Math 30-1 Practice Final One 30-1 Practice Final - Exam One When is divided by x - 2, the remainder is 20. The same polynomial has a factor of x + 2. Two equations that can be used

Math 30-1 Practice Final

Exam One

All of the questions in this practice exam are examples from the workbook that have been modified to reflect the multiple choice and numeric response format commonly found on exams.

Most questions in this practice exam are at the standard of excellence level of difficulty.

The formula sheet, student response sheet, and answer keycan be found at the back of the exam.

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www.math30.caMath 30-1 Practice Final - Exam One

When is divided by x - 2, the remainder is 20. The same polynomial has a factor of x + 2. Two equations that can be used to determine the values of m and n are:

2.

A.

C.

D.

B.

1. If the polynomial is represented with the form

A.

C. 1D. 2

B.

The graph of is shown below.

, the value of a is:

The information in this box is required to answer the next question.

3. The height of the ladder as a function of its base distance d is:

A.

C.

D.

B.

The information in this box is required to answer the next two questions.

A ladder that is 3 m long is leaning against a wall. The base of the ladder is d metres from the wall, and the top of the ladder is h metres above the ground.

d

h3 m

4. When the top of the ladder is metres above the ground, the distance from the wall to the base of the ladder is:

A. 1 m

C. 2 m

D. 2.2 m

B. 1.5 m

Math 30-1 Practice Final - Exam Onewww.math30.ca

a) b)

c) d)

Graphs:

Randomly Sorted Functions:

1.

2.

3.

4.

NR 1. The correct order of the functions to graphs a, b, c, and d is:


Graph a b c d

Function

Potential solutions for the equation can be found by solving:5.

A.

C.

D.

B.

, and there are no extraneous roots.

, and there is one extraneous root.

, and there are no extraneous roots.

, and there is one extraneous root.


6.

A.

C.

B.

D.


The equation can be solved by finding the x-intercepts of the related function, .

The graph of and its x-intercept are correctly shown in:


7. The transformation order that describes the spaceship’s new size and position (without colliding with the rocks) is:

A. reflection about the x-axis; vertical translation 7 units down; reflection about the y-axis; horizontal stretch by a scale factor of 1/2; and a horizontal translation 5 units right.

C. horizontal translation 5 units right; reflection about the x-axis; reflection about the y-axishorizontal stretch by a scale factor of 1/2; vertical translation 7 units down.

D. reflection about the x-axis; vertical translation 7 units down; horizontal translation 5 units right; reflection about the y-axis; horizontal stretch by a scale factor of 1/2.

B. horizontal stretch by a scale factor of 1/2; reflection about the x-axis; reflection about the y-axis; horizontal translation 5 units right; vertical translation 7 units down.


The goal of the video game Space Rocks is to pilot a spaceship through an asteroid field without colliding with any of the asteroids.

Original position of ship

Final position of ship

The spaceship acquires two power-ups. The first power-up halves the original width of the spaceship, making it easier to dodge asteroids. The second power-up is a left wing cannon.


8. Given the functions and , the graph of

A.

C.D.

B.

is identical to the transformation:

10. A function that expresses the area of the circular wave as a function of time is:


A pebble dropped in a lake creates a circular wave that travels outward at a speed of 30 cm/s. The radius of thewave can be represented with , and the areaof a circle is .

A.

C.D.

B.

9. The function can be formed from the function composition:

A.

C.D.

B.and, where .

and, where .

and, where ..and, where


11. The equation has:

A. no solution.

C. one solution at x = 1.5.D. two solutions.

B. one solution at x = -1.5.

12. One-third of 3234 is equal to:

A.

C.D.

B.

13. The value of x in can be determined by solving the equation:

A.

C.

D.

B.

14.

A.

C.

D.

B.

A vertical translation of the form is applied to the graph of so the image has an x-intercept of (9, 0). This can be represented with the transformation equation:


The strength of an earthquake is calculated using Richter’s formula:

where M2 is the magnitude of the strong earthquake, M1 is themagnitude of the weak earthquake, and A2 / A1 is the seismographamplitude ratio for the two earthquakes.

