1) Consider the sets: A={1, 3, 4, 7, 8, 9} B={1, 2, 3, 4, 5} C={1, 3}

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1 Math 301 Midterm Review Unit 1 Set Theory 1) Consider the sets: A={1, 3, 4, 7, 8, 9} B={1,, 3, 4, 5} C={1, 3} (a) Are any of these sets disjoint? Eplain. (b) Identify any subsets. (c) What is A intersect B? (d) What is A union B? (e) Identify, and. ) In a class there are: 8 students who play football and hockey 7 students who do not play football or hockey 13 students who play hockey 19 students who play football How many students are in the class? 3) In a school canteen there are 45 children. Today s menu includes: fish, chips. There are 16 who have finished eating. There are 6 eating chips (French fries) and 17 eating fish. How many students are eating fish and chips? How many students are eating only chips? 4) In a school of 30 students, 85 students are in the band, 00 students are on sports teams, and 60 students participate in both activities. How many students are involved in either band or sports? How many students are not involved with either? 5) All the members of a group of 30 teenagers belong to at least one club.there are 3 clubs: chess, drama and art. 6 of the teenagers belong to only the art club. 5 of the teenagers belong to all 3 clubs. of the teenagers belong to the chess and art clubs but not to the drama club. 15 of the teenagers belong to the art club. of the teenagers belong only to the chess club. 3 of the teenagers belong only to the drama club. (a) (b) How many of the group do chess and drama but not art? How many of the group belong to the chess club?

2 6) In a class of 3 pupils: 5 pupils live in New Town, travel to school by bus and eat school dinners 3 pupils live in New Town, travel to school by bus but do not eat school dinners 9 pupils do not live in New Town, do not travel to school by bus and do not eat school dinners 11 pupils live in New Town and have school dinners 16 pupils live in New Town 9 pupils travel by bus and eat school dinners 13 pupils travel by bus How many pupils eat school dinners? 7) A veterinarian surveys 6 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets? 8) 70 students were surveyed to determine their travel interests. 10 students wanted to go to all three destinations. 18 students wanted to go to Paris and Spain 16 students wanted to go to New York and Paris 44 students wanted to go to Paris 7 students wanted to go to New York. 3 students wanted to go to Spain. 4 students did not want to go to either of these locations How many students wanted to go to New York and Spain but not Paris? 9) A survey of 10 first-graders was conducted concerning the types of animals that were in the last book each of them read. The following results were obtained: 48 read about an elephant 56 read about a monkey 44 read about a tiger 7 read about an elephant and a tiger but not a monkey 13 read about an elephant and a monkey but not a tiger 14 read about a monkey and a tiger but not an elephant 18 students did not read about any of these animals. How many students read a book about all three animals? 10) Consider the following sets: C={c (a) List the elements of each set. (b) What is S union C? (c) What is S intersect C?

3 Unit Counting Methods 1. How many ways can the letters in the word MISSISSIPPI be arranged?. If a multiple choice test has 10 questions, of which one is answered A, 4 answered B, 3 answered C, and answered D, how many answer sheets are possible? 3. How many 3-digit numbers can be formed? 4. There are si different coloured balls in a bo and you pull them out one at a time. How many different ways can you pull out four balls? 5. How many ways can you order the letters from the word TREES if: A) a vowel must be at the beginning? B) it must start with a consonant and end with a vowel? C) the R must be in the middle D) It begins with an E? E) It begins with eactly one E? F) Consonants and vowels alternate 6. How many 3-digit, 4-digit, or 5-digit numbers can be made using the digits of ? 7. How many ways can 4 rock, 5 pop, and 6 classical albums be ordered if all the albums of the same genre must be kept together? 8. How many ways can you order the letters in FORTUNES if all the vowels must never be together? 9. If an ice cream dessert can have toppings, and 9 are available, how many different topping selections can you make? 10. There are 9 possible toppings for a sandwich, but you only want 4 toppings, one of which must be pickles. How many different sandwiches can be made? 11. If a crate of radio controlled cars contain 10 working cars and 4 defective cars, how many ways can you take out 5 cars and have only three work? 1. If a student must select two courses from Group A (Math 301, Chemistry 30, Physics 304 and Biology 301), two courses from Group B(English 301, World Geography 30) and one course from Group C (Math 308, Earth Systems 308, French 301), how many combinations are there? 13. There are 8 parents and 43 students going on a field trip. Two groups are made, a large one with 30 students and 5 parents and a small group with 13 students and 3 parents. A) How many different ways can the parents be chosen for the small group? B) How many ways can the students be chosen for the large group if Stefan and Dylan must be in the small group? C) How many ways can the students be chosen for the small group if Wade must be in the small group? 14. A student council of 5 members is to be formed from a selection pool of 6 boys and 8 girls. How many councils can have A) Jason on the council B) Katie, but not Ale C) Zach is on the council and Caroline, Allison and Jamie are not D) At least 3 boys, but one of these boys can t be Brian 15. A research team of 6 people is to be formed from 10 chemists, 5 politicians, 8 economists and 15 biologists. How many teams have: A) At least 5 chemists? B) Eactly three economists C) Eactly four chemists, but no economists D) At least two biologist 16. It there are 14 boys & 1 girls in a selection pool and a school council of President, VP, treasurer and Secretary to be formed, in how many ways can A) eactly one boy be on council B) eactly two girls be on council C) no boys on council

