( )4

16281 yx

* 18 Solve the following equations:

(a) 8132 =x (b) 10242 53 =x

(c) 16

1

4

342=

xx

19. A strain of bacteria grows at a rate of 15% per day. If a culture has 300 cells, how many will it have after sevendays? Round to the nearest cell.

20. Carbon-14 has a half-life of 30 minutes. What will be the mass of a 300 mg sample after 6 hours? Round your

answer to two decimal places.


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Sequence and Series

21. A sequence begins with ...,6,3,2

3,

4

3.

(a) What is the general term of thesequence?

(b) What 10th term. (c) What is the sum of the first 10terms of this sequence?

22. The first term of an arithmetic sequence is 27, and the common difference is -5

(a) What is the tenth term of thesequence?

(b) What is the simplified generalterm of the sequence?

(c) What is the sum of the first 25terms of the sequence?

23. What is the sum of the series 3 + 10 + 17 + + 94

24. A sequence is defined by 21 += nn tt . If 571 =t , write the next three terms and use sequence and series formulae

to calculate the sum of the first 15 terms.

Expanding Binomials using Pascals Triangle (The Binomial Theorem)

* 25. Expand and Simplify.

(a) ( )6yx (b) ( )42 ba+ (c) ( )53 2ba + (d) ( )52 3x

Financial Mathematics

26. Explain the differences between simple interest and compound interest.

27. A $300 investment is made at 2% annual interest, compounded monthly for 10 years. How much money will youearn in interest?

28. In seven years, you want to have $10 000 to help you buy a car. You found a seven-year bond which offers 4%interest compounded monthly. How much should you invest now to mean your goal of $10 000 in seven years?

29. To help pay for your university education, your parents deposit $250 at the end of every month into an account thatearns 3% annual interest compounded monthly.

(a) After ten years, how much money is in this account?(b) How much interest will have been earned over the ten years?

30. While you are at university, you set up an annuity which will give you $250 at the end of every two weeks, for four

years. Your financial advisor has found an annual interest rate of 3.54%, compounded biweekly.(a) How much money do you need to invest now so that you can make these regular biweekly withdrawals?(b) What is the amount you will earn in interest over the four years?

31. You take out a $15 000 car loan at an annual interest rate of 4%, compounded bi-weekly. You plan to pay back thecar loan with regular bi-weekly payments, starting two weeks from now, and you will have the loan paid off in fiveyears.(a) What will be your regular loan payment?(b) What will be the total amount of money you will have to pay out?(c) What is the cost of the loan due to interest?

The End! You can check your answers on my web sites exam outline page.


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Mr. Gardners Definitive MCR3U Exam Review 2012ANSWERS(If you see a typo, please tell me or email me ASAP!)

1. (a) -8 (b) x= 6 (c) 24

1+= xy (d)

4

13

2. (a) 17 (b) 5,1=x (c)

2

72

+=

xy (d) Not a function. To make it a function, set the domain of the

original function to 2x or 2x (or you could use 2>x or 21. Note, ifx< 1 then3

71 xy = would be the answer.

4. (a) 24 (b) 11 i (c) i34 (d) 32 (e) i31 (f)2

63 i+

5. (a) 2,3,5

3

x

x(b)

( )0,2,3,

2

62

+

xxx

(c)( )

3,3,)3()3(

1262

+

x

xx

x

6.

Note: 90o is not really an acute angle, but I haveapplied it to this situation.

7.91

10csc =

8. (a)2

1

2

3(b)

3(c)

2(d)

9. (a) 31.3o, 328.7 o, (b)4

3,

4

(c)

6

7,

6

(d) 195.5 o, 344.5 o

10. (a) 53.1 o (b) 30.5 o and 149.5 o (c) 6.6 o (e) 20.9 o 11. 71.14 m

12. (a) BC = 3768 m, DB = 404.9 m, BC is closer (b) 599.1 m

13. (a) Change left side tanand add (b) switch everything to sinx

and cosx. Work both sides. (c) Switch everything to sinxandcosx, work left side using common denominators.

14. Max 2, Min -4, Range 24 y , Domain R , Amp = 3, Vertical

Displacement = -1, Phase Shift4

, Period . GRAPH

15. g(x) = 3 cos x+ 2 , h(x) = 2 sin 2(x 45) 3

16. (a) all real numbers (b) y>-4 (c) -3.5(d) y=-4 (e) right 1 down 4 (f) GRAPH

17. (a)625

1(b) -3 (c)

8

1(d)

x

y23

3

18. (a) x=2 (b) x=5 (c) x= 52

19. 798 cells 20. 0.07 mg 21. (a) ( ) 124

3 =

nnt (b) 384 (c) 767.25

22 (a) -18 (b) ntn 532 = (c) -825 23. 679 24. sum is 1065

25. (a) 6542332456 51520156 yxyyxyxyxyxx +++

(b) 432234 8243216 babbabaa ++++

(c) 54336291215 3280804010 abbabababaa +++++

(d) 2434052709015 246810 ++ xxxxx

Degrees 270o -315o 450o 330o

Radian measure2

3

4

7

2

5

6

11

Related Acute Angle 90o 45o 90o 30o

One more co terminal angle 630o 405o 810o 690o


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26. Compound interest is modeled with an exponential function, where as simple interest is modeled with a linearfunction. The interest you earn is deposited directly back into your account, and becomes part of the principal forthe next time interest is calculated. Because of this, your interest earns interest and your money grows faster(exponentially) when compared to simple interest. Most of the financial world uses compound interest these days. Agraph will show the difference between compound and simple interest. On page 1, the lighter line shows a linearsimple interest model and the darker exponential curve shows the exact same investment but with a compound

interest model. As you can see, the compound model earns more interest at a faster rate then the simple interestmodel. The more the compound periods per year, the more interest is calculated and paid to you, and the moreinterest you will earn.

27. $66.36 28. $7561.36 29. $34,935.35, $4,935.35 30. $24, 227.75, $1, 772.25

31. $127.40, $16, 561.46, $1,561.46

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Grade 11 Math Final Exam Review 2012