MCR 3U Practice Exam (F10) Page 1 of 10 Name: PART A (23 marks) Write only your answer for each of the following questions in the space provided. Each correct answer has a value of one (1) mark. 1. For the function y = 2(x + 3)2 − 5:

a) State the domain. b) State the range.

__________________ __________________

2. Given kxxy ++= 62 , for what value of k will the graph of the relation have only one x-intercept?

__________________

3. If 512)( −+= xxf , determine )3(f . __________________

4. The graph of 42 +−= xy is translated 5 units to the right. State the defining equation of the new graph.

__________________

5. A point on the graph of )(xfy = is (2, 4). The corresponding point on the

graph of )2( xfy = is:

__________________

6. State the equation of the asymptote(s) for:

a) 2)4(

1)( +

−=

xxf

b) 23)( 1 += −xxf

__________________ __________________

7. State the restrictions on62

3)(

++=

x

xxf .

__________________

8. Express x

64

1 as a power of 4.

__________________

9. Simplify, stating your answer using positive exponents: 32

3

2

6

yx

yx−

__________________

10. Write 4

3

)16( a in radical form. __________________

11. Simplify completely: b123

__________________

MCR 3U Practice Exam (F10) Page 2 of 10 Name:

12. Simplify: 2732 +

__________________

13. One solution to the equation 9848.0cos =θ is °⋅=10θ . Determine another value of θ to the nearest degree where °≤≤° 3600 θ .

__________________

14. Evaluate to 4 decimal places: cot 193°

__________________

15. Point P(4,–5) is on the terminal arm of an angle of measure θ in standard

position. Determine the exact value of θsin .

__________________

16. For the given periodic function, state:

(a) the amplitude (b) the period

__________________ __________________

17. Determine the equation xxf sin)( = as a cosine function.

__________________

18. The first term of a sequence is –5 and the common difference is –4. State the general term.

__________________

19. Classify the Fibonacci sequence arithmetic, geometric or neither. __________________

20. Write the recursion formula for the sequence 3, 9, 81, …

__________________

MCR 3U Practice Exam (F10) Page 3 of 10 Name: PART B (43 marks) Each of the following questions requires a short answer completion in the space provided. Show all work. Mark values for each question appear in the left margin. 1. Simplify:

a) 2x

x +1÷ 4x 3

x 2 −1 b) )32)(32( +−++ xx

[3]

[3]

2. Given the graph of )(xfy = , sketch the graph of ( )1+−= xfy .

[2]

-8 -6 -4 -2 2 4 6 8

-8

-6

-4

-2

2

4

6

8

x

y

MCR 3U Practice Exam (F10) Page 4 of 10 Name:

3. a) Describe the transformations on xy 3= to sketch 1)3(2 +−= − xy .

[3]

b) Rewrite the equation in function notation, where xxf 3)( = [1]

4. a) If you were given a function in the form )(xfy = , explain how you would determine the

defining equation of its inverse, namely )(1 xfy −= .

[2]

b) Consider the statement: “If a given relation, )(xfy = , is a function, then its inverse,

)(1 xfy −= , is always a function.” Is this statement true? Explain your answer.

[2]

MCR 3U Practice Exam (F10) Page 5 of 10 Name: 5. The profit, P(x), of a video company, in thousands of dollars, is given by the equation

50005505)( 2 −+−= xxxP , where x is the amount spent on advertising, in thousands of dollars. Determine the least amount spent on advertising that will result in a profit of at least $4 000 000.

[3]

6. The value of a new sports car depreciates at a rate of 8% per year. If the vehicle was bought for $45000, how much is it worth after 10 years?

[2]

MCR 3U Practice Exam (F10) Page 6 of 10 Name: 7. Write the equation of the graph below.

[2]

(–3, 9)

(–2, 5)

(–1, 3) (0, 2)

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

6

7

8

9

10

–1

–2

–3

–4

y

8. In a company telephone tree, each employee is to phone three other employees. In the first round,

three people are called. Each person phones three others, and so on.

a) During which round are 729 employees called? Show your work. [2]

b) What is the total number of people who have been called in the first seven rounds? Show your

work.

[2]

MCR 3U Practice Exam (F10) Page 7 of 10 Name: 9. You will be scheduled to work 40 hours during the March Break. You can choose the method of

payment from the following:

Choice 1: You can be paid $15 per hour Choice 2: You can be paid $1 for the first hour, $2 for the second hour, $3 for the third

hour, and the pattern continues.

What is your choice? Justify your answer. [3]

10. Sketch one cycle of the following trigonometric function:

( )�903sin2 +−= xy [3]

x

y

MCR 3U Practice Exam (F10) Page 8 of 10 Name:

11. Prove the identity: tanx + cosx

1+ sinx= secx

[3] 12. Two guy wires as shown in the diagram support a microwave tower. What is the height, h metres,

of the tower, to the nearest metre?

[3]

50 m 75 m

T

P R Q 100

h m

MCR 3U Practice Exam (F10) Page 9 of 10 Name: 13. The inside temperature of a building is modelled by T(t) = 3cos(15t) + 22, where T is the

temperature in °C and t is the number of hours elapsed since 5 A.M. The graph is shown below.

a) Using an appropriate calculation, explain why the coefficient of t in the equation is 15.

[2]

b) In another building, the temperature fluctuates in a similar manner except that the maximum temperature is 27°C and the minimum temperature is 23°C. Determine the defining equation that models the temperature in this other building.

[2]

12 24

2468

1012141618202224262830

T (°C)

5 A.M. 5 P.M.

5 A.M.

MCR 3U Practice Exam (F10) Page 10 of 10 Name: Formula Sheet (may be detached from the exam)

x = −b ± b2 − 4ac

2a

r

y=θsin r

x=θcos x

y=θtan

c

C

b

B

a

A sinsinsin ==

Abccba cos2222 −+=

tanx = sinx

cosx cotx = cosx

sinx

1cossin 22 =+ xx sec2 x =1+ tan2 x csc2 x =1+ cot2 x

1)( −== n

n arnft

dnanftn )1()( −+==

])1(2[2

dnan

Sn −+= or )(2 nn tan

S +=

Sn = a(rn −1)

r −1,r ≠1 or Sn = a(1− rn )

1− r,r ≠1