4 17. If a sports team with si unique positions is to be formed from 5 men and 7 women, in how many ways can two positions be filled by men and four positions by women? 18. Simplify: 19. Solve: A) B) A) B) Unit 3 Probability 1. Trey has 9 coins in his pocket, of which are quarters. He pulls out a coin at random. Determine: a) the probability of the coin being a quarter. b) the odds in favour of the coin being a quarter.. Penny draws a card at random from a standard deck of 5 playing cards. Determine: a) the probability of the card being black. b) the odds against the card being a club. c) the odds in favour of the card being a king. 3. Kevin plays Triple A hockey. He has scored 5 times in 35 shots on goal this year. What are the odds in favour of him scoring in the net game? 4. The odds in favour of two students in a Math 301 class sharing a birthday are 8:3. Determine the probability of two students sharing a birthday. 5. The coach of a soccer team says the odds in favour of the team winning are 3:1; the odds in favour of the team losing are 1:4 and the odds against a tie are 9:1. Are these odds possible? Eplain. 6. Zachary plays ball hockey. He has scored 5 times in 30 shots on goal. He says that the odds in favour of him scoring are 1 to 6. Is he right? Eplain. 7. Colin, Jason and Brian are competing with 9 other boys to be on their school's cross - country team. All the boys have an equal chance of winning the trial race. Determine the probability that Colin, Jason and Brian will place first, second and third, in any order. 8. A radio show in Ontario is advertising a contest. The DJ has letter tiles that spell out MISSISSAUGA. He turns them face down and mies them up. A contestant will win a $5 000 prize if he/she turns the tiles face up and they spell MISSISSAUGA. Determine the probability that a contestant will win the $5 000 prize.

5 9. Every player in a particular online game must create a password consisting of capital letters followed by 4 digits. Determine the probability that a password chosen at random will contain the letters A and B if: a) repetitions are not allowed b) repetitions are allowed. 10. A student graduation committee consists of 1 girls and 8 boys. To form a subcommittee, 6 students are randomly selected from the committee. Determine the odds in favour of 3 girls and 3 boys being on the subcommittee. 11. Jamie tosses 3 coins. Determine the probability that at least one coin will land as heads. 1. Five friends, including Hilary and Annie, are sitting in a row at a movie theatre. a) Determine the probability that Hilary and Annie are sitting together. b) Determine the probability that Hilary and Annie are not sitting together. 13. Suzanne has letter tiles that spell CHAIR. Determine the probability that 3 letter tiles chosen at random consist of vowels and 1 consonant. 14. Amy is about to draw a card at random from a standard deck of 5 cards. If she draws a face card or a heart she wins a point. a) Draw a Venn diagram to represent the events. b) Are the events mutually eclusive? Why or why not? c) Determine the probability that Amy will win a point. 15. The probability that Cara will go shopping on Thursday is The probability that she will do school work is 0.4. The probability that she will do neither is 0.3. a) Draw a Venn diagram to represent the events. b) Are the events mutually eclusive? c) Determine the probability that Cara will do at least one of these activities on Thursday. 16. A car manufacturer reports that 56% of the available model B cars have heated leather seats, 49% have a sunroof, and 7% have neither. What is the probability of a model B car having a sunroof but no heated leather seats? 17. Kendra has been selected to win a prize at a party. She must draw a piece of paper from a hat. 6 pieces of paper say "ring," 4 say "necklace," 3 say "bracelet," say "perfume," and 1 says "watch." Determine the odds in favour of her winning a necklace or bracelet.

6 18. If you draw a single card from a standard deck of 5 playing cards, determine the probability of drawing: a) a 7 or an ace. b) a black card or a face card. 19. If there are children in a family, determine the probability that: a) both children are girls. b) one child is a boy and one child is a girl 0. Amanda has 4 tickets for a ticket draw. At the time of the draw, 100 tickets have been sold. There are prizes and the ticket that is drawn for the first prize is returned for the second prize draw. a) Determine the probability that Amanda will win both prizes. b) Determine the probability that she will win no prizes. 1. Michael draws a card from a standard deck of 5 cards, and then draws another card. Determine the probability that both cards are clubs if: a) the first card is replaced b) the first card is not replaced.. David has 3 loonies, 4 quarters and 5 dimes in his pocket. He needs quarters for a parking meter. He takes coins out of his pocket. What is the probability that both coins are quarters? 3. Based on a soccer team's record, it has a 70% chance of winning on days without rain and a 50% chance of winning on days with rain. The forecast for Friday indicates a 0% chance of rain. What is the probability that the soccer team will win on Friday? 4. A manufacturer knows that in a bo of 10 light bulbs, 3 will be defective. Isabella picks out light bulbs from a bo of 10. Determine the probability that Isabella will pick: a) defective light bulbs b) non-defective light bulbs c) eactly 1 defective light bulb 5. James asked Matthew to choose a number between 10 and 30 and state one fact about the number. Matthew says that the number is a multiple of 4. Determine the probability that the number is also a multiple of 3.

7 Unit 4 Rational Epressions and Equations 1. Find an equivalent rational epression for each epression i 3. State the non-permissible values and simplify. ii i iv) Simplify and state restrictions on the variable. 15y 14z i 7z 5y ii 8a 3a a 8a a 8a a 1a 4 8 a iv) a 9 1a 6a v) 3 3a 9 15a 4. Simplify and state the non-permissible values. v i ii 3 4 iv) Solve and verify. 5n 3 5n 14 n 7 n 1 i ii iv) 54 3a 7 a 3a 9

8 6. Adam and Steve start up a part-rime business shovelling driveways. Adam can shovel a regular driveway in 40 minutes. Steve can shovel a regular driveway in 50 minutes. How long would it take to shovel a regular driveway if they work together? 7. Ma drove 308 km in the same time that Karla drove 39 km. If Karla drove 6 km/h faster than Ma, calculate her speed for the trip Taylor purchased a large bo of comic books for $300. He gave 15 comic books to his brother. Then he sold the rest of the comic books on the internet for $330, making a profit of $1.50 on each comic book. How many comic books did he buy originally?