Math 30-1 Practice Final Exam One

Transcription

1 Math 30- Practice Final Exam One

2 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 key can be found at the back of the exam.

3 The information in this box is required to answer the next question. The graph of is shown below.. If the polynomial is represented with the form, the value of a is: 2 2. 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:

4 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. h 3 m d 3. The height of the ladder as a function of its base distance d is: 4. When the top of the ladder is metres above the ground, the distance from the wall to the base of the ladder is: m.5 m 2 m 2.2 m

5 The information in this box is required to answer the next question. Graphs: a) b) Randomly Sorted Functions:. 2. c) d) NR. The correct order of the functions to graphs a, b, c, and d is: Graph a b c d Function 5. Potential solutions for the equation can be found by solving:, 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 The information in this box is required to answer the next question. The equation can be solved by finding the x-intercepts of the related function,. 6. The graph of and its x-intercept are correctly shown in:

7 The information in this box is required to answer the next question. 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. 7. The transformation order that describes the spaceship s new size and position (without colliding with the rocks) is: reflection about the x-axis; vertical translation 7 units down; reflection about the y-axis; horizontal stretch by a scale factor of /2; and a horizontal translation 5 units right. horizontal stretch by a scale factor of /2; reflection about the x-axis; reflection about the y-axis; horizontal translation 5 units right; vertical translation 7 units down. horizontal translation 5 units right; reflection about the x-axis; reflection about the y-axis horizontal stretch by a scale factor of /2; vertical translation 7 units down. 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 /2.

8 8. Given the functions and, the graph of is identical to the transformation: 9. The function can be formed from the function composition:, where and., where and., where and., where and. The information in this box is required to answer the next question. A pebble dropped in a lake creates a circular wave that travels outward at a speed of 30 cm/s. The radius of the wave can be represented with, and the area of a circle is. 0. A function that expresses the area of the circular wave as a function of time is:

9 . The equation has: no solution. one solution at x = -.5. one solution at x =.5. two solutions. 2. One-third of is equal to: 3. The value of x in can be determined by solving the equation: 4. 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:

10 The information in this box is required to answer the next question. The strength of an earthquake is calculated using Richter s formula: where M 2 is the magnitude of the strong earthquake, M is the magnitude of the weak earthquake, and A 2 / A is the seismograph amplitude 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 The information in this box is required to answer the next question. The coordinates of a point on the unit circle can be expressed in the form, where θ is the angle measured in radians. 3 rad The point is shown in the diagram to the right. 5. Rounded to four decimal places, the values of a and b are: a = , b = a = , b = a = , b = 0.4 a = , b =

11 The information in this box is required to answer the next question. The graphs of and intersect at the points shown If the amplitude of each graph is quadrupled, the new points of intersection are:

12 The information in this box is required to answer the next question. A person is watching a helicopter ascend from a distance 50 m away from the takeoff point. Assume that the height of the person is negligible compared to the height of the helicopter. h θ 50 m 7. The height of the helicopter as a function of the angle of elevation, and its domain, is:

13 The information in this box is required to answer the next two questions. For Grand Prairie, a trigonometric function that gives the number of daylight hours as a function of day number is: d(n) n NR 3. To the nearest hundredth, the number of daylight hours on May 2 (day number 2) is ab.cd The values of a, b, c, and d are: a b c d NR 4. Rounded to the nearest day, the number of days with more than 7 daylight hours is:

14 8. The equation has the solution(s): only. and only. and The information in this box is required to answer the next question. The equation can be solved by factoring the left side to get. 3 2 Each factor can be set equal to zero to get the solution set: - π 2π -2 The graph of is shown on the right If the related functions of each factor of it can be observed that: are graphed, 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. contributes three solutions to the solution set.

15 The information in this box is required to answer the next two questions. 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. W N E Note: North of point P is a positive distance, and south of point P is a negative distance. S d The tangent function expresses the distance θ 4 m P 8 m where the water splashes the wall as a function of the rotation angle θ. 20. The graph that most accurately represents the stream of water hitting the wall is: d d π π 3π 2π θ π π 3π 2π θ d d π π 3π 2π θ π π 3π 2π θ

16 The information in this box is required to answer the next question. A student attempted the proof of a trigonometric identity, but made an error. I II III IV 2. The error occured in step: I II III IV

17 The information in this box is required to answer the next question. Each graph shows the graphical solution of a trigonometric equation. I II π 2π π 2π - - III IV π 2π π 2π All of the equations and graphs above contribute to the solution set of except: I II III IV

18 The information in this box is required to answer the next question. Each of the trigonometric expressions below can be simplified to a numeric value NR 5. The ascending numeric order of the simplified trigonometric expressons is: 23. If the value of, the value of within the same domain is:

19 The information in this box is required to answer the next question. Randomly Sorted Steps: A selection of the steps required to complete the proof of: have been randomly sorted. 4. NR 6. The order in which the steps appear as the proof is completed is: The information in this box is required to answer the next question. Simplify each expression using a double angle identity so that it contains just one trigonometric ratio. a) b) c) Randomly Sorted Answers: d) 4. NR 7. When a, b, c, and d are simplified, the order of the answers is: a b c d

20 The information in this box is required to answer the next question. In the diagram on the right, it can be determined that: and x 57 The value of x can then be found by solving the equation: B 53 A 24. Rounded to the nearest tenth, the value of x is: The trigonometric equation,, has the solution:

21 The information in this box is required to answer the next three questions. If a cannon shoots a cannonball θ degrees above the horizontal, the horizontal distance traveled by the cannonball before it hits the ground can be found with the function: θ, where the initial velocity of the cannonball is 36 m/s. 26. The distance function can be written with a single trigonometric function as: 27. The cannonball will travel its maximum distance when the angle of the cannon is: If the cannonball travels a horizontal distance of 00 m, possible cannon angle(s) are: 24.6 or or or only

22 29. The equation can be simplified to the quadratic equation: The information in this box is required to answer the next question. Question: If a 5-card hand is dealt from a deck of 52 cards, how many distinct 5-card hands are there if: a) the ace of spades and two of diamonds must be in the hand? 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 4 Randomly Sorted Answers: A deck of cards contains 52 cards and is subdivided into: 3 black clubs 3 black spades 3 red diamonds 3 red hearts. 4. NR 8. The correct order of the answers to questions a, b, c, and d is: a b c d 30. How many ways can six people be split into two equal-sized groups?

23 The information in this box is required to answer the next question. Questions: a) A Grade 2 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? One Possible Timetable Block Block Block 2 Block 3 Block 4 Block 5 Course Math 30- Spare Physics 30 English 30- Biology 30 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 B C c) How many ways can four bottles of different spices be arranged on a spice rack with holes for six spice bottles? One Possible Arrangement Parsley Sage Garlic Thyme 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? Randomly Sorted Answers: NR 9. The correct order of the answers to questions a, b, c, and d is:

24 3. 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. If there are 8 rock songs and 9 pop songs available, how many unique playlists containing 3 rock songs and 2 pop songs are possible? The information in this box is required to answer the next question. One Possible Answer Key A multiple choice test contains 5 questions, and each question has four possible responses A C D A C D A B D A B C A C D NR 0. The number of unique answer keys that are possible is:

25 The information in this box is required to answer the next question. A Example: How many unique pathways exist between points A and B? B Step : Write s at all the verticies along the left and top sides. (We will be using a Pascal s Triangle pattern to solve this.) Step 2: Fill in the inner verticies by adding together the adjacent diagonal verticies using the pattern shown. A A B B Step 3: Continue the pattern by sliding the 5 and 0 as shown. A Step 4: Continue adding together adjacent diagonal verticies until reaching Point There are 66 pathways between points A and A B B The question corresponding to this information is on the next page.

26 This question uses the information found on the previous page. A B 33. The number of pathways between points A and B in the diagram shown is: The information in this box is required to answer the next question. The expansion of the binomial is shown below: NR. The value of a in the binomial expansion is: NR 2. In the expansion of, the coefficient of the term containing b 2 is:

27 This sheet may be used to record your answers NR NR NR 3. NR NR NR 6. NR NR NR NR NR. NR 2.

28 Mathematics 30- Trigonometry I The Unit Circle Formula Sheet Trigonometry II Note: The unit circle is NOT included on the official formula sheet. Transformations & Operations Exponential and Logarithmic Functions Permutations & Combinations Polynomial, Radical & Rational Functions

29 ANSWER KEY Video solutions are in italics.. A Polynomial Functions, Example 8b 2. A Polynomial Division, Example 4 3. D Radical Functions, Example 4a 4. C Radical Functions, Example 4c NR. 342 Rational Functions II, Examples 2a, 4, 5, 7 5. D Rational Functions II, Example 2a 6. B Rational Functions II, Example 0 7. B Combined Transformations, Example d 8. A Function Operations, Example 5a 9. C Function Composition, Example 8c 0. C Function Composition, Example a. A Exponential Functions, Example 4b 2. C Laws of Logarithms, Example 7c 3. D Laws of Logarithms, Example 9a 4. B Logarithmic Functions, Example 0c NR Logarithmic Functions, Example 2g 5. C The Unit Circle, Example 3e 6. C Trigonometric Functions II, Example 6e 7. C Trigonometric Functions II, Example 0 (a, b) NR Trigonometric Functions II, 3d NR Trigonometric Functions II, 3e 8. D Trigonometric Equations, Example 2a 9. B Trigonometric Equations, Example 6c 20. B Trigonometric Equations, Example 20b 2. C Trigonometric Identities I, Example 4a 22. D Trigonometric Identities I, Example 6c NR Trigonometric Identities I, Examples 0c, 9c, b, 5a 23. C Trigonometric Identities I, Example 8b NR Trigonometric Identities II, 0c NR Trigonometric Identities II, 6b 24. D Trigonometric Identities II, Example B Trigonometric Identities II, Example 6b 26. B Trigonometric Identities II, Example 4a 27. C Trigonometric Identities II, Example 4b 28. A Trigonometric Identities II, Example 4c 29. D Permutations, Example 3c NR Combinations, 4d, 5 (c, d, h) 30. A Combinations, Example 6a NR Perms 3a, Combs 3a, 4f, 2h 3. B Combinations, Example 3f 32. D Combinations, Example 4g NR Combinations, Example 5e 33. C Binomial Theorem, Example 3d NR. 080 Binomial Theorem, Example 5c NR Binomial Theorem, Example 8b

30 Math 30- Practice Final: Tips for Students Every question in the practice exam has already been covered in the Math 30- workbook found at. It is recommended that students refrain from looking at the practice exam until they have completed their studies for the course. Do not guess on a practice exam. The practice exam is a self-diagnostic tool that can be used to identify knowledge gaps. Leave the answer blank and study the solution later.