NR 2. Rounded to the nearest tenth, the magnitude of an earthquake with triple the seismograph amplitude of a magnitude 5.0 earthquake is a.b. The values of a and b are:


a b

15.

A.

C.

D.

B.


Rounded to four decimal places, the values of a and b are:

3 radThe coordinates of a point on the unit circle can be expressed in the form , where θis the angle measured in radians.

a = -0.9986, b = 0.0523

a = -0.9900, b = 0.1411a = -0.8660, b = 0.5000

a = -0.5000, b = 0.8660


The point is shown in the diagram to the right.

16.

A.

C.

D.

B.

If the amplitude of each graph is quadrupled, the new points of intersection are:


The graphs of and intersect at the points shown.

0

5

-5


17.

A.

C.

D.

B.


The height of the helicopter as a function of the angle of elevation, and its domain, is:

θ

h

150 m

A person is watching a helicopter ascend from a distance 150 m away from the takeoff point. Assume that the height of the person is negligible compared to the height of the helicopter.



For Grand Prairie, a trigonometric function that gives the number of daylight hours as a function of day number is:

n

d(n)

-50 0 50 100 150 200 250 300 350 400

4

8

12

16

20

24

NR 3. To the nearest hundredth, the number of daylight hours on May 2 (day number 121) is ab.cdThe values of a, b, c, and d are:

NR 4. Rounded to the nearest day, the number of days with more than 17 daylight hours is:

a b c d


18.

A.

C.

D.

B.

The equation has the solution(s):

and

and


19.

A.

C.

D.

B.

If the related functions of each factor of are graphed, it can be observed that:

contributes three solutions to the solution set.

contributes only one solution to the solution set.does not contribute any solutions to the solution set.

contributes only one solution to the solution set.

-3

3

-2

-1

2

1

2ππ

The equation can be solved by factoring the left side to get .

Each factor can be set equal to zero to get the solution set:

The graph of is shown on the right.


only.

only.


20. The graph that most accurately represents the stream of water hitting the wall is:

A rotating sprinkler is positioned 4 m away from the wall of a house. The wall is 8 m long. As the sprinkler rotates, the stream of water splashes the house d meters from point P.

Note: North of point P is a positive distance, and south of point P is a negative distance.

Pθ

d

N

S

W E

8 m4 mThe tangent function expresses the distance

where the water splashes the wall as a function of therotation angle θ.

-8

8

4

-4

θ

d

2π π 3

2π 2π

A.

-8

8

4

-4

θ

d

2π π 3

2π 2π

C.

-8

8

4

-4

θ

d

2π π 3

2π 2π

B.

-8

8

4

-4

θ

d

2π π 3

2π 2π

D.




21. The error occured in step:

A student attempted the proof of atrigonometric identity, but madean error.

A. I

C. III

D. IV

B. II

I

II

III

IV


Each graph shows the graphical solution of a trigonometric equation.

-1

1

2ππ

I

-1

1

2ππ

II

-1

1

2ππ

III

-1

1

2ππ

IV

22. All of the equations and graphs above contribute to the solution set of except:

A. I

C. III

D. IV

B. II




Each of the trigonometric expressions below can be simplified to a numeric value.

2.

3.

1.

4.

NR 5. The ascending numeric order of the simplified trigonometric expressons is:

If the value of , the value of within the same domain is:

23.

A.

C.

D.

B.


NR 6. The order in which the steps appear as the proof is completed is:

Randomly Sorted Steps:

1.

2.

3.

4.

A selection of the steps required to complete the proof of:

have been randomly sorted.


Randomly Sorted Answers:

1.

2.

3.

4.

Simplify each expression using a double angle identityso that it contains just one trigonometric ratio.

a)

b)

c)

d)

NR 7. When a, b, c, and d are simplified, the order of the answers is:


a b c d



24. Rounded to the nearest tenth, the value of x is:

A. 80.1

C. 89.3

D. 92.9

B. 87.5

57

176

153

104

A

B

xIn the diagram on the right, it can be determined that:

The value of x can then be found by solving the equation:

and

25. The trigonometric equation , , has the solution:

A.

