MDM4U Some Review Questions

Transcription

1 1. Expand and simplify the following expressions. a) ( y 1) 7 b) ( 3x 2) 6 2x In the expansion of ( ) 9 MDM4U Some Review Questions, find a) the 6 th term b) 12 the term containing x n + 7 n + 6 n Prove that = +. r + 7 r + 6 r The black disk at the bottom of the board can be moved in the upwards direction to the square directly above it or to either of the two squares diagonally above it BUT it may not move onto a black square. How many ways can the disc be moved to the top row?, if one exists 6. a) State the value of P(15, 3). b) Solve for if. 7. Using a standard deck of cards, determine the number of ways you could get a) a flush (all 5 cards the same suit) b) a straight (5 cards in numerical order, not necessarily the same suit) c) a straight flush (5 cards in numerical order, all the same suit) 8. There is a 15% chance of winning a prize in a contest. What are the odds of winning a prize? 9. The probability of A is 0.25 and the probability of B is 0.8. If the probability of A and B is 0.3, what is the probability of A given B? 10. Fifty percent of Americans believed the country was in a recession, even though technically the economy had not shown two straight quarters of negative growth. If a group of 20 Americans was surveyed, make the following calculations. a) What is the probability that exactly 12 people believed the country was in a recession? b) What is the probability that no more than five people believed the country was in a recession? 11. Fill in the Venn Diagram that would represent these data. 200 people were asked which of these grand slam tournaments that they have attended. The tournaments inquired about were: US Open, Wimbledon, or Australian Open. 30 people have not attended any of these tournaments. 10 people have been to all three tournaments. 25 people have been to Wimbledon and the Australian Open. 20 people have been to the US Open and the Australian Open but not to Wimbledon. 65 people have been to exactly two of the tournaments. 165 people have been to the US Open or to Wimbledon. 120 people have been to Wimbledon or to the Australian Open.

2 12. Consider the word NUMBERS. a) How many different arrangements are there of the letters? b) How many arrangements are there if b is the first letter? c) How many arrangements have the letters run grouped together? 13. A door can be opened only with a security code that consists of five buttons: 1, 2, 3, 4, 5. A code consists of pressing any one button, or any two, or any three, or any four, or all five. (You are to press all the buttons at once, so the order doesn't matter.) a) How many possible codes are there? b) To open the door you must press three consecutive codes. How many possible ways are there to open the door? 14. Explain the difference between the terms population and sample. 15. The quiz marks for a class of students were as follows: 13, 17, 12, 18, 14, 15, 20, 8, 11, 18, 16, 11, 15, 13, 8, 19, 15, 13, 10, 11, 18, 17, 13 Determine the median of these marks. 16. The class scores from a mathematics quiz are as follows: 8, 6, 10, 5, 8, 6, 9, 7, 8, 10, 4, 5, 