Grade 12 Prototype Examination. Foundations of Mathematics 30. Course Code Barcode Number. Date of Birth

Transcription

1 Grade 12 Prototype Examination Foundations of Mathematics 30 Course Code 8425 Barcode Number Month Date of Birth Day

2

3 TIME: Two and One-Half Hours Foundations of Mathematics 30 Calculating devices MUST meet the requirements of the Calculator Use Policy. Before an examination begins, devices must be removed from their cases and placed on the students desks for inspection by a mathematics or science teacher. Cases must be placed on the floor and left there for the duration of the examination. Students using a standard scientific or graphing calculator must clear all information stored in its memory before the examination begins. Devices such as cell phones, tablets, and ipods may be used as a calculating device if they meet the requirements of the Calculator Use Policy. The school or writing center must be able to lock and control the device using a feature such as Guided Access, or a management software that limits its functionality to permissible graphing and financial applications (apps) with similar functionality to an approved graphing calculator. It is the student s responsibility to ensure their device complies with the Calculator Use Policy in advance of the departmental examination session. Do not spend too much time on any question. Read the questions carefully. The examination consists of 38 multiple-choice questions and 7 numeric response questions of equal value which will be machine scored. Record your answers on the Student Examination Form which is provided. Each multiple-choice question has four suggested answers, one of which is better than the others. Select the best answer and record it on the Student Examination Form as shown in the example below: Student Examination Form: Multiple-Choice Questions What subject is this examination is being written in? A. Chemistry. B. Foundations of Mathematics. C. Pre-calculus. D. Workplace and Apprenticeship Mathematics. Numeric Response Questions Record your answer in the numeric response section on the answer sheet. What is 10% of $2000? (Round to the nearest dollar.) 1. A B C D i

4 What is 10% of $248.50? (Round to the nearest dollar.) What is 10% of ? (Round to the nearest whole number.) Use an ordinary HB pencil to mark your answers on the Student Examination Form. If you change your mind about an answer, be sure to erase the first mark completely. There should be only one answer marked for each question. Be sure there are no stray pencil marks on your answer sheet. If you need space for rough work, use the space in the examination booklet beside each question. Do not fold either the Student Examination Form or the examination booklet. Check that your personal information on the Student Examination Form is correct and complete. Make any necessary changes, and fill in any missing information. Be sure to complete the Month and Day of Your Birth section. ii

5 Foundations of Mathematics 30 Simple Interest I Prt A P Prt OR A P I Compound Interest n r A P 1 + i OR A P 1 + n nt A nt r R 1 1 n r n S n t 1 1 r 1 r n Payment M nt r r 1 n n P nt r 1 1 n Pi OR 1 i M n i n 1 1 OR P M 1 1i i n Permutations and Combinations n P r n! ( n r)! n C r n! ( n r)! r! Probability P( AB) P( A) P( B) P( AB) P( A) P( B) P( AB) P( A) P( B) P( AB) P( AB) P( A) P( B A) iii

6 iv

7 GRADE 12 DEPARTMENTAL EXAMINATION FOUNDATIONS OF MATHEMATICS 30 PROTOTYPE, NOVEMBER 2016 VALUE 90 (45 2) Answer the following 45 questions on the computer sheet entitled Student Examination Form. MULTIPLE CHOICE QUESTIONS 1. Jordan has invested $4000 in an account that earns 3.6% interest compounded annually. Approximately how many years will it take for his money to double? A. 5 years B. 15 years C. 20 years D. 56 years 2. Albert invests $150 at the end of each month in an account that has an annual interest rate of 3.7% compounded monthly. At the end of 10 years, how much money will he have in this account? A. $ B. $ C. $ D. $

8 3. A $5000 investment grew to $8045 after 6 years when the annual interest rate was compounded quarterly. What was the annual interest rate? A. 2.0% B. 3.3% C. 6.2% D. 8.0% 4. Dakota is saving $400 per month for a car that he would like to buy in 2 years. Which of the following interest options will give Dakota the highest rate of return on his savings? A. 1.5% compounded daily B. 2.0% compounded monthly C. 2.5% compounded monthly D. 2.5% compounded yearly 5. Four brothers are comparing the growth of their individual investment portfolios over the past 5 years. The information about their portfolios is below: Total interest earned Total money invested Tom $ $ Bill $ $ Brad $ $ Mark $ $ Who has the highest rate of return for their portfolio? A. Tom B. Bill C. Brad D. Mark - 2 -

9 6. Debbie wants to buy her own golf cart. She needs to finance the entire amount and can get a 1-year loan with an annual interest rate of 12% compounded monthly. If the maximum monthly payment she can afford is $260, what is the most expensive golf cart that she can purchase with the terms of this loan? A. $2785 B. $2926 C. $3120 D. $ For a camping trip, you have 2 options available: Option A buy a used camper for $ , financed with a loan requiring monthly payments of $ over 2 years and then pay a campground site fee of $20/night Option B rent a cabin at the lake for $165/night After how many nights of renting the cabin does it become cheaper to have purchased the camper? A. 30 B. 32 C. 34 D

10 8. Jenn is purchasing a $ home and is considering the 2 financing options below: Option A monthly payments on a 20-year mortgage with an annual interest rate of 4.75% compounded monthly Option B a 10% down payment followed by monthly payments on a 25-year mortgage with an annual interest rate of 2.99% compounded monthly How much cheaper is Option B than Option A? A. $ B. $ C. $ D. $ Which of the following represents a polynomial function? A. B. C. ( x 3) y ( x 2) 2 y x x 3 y 5 x x D. y ( x 3)( x 2) - 4 -

11 10. Pat took an allergy medication that contained 50 mg of antihistamine. The amount of antihistamine in his body was then measured for a 12-hour period and graphed below: What situation best describes the amount of antihistamine in Pat s body? A. It is growing linearly. B. It is decaying linearly. C. It is growing exponentially. D. It is decaying exponentially

12 11. Sound can be represented by a sinusoidal graph. When the amplitude of the wave increases, the volume gets louder. Which graph below best illustrates the softest volume? A. B. C. D

13 12. The graphs of 2 different log functions are shown below: f( x) log x g( x )? Which of the following equations best represents g( x )? A. g( x) 0.5log x B. g( x) 10log x C. g( x) 0.5log x D. g( x) 10log x 13. Which of the following statements best describes the end behaviour of the x graph of an exponential function, y ab ( ), where a 0, b 0, and b 1? A. The graph extends from quadrant II to quadrant I. B. The graph extends from quadrant I to quadrant IV. C. The graph extends from quadrant III to quadrant I. D. The graph extends from quadrant IV to quadrant II

14 14. What are the period and the equation of the midline for the sinusoidal function graphed below? A. The period is 360 and the equation of midline is y 2. B. The period is 360 and the equation of midline is y 1. C. The period is 180 and the equation of midline is y 2. D. The period is 180 and the equation of midline is y What are the intercepts of the logarithmic function y alog b x, where b 0, b 1, and a 0? A. no x-intercept, no y-intercept B. no x-intercept, y-intercept at (0, b) C. x-intercept at (1, 0), no y-intercept D. x-intercept at (1, 0), y-intercept at (0, b) - 8 -

15 16. Which of the following statements is true for the graph shown below? A. The graph represents an even degree polynomial with a positive constant term. B. The graph represents an even degree polynomial with a negative leading coefficient. C. The graph represents a polynomial with a negative constant term and a positive leading coefficient. D. The graph represents a polynomial with a negative constant term and a negative leading coefficient. 17. The average hours of daylight for Maple Creek can be approximated by the function (expressed in radians), D 4.03 sin 0.51( m 2.90) 11.96, where D is the number of daylight hours and m is the month number. What is the minimum number of daylight hours in Maple Creek? A hours B hours C hours D hours - 9 -

16 18. A rectangular box has a volume of 650 cm 3. The length of the box is twice the width and the height is 3 cm more than the length. If w represents the width and the formula for the volume of a rectangular box is V lw h, which equation can be used to solve for the width? 3 A. 0 4w 647 B ( w 3w 325) C. 0 2(2w 3 3w 2 325) D ( w 3w 162.5) 19. Travis was asked to identify all the intercepts and explain the end y behaviour of x 10. Travis took the following steps: y Step 1: Travis rearranged x 10 to y log 10 x. Step 2: Travis determined that the graph would start in quadrant III and end in quadrant I. Step 3: Travis determined that the x-intercept would be at (1, 0). Step 4: Travis determined the y-intercept must be a negative value. In which step did Travis make his first mistake? A. Step 1 B. Step 2 C. Step 3 D. Step

17 20. The Venn diagram shown below represents participation in specific school activities: Grade 12 Students Drama Student Council Football Which region represents a grade 12 student who plays football and participates in drama, but who is not a member of student council? A. Region 2 B. Region 3 C. Region 4 D. Region

18 21. What is the contrapositive statement of the following conditional statement? If it is July 1st, then it is Canada Day. A. If it is Canada Day, then it is July 1st. B. If it is not Canada Day, then it is July 1st. C. If it is not July 1st, then it is not Canada Day. D. If it is not Canada Day, then it is not July 1st. 22. In the Venn diagram shown below, what are the elements of B C? A. {4, 9} B. {4, 7, 9} C. {4, 6, 7, 9, 11} D. {2, 3, 4, 5, 7, 8, 9}

19 23. What set notation represents the phrase the elements in set A or B, if A and B are non-mutually exclusive sets? A. A\ B B. A B C. A B D. na ( ) nb ( ) 24. Which of the following conditional statements is always TRUE about the Venn diagram shown below? Get a good mark Study hard A. If I got a good mark, then I studied hard for the test. B. If I study hard for the test, then I will get a good mark. C. If I study hard for the test, then I may not get a good mark. D. If I got a good mark, then I may not have studied hard for the test

20 25. A home and garden website conducted an internet survey, but lost parts of the information due to a computer virus. The following information was salvaged: 13 people lived in urban setting 12 people lived in brick house 12 people had a garden 7 people who lived in a brick house lived in a rural setting 9 people who did not have a garden lived in rural setting 2 people who lived in an urban setting but not in a brick house had a garden 5 people who did not live in a brick house nor did not have a garden lived in a rural setting 2 people who lived in a brick house and had a garden lived in an urban setting Sophia needs to establish how many people surveyed lived in a rural setting for advertising purposes. Which of the following Venn diagrams will BEST help her determine that information and why? A. Those who live in a rural setting are the complement of those who live in an urban setting and can be found by adding the values in c, f, and g. Urban a d b e g Garden Brick f c B. Those who live in a rural setting are the complement of those who live in an urban setting and can be found by the value of c. Urban Rural a b c

21 C. Those who live in a rural setting are a sub set of all the information and can only be found by adding the values in a, c, d, f, g, j, k and o. Urban e Rural a c d f i j n o m Garden g b h Brick l k D. These situations are all mutually exclusive events and those who live in a rural setting can be found by finding b. Urban a Rural b People surveyed c Brick d Garden

22 26. Brenda knows the basic rules of Sudoku are as follows: There is only 1 valid solution to each Sudoku puzzle. The only way the puzzle can be considered solved correctly is when all 81 boxes contain numbers and the other Sudoku rules have been followed. When you start a game of Sudoku, some blocks will be pre-filled for you. You cannot change these numbers in the course of the game. Each column must contain all of the numbers 1 through 9 and no two numbers in the same column of a Sudoku puzzle can be the same. Each row must contain all of the numbers 1 through 9 and no two numbers in the same row of a Sudoku puzzle can be the same. Each 3 3 block must contain all of the numbers 1 through 9 and no two numbers in the same block of a Sudoku puzzle can be the same. When Brenda attempts the following puzzle, she places the number 1 in the cell located where Column A meets Row g, or cell Ag, as circled below: A B C D E F G H I a 5 b c d e f g h i Is Brenda s placement of the number 1 correct? A. Yes, because there must be a 1 in the bottom left 3 3 block. B. No, because based on Row h and Row i, a 4 must be placed in cell Ag. C. Yes, because there are 1 s already in Row h, Row i and a 1 is needed in Row g. D. No, because based on Column B, Column C, and Row h, an 8 must be placed in cell Ag

23 27. A volleyball team is deciding on its team name and colours. Their choices for names include Lightning (L) or Thunder (T). The uniforms and numbers could be black (b), red (r), or gold (g), however, the colour of the uniform must be different from the colour of the number. Which tree diagram best represents the possible choices for name, uniform colour, and number colour? A. B. C. D

24 np3 28. What is the value of n in the equation 2 8( C )? n 2 A. 6 B. 10 C. 14 D Sets A, B, C and D are defined as follows: Set A = {3, 5} Set B = {1, 3, 5, 7, 9} Set C = {1, 4, 9} Set D = {3, 6, 9} Which of these sets are mutually exclusive? A. Set A and Set B B. Set A and Set C C. Set B and Set C D. Set C and Set D 30. If the odds in favour of an event occurring are x: y, which expression best represents the probability of that event occurring? A. B. C. D. x y y x x x y y x y

25 31. An on-line computer company estimates new customers will begin using their service every month. The company provides each customer with an automatically generated unique 6-digit password using the digits from 0 to 9. If the password digits can be repeated, after how many years will the company need to reset its password requirements? A years B years C years D years 32. When buying a new washing machine, Maxine has the option to purchase a 4-year warranty for $275. Maxine s research shows that during the first 4 years the probability of her machine breaking down during a load of wash is 0.5% and the average cost of each repair is $200. Maxine does about 100 loads of wash each year. Based on the information given, should Maxine purchase the extra warranty? A. No, the extra warranty may potentially cost her $75. B. No, the extra warranty may potentially cost her $300. C. Yes, the extra warranty may potentially save her $125. D. Yes, the extra warranty may potentially save her $ A student guesses the answers for a 3-question multiple choice quiz. Each question has 4 choices and only 1 choice is correct. What is the probability of getting 100% on this quiz by guessing on all 3 questions? A. B. C. D

26 34. Karen s sock drawer contains 8 individual white socks and 10 individual black socks. She randomly chooses 2 socks from this drawer. What are the ODDS that both are black socks? A. 5:12 B. 5:17 C. 12 : 5 D. 25 : How many arrangements of the word NIPAWIN can be made if the first and last letters must both be N? A. 60 B. 120 C D In September, each student s name is put into a draw box twice. Each Friday, 1 name is drawn for the weekly homework check and not replaced after drawing. If there are 20 students in your class, what is the probability that you will be chosen in both the first week and the second week? A. B. C. D

27 37. Which of the following diagrams has correctly shaded in grey the complement of Event A B? A. B. C. D

28 38. An artist is organizing square tiles in a straight horizontal row as shown below: If there are 2 red tiles, 3 blue tiles, 1 green tile, and 1 yellow tile available, how many different arrangements can be made using all 7 tiles? A. 420 B. 840 C D

29 NUMERIC RESPONSE QUESTIONS Record your answer in the Numeric Response section of the Student Examination Form. 39. You invest money in a mutual fund that pays an annual interest rate of 5% interest compounded semi-annually. How much money would you need to invest now in order to have $6000 after 12 years? (Round to the nearest dollar.) 40. In 2012, the reported population of a city was people. Based on population growth of the past decade, it is predicted that the population of this city will continue to increase by 5% each year. City engineers are concerned that the maximum population this city s infrastructure can sustain is people. During what calendar year will this city expand beyond this maximum capacity? 41. To play a logic game, 2 players take turns removing coins from a starting group of 11 coins. The player that removes the LAST coin loses the game. A player has 2 options on his or her turn: remove 1 coin; or, remove 2 coins. If you want to ensure you win every time, how many coins do you want to leave for your opponent after your 2nd last turn of the game?

30 42. In a group of 100 students, 60 have dimples and the rest do not have dimples. Fifty of the students can roll up the edges of their tongues and the rest cannot. There are 10 students who do not have dimples AND are unable to roll their tongues. In this group, how many students with dimples can also roll their tongues? 43. A business woman has 6 different blouses, 4 different skirts, and 3 different jackets. How many outfits can she create if the outfit can consist of just a blouse and skirt OR it can consist of a blouse, skirt, and jacket? 44. The odds of choosing a green marble from a bag of marbles are 4:10. What is the probability of NOT choosing a green marble? (Round to the nearest percent.) 45. Michelle surveyed 100 students in her school to see who had a driver s licence and who owned a vehicle. She obtained the following results: 63 had a driver s licence; 28 owned a vehicle; and, 2 owned a vehicle but did not have a driver s licence. What is the probability that a student in her school will have a driver s licence or own a vehicle? (Round to the nearest percent.)

31 (See Explanation of Answers) GRADE 12 DEPARTMENTAL EXAMINATION FOUNDATIONS OF MATHEMATICS 30 PROTOTYPE EXAM Answer Key 1. C 11. B 21. D 31. C D 12. D 22. B 32. C D 13. A 23. B 33. A C 14. D 24. B 34. A A 15. C 25. A 35. A B 16. A 26. D 36. B 7. D 17. C 27. A 37. C 8. A 18. C 28. B 38. A 9. D 19. B 29. B D 20. C 30. C Explanation of Answers 1. C. To determine the doubling period of an investment, use the Rule of years i D A $ A $ i - Foundations of Mathematics, Prototype Exam Answer Key

32 3. D. 24 A P(1 i) i $8045 $ i i i i i n C. A 1.5% compounded daily returns $ B 2.0% compounded monthly returns $ C 2.5% compounded monthly returns $ D 2.5% compounded yearly returns $ OR Option C must be higher than option D because they have the same interest rate but option A has more compounding periods. Option C must be higher than option B because they have the same compounding periods but option B is at a lower interest rate. Option A must be the lowest of them all because it has a lower interest rate. Even though it has more compounding periods, the number of compounding periods makes a very slight difference in the overall rate of return. - ii - Foundations of Mathematics, Prototype Exam Answer Key

33 5. A. Rate of return is the interest earned divided by money invested Tom: Bill: $ or 43.59% $3500 $ or 25% $1000 Brad: $ or 25.32% $41000 $ Mark: or 38.54% $ B $260 P $260 P( ) $ P 7. D. Total cost of buying the camper: $ $ With a camper you still have daily campground fees of $20 so the difference between renting a cabin and paying fees per night is $165 $20 $145 / night Now you need to find out how many nights at $145 can be rented for the total cost of your camper: $ $ or 36 nights - iii - Foundations of Mathematics, Prototype Exam Answer Key

34 8. A. Option A M $ M $ ($ )(240) $ Option B Down payment: If you pay 10% as a down payment, there is 90% that you will be financing: $ $ M M $ $ ($ )(300) $ $ $ ( down payment) $ Option A costs more by $ $ $ D. By definition, polynomial functions is an expression in the form n n ax 1 2 1, n an x ax ax a 0 where a,,... 0 a1 an are real numbers with a 0 and n is a positive integer. Options B and C contain non-integer exponents and option A is a rational function. Therefore, option D is the correct choice. 10. D. As x increases y is decreasing exponentially. Therefore it is decaying exponentially. - iv - Foundations of Mathematics, Prototype Exam Answer Key

35 11. B. Amplitude is the distance from the midline to a maximum or minimum. So graph B has the lowest amplitude or lowest volume. 12. D. The a value in fx ( ) alogx determines whether a function is increasing (when a 0 ) or decreasing (when a 0 ). Since the decrease is pronounced, the a value in g( x) must be negative and larger than that in fx ( ). Option D is the best match. g( x) 10log x 13. A. Exponential equations that have positive bases and positive a values, when graphed, look like: In either case, the graph extends from quadrant II to quadrant I, when reading the graph from left to right. - v - Foundations of Mathematics, Prototype Exam Answer Key

36 14. D. max min 4 ( 2) 6 The amplitude is found by The equation of the midline can be found a number of ways: 1) Max amplitude: 4 31 so y 1 2) Min + amplitude: 231 so y 1 max min 4 ( 2) 2 3) 1 so y The period represents how many degrees it takes to complete one cycle. In the graph, 2 cycles are completed in the 360, therefore the period is C. Logarithmic functions of this form have no y-intercept and they have a vertical asymptote of 0 x x 0, x. All x. Thus, they have a restricted domain of log functions of this form have an x-intercept of A. Having the graph extend from quadrant II into quadrant I denotes an even degree because the graph behaves the same on both sides of the y-axis (both extending upward). Since the graph intercepts the y-axis at 17, the equation has a positive constant term. 17. C. Minimum daylight hours for Maple Creek: vertical shift amplitude: vi - Foundations of Mathematics, Prototype Exam Answer Key

37 18. C. The volume of the box can be represented as: V wl h, where l 2w h l3 (2 w) w(2 w)(2w3) w (2w3) 650 4w 6w w 6w 650 Therefore, the factored equation is (2w 3w 325) 19. B. Because the original function x 10 y was not written in terms of y, Travis did so correctly in Step 1. Travis made his first error in Step 2. Although the graph is an increasing function the graph will not start in quadrant III but in quadrant II. His second error is based on this one, causing Travis to deduce there is a negative y-intercept. The y-intercept can be found by substituting x 0 into y log 0 and solving for y, which is impossible as there is nothing that 10 can 10 be raised to, to give a result of 0. y log 0? y C. A grade 12 student is part of the Universal set. This student is part of football, which is regions 3, 4, 6, 7 and drama, so only regions 3 and 4. However the student is not part of student council so not part of region 3. This means the student is in region D. Contrapositive statements are formed by changing the if p, then q statement to if not q, then not p. Therefore the statement should be: If it is not Canada Day, then it is not July 1st. - vii - Foundations of Mathematics, Prototype Exam Answer Key

38 22. B. The elements of set B are {2, 3, 4, 7, 9}. The elements of set C are {4, 5, 6, 7, 8, 9, 11}. Therefore the elements found in the overlap region B C are {4, 7, 9}. 23. B. In mathematics, the word or means union, so the notation for the elements in set A or B is A B. 24. B Studying hard would be one part of getting a good mark, as there are potentially other factors that will lead to getting good mark. However, all conditional Venn diagrams are shown as below: Then q If p So the best conditional statement, if p then q, would be if I studied hard for the test, then I will get a good mark. - viii - Foundations of Mathematics, Prototype Exam Answer Key

39 25. A The number of rural people would be those not in the set marked urban. Hence the number of rural people can be found from c f g in the Venn diagram below. The Venn diagram drawn in B is not a correct diagram based on the information given as it does not represent the bulk of the information. The Venn diagram in C is not a correct diagram based on the information given as it has overlap regions of Urban and Rural in regions c, f, j, and o which is not possible. The Venn diagram drawn in D is not correct as it indicates the 4 events as disjoint (no interlocking circles) and that is not the case. (For example, there can be Urban brick house dwellers). - ix - Foundations of Mathematics, Prototype Exam Answer Key

40 26. D. This can be solved by logic. Considering Columns A, B, and C, we see an 8 in Cc, Bd, so therefore an 8 must appear in either Ag or Ah. This would satisfy the rule of each column must contain all of the numbers 1 through 9 and no two numbers in the same column of a Sudoku puzzle can be the same. However, since Fh has an 8 already, the only open spot for the 8 is Ag, as no rows can contain a duplicate number. Therefore, the number 1 cannot go in Ag. A B C D E F G H I a 5 b c d e f g 9 6 h i It could also be solved by partially completing or completing the puzzle. A B C D E F G H I a b c d e f g h i x - Foundations of Mathematics, Prototype Exam Answer Key

41 27. A. The tree diagram must represent (2 names, 3 uniform colors and then 2 colors that are different than the uniform color). Option B only represents a team name and 1 color. Option C allows for the number and uniform to be the same color which is not allowed and Option D does not realize that there could be a second number color once the uniform colour is set. (e.g. blue uniform with red numbers or blue uniform with gold numbers). Therefore, choice A is correct. 28. B. The problem can be solved by working backwards and substituting values into the equation and checking to see which value works. n P3 8( 10C2) (45) OR it can be solved using factorial notation. n! ( n 3)! n! 8 2 2!( n 2)! n! n! 16 ( n3)! 2!( n2)! 2!( n 2)! n! 16 ( n3)! n! 2( n2)( n3)( n4) ( n3)( n4)... 2( n 2) 16 n 28 n 10 - xi - Foundations of Mathematics, Prototype Exam Answer Key

42 29. B. Mutually exclusive means the two sets do not have any elements in common. Sets A and B have 3 and 5 in common Sets A and C have nothing in common Sets A and D have 3 in common Sets B and C have 1 and 9 in common Sets B and D have 3 and 9 in common Sets C and D have 9 in common 30. C. By definition, odds in favour of an event occurring is the number of desired outcomes, to the number of non-desired outcomes. Probability is the ratio of the number of desired outcomes divided by the total number of outcomes (desired and non-desired). 31. C There are 10 digits to choose from and each digit could be repeated, therefore 6 there are (10) possible passwords available months years C. During the 4 years Maxine would expect to do 400 (100 loads per year 4 years) loads of laundry. If there will be a problem 0.5% of the time she should expect breakdowns. If each repair costs $200 then her total cost for repairs should be$400 = ($ 200 2). Therefore she should purchase the extra warranty as the expected cost of repairs is $400 $275= $ xii - Foundations of Mathematics, Prototype Exam Answer Key

43 33. A. The events are independent of each other. P(question 1 correct) and P(question 2 correct) and P (question 3 correct) A. These are dependent events since the socks are chosen at once P(Black) and P(Black) This represents 5 desired outcomes and a total of 17 outcomes, or nondesired outcomes. Therefore the odds will be 5:12 (desired events : non-desired events). 35. A. 36. B 15! P(you are picked week 1) and P(you are picked week 2) xiii - Foundations of Mathematics, Prototype Exam Answer Key

44 37. C. The complement of an event is all the elements of a universal set that do not belong to a subset of it. The complement to the events in set A or set B would be the area represented by the shading outside section A B. 38. A. 7! 2!3! Numeric Response: 3317 A P(1 i) 0.05 $6000 P 1 2 $6000 P $6000 P $ P Range: $ $3334 n 40. Numeric Response: 2019 Create a table: Years Population OR Create an equation: Population is an exponential function. Using either the exponential regression function on the graphing calculator or understanding that the function is be based on the initial population of with a common ratio of 0.05, the equation would be y x (1.05). - xiv - Foundations of Mathematics, Prototype Exam Answer Key

45 41. Numeric Response: 4 If you leave your opponent 4 chips in your 2nd last play, then they can either: take 1 of the 4 remaining, leaving you with 3 and you can take 2 on your turn and they take the last one; or, take 2 of the 4 remaining, leaving you with 2 then you can take 1 on your turn and they still take the last one. 42. Numeric Response: without dimples 60 with dimples There are 10 students without dimples that can t their tongues. Therefore there are 30 without dimples that can roll their tongues There are 40 with dimples that can roll their tongues, since there are 50 that cannot do so and 10 of those do not have dimples There are 20 students with dimples can roll their tongue 43. Numeric Response: 96 Outfits = (# of skirts # of blouses) OR (# of skirts # of blouses # of jackets) Numeric Response: 71 4 :10 are the odds for green. Therefore there are 4 green marbles and 10 non-green marbles and 14 marbles in total. 10 P(not green) % - xv - Foundations of Mathematics, Prototype Exam Answer Key

46 45. Numeric Response: 65 If there are 28 who owned a vehicle and 2 had a vehicle without a license, then there would be 26 with a vehicle and a license P(licence) + P(own a vehicle) P(licence and own a vehicle) % Question by Outcome Question Outcome Question Outcome Question Outcome 1. FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM FM30.5 Content Area Outcomes Multiplechoice Questions Numeric Response Questions Financial Mathematics Relations and Functions Logical Reasoning Probability xvi - Foundations of Mathematics, Prototype Exam Answer Key