C.

D.

B.

27. The cannonball will travel its maximum distance when the angle of the cannon is:

A. 0°

C. 45°

D. 90°

B. 30°

28. If the cannonball travels a horizontal distance of 100 m, possible cannon angle(s) are:

A. 24.6° or 65.4°

C. 32.1° or 57.9°

D. 45.0° only

B. 30.0° or 60.0°

The information in this box is required to answer the next three questions.

26. The distance function can be written with a single trigonometric function as:

A.

C.

D.

B.

θ

If a cannon shoots a cannonball θ degrees above the horizontal,the horizontal distance traveled by the cannonball before it hitsthe ground can be found with the function:

where the initial velocity of the cannonball is 36 m/s.

,


29.

A.

C.

D.

B.

The equation can be simplified to the quadratic equation:

5♣ 6♥ 2♦

A 4♥

b) all of the cards are the same color?

c) all of the cards are the same suit?

d) the hand has two pairs?

a) the ace of spades and two of diamonds must be in the hand?

Question: If a 5-card hand is dealt from a deck of 52 cards, how many distinct 5-card hands are there if:


1.

2.

3.

4.

NR 8. The correct order of the answers to questions a, b, c, and d is:

A deck of cards contains 52 cardsand is subdivided into:

13 black clubs13 black spades13 red diamonds

13 red hearts.


a b c d

30.

A.

C.

D.

B.

How many ways can six people be split into two equal-sized groups?



1.

2.

3.

4.

b) A set of tiles contains eight letters, A - H. If two of these sets are combined, how many ways can all the tiles be arranged?

A BC

a) A Grade 12 student is taking Biology, English, Math, and Physics in her first term. If a student timetable has room for five courses (meaning the student has a spare), how many ways can she schedule her courses?

Block 1Block 2Block 3Block 4Block 5

CourseMath 30-1

SparePhysics 30

English 30-1Biology 30

BlockOne Possible Timetable

c) How many ways can four bottles of different spices be arranged on a spice rack with holes for six spice bottles? SageParsley Garlic Thyme

One Possible Arrangement

d) A stir-fry dish comes with a base of rice and the choice of five toppings: broccoli, carrots, eggplant, mushrooms, and tofu. How many different stir-fry dishes can be prepared if the customer can choose zero or more toppings?

Questions:

NR 9. The correct order of the answers to questions a, b, c, and d is:



31.

A.

C.

D.

B.

If the letters in SASKATOON are arranged such that the letters K and T are kept together (and in the order KT), the number of unique arrangements is:

32.

A.

C.

D.

B.

If there are 8 rock songs and 9 pop songs available, how many unique playlists containing3 rock songs and 2 pop songs are possible?

A multiple choice test contains 5 questions, and each question has four possible responses.

A C D1.

A C D2.

A B D3.

A B C4.

A C D5.

One Possible Answer Key

NR 10. The number of unique answer keys that are possible is:



A

B

1 1 1 1 1

1

1

1

1

Step 1: Write 1’s at all the verticies alongthe left and top sides. (We will be using aPascal’s Triangle pattern to solve this.)

A

B

1 1 1 1 1

1

1

1

1

2 3 4 5 6

3 6

4 10

5 15

+ + + + +

+ +

+ +

+ +

Step 2: Fill in the inner verticies by addingtogether the adjacent diagonal verticies using the pattern shown.

A

B

1 1 1 1 1

1

1

1

1

2 3 4 5 6

3 6 5

4 10 10

5 15

Step 3: Continue the pattern by sliding the 5 and 10 as shown.

A

B

1 1 1 1 1

1

1

1

1

2 3 4 5 6

3 6 5 11

4 10 10 15 26

5 15 25 40 66

+

++

+

+

+

Step 4: Continue adding together adjacent diagonal verticies until reaching Point B.There are 66 pathways between points A and B.

A

B

Example: How many unique pathways existbetween points A and B?


The question corresponding to this information is on the next page.


33.

A. 44

C. 54

D. 65

B. 48

The number of pathways between points A and B in the diagram shown is:

A

B

This question uses the information found on the previous page.

The expansion of the binomial is shown below:

NR 11. The value of a in the binomial expansion is:


NR 12. In the expansion of , the coefficient of the term containing b12 is:



Math 30-1 Practice Final - Exam OneThis sheet may be used to record your answers.

2. ____

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1. ____

NR 1. __ __ __ __

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6. ____

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9. ____

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11. ____

12. ____

13. ____

14. ____

NR 2. __ __

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NR 3. __ __ __ __

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NR 5. __ __ __ __

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NR 8. __ __ __ __

30. ____

NR 9. __ __ __ __

31. ____

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NR 10. __ __ __ __

33. ____

NR 11. __ __ __ __

NR 12. __ __ __ __

18. ____

19. ____

20. ____

28. ____

29. ____

Trigonometry IFormula Sheet

www.math30.ca

The Unit Circle

Note: The unit circle is NOT included on the official formula sheet.

Trigonometry II

Exponential andLogarithmic Functions

Permutations &Combinations

Transformations& Operations

Polynomial, Radical& Rational Functions

Mathematics 30-1Formula Sheet


Math 30-1 Practice Final - Exam One ANSWER KEYVideo solutions are in italics.

2. A Polynomial Division, Example 14

3. D Radical Functions, Example 14a

4. C Radical Functions, Example 14c

1. A Polynomial Functions, Example 8b

NR 1. 3142 Rational Functions II, Examples 2a, 4, 5, 7

5. D Rational Functions II, Example 12a

6. B Rational Functions II, Example 10

7. B Combined Transformations, Example 11d

8. A Function Operations, Example 5a

9. C Function Composition, Example 8c

10. C Function Composition, Example 11a

11. A Exponential Functions, Example 14b

12. C Laws of Logarithms, Example 17c

13. D Laws of Logarithms, Example 19a

14. B Logarithmic Functions, Example 10c

NR 2. 55 Logarithmic Functions, Example 12g

15. C The Unit Circle, Example 13e

16. C Trigonometric Functions II, Example 6e

17. C Trigonometric Functions II, Example 10 (a, b)

NR 3. 1586 Trigonometric Functions II, 13d

NR 4. 64 Trigonometric Functions II, 13e

21. C Trigonometric Identities I, Example 14a

22. D Trigonometric Identities I, Example 16c

NR 5. 2314 Trigonometric Identities I, Examples 10c, 9c, 11b, 5a

23. C Trigonometric Identities I, Example 18b

NR 6. 3142 Trigonometric Identities II, 10c

NR 7. 2413 Trigonometric Identities II, 6b

26. B Trigonometric Identities II, Example 14a

27. C Trigonometric Identities II, Example 14b

28. A Trigonometric Identities II, Example 14c

29. D Permutations, Example 13c

NR 8. 1432 Combinations, 4d, 15 (c, d, h)

30. A Combinations, Example 16a

NR 9. 3421 Perms 3a, Combs 13a, 14f, 12h

31. B Combinations, Example 13f

32. D Combinations, Example 14g

NR 10. 1024 Combinations, Example 15e

33. C Binomial Theorem, Example 3d

NR 11. 1080 Binomial Theorem, Example 5c

NR 12. 1620 Binomial Theorem, Example 8b

20. B Trigonometric Equations, Example 20b

24. D Trigonometric Identities II, Example 19

25. B Trigonometric Identities II, Example 16b

18. D Trigonometric Equations, Example 12a

19. B Trigonometric Equations, Example 16c

Math 30-1 Practice Final: Tips for Students

• Do not guess on a practice exam. The practice exam is a self-diagnostic tool that can beused to identify knowledge gaps. Leave the answer blank and study the solution later.

• Every question in the practice exam has already been covered in the Math 30-1 workbookfound at www.math30.ca. It is recommended that students refrain from looking at the practice exam until they have completed their studies for the course.

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Math 30-1 Practice Final One 30-1 Practice Final - Exam One When is divided by x - 2, the remainder is 20. The same polynomial has a factor of x + 2. Two equations that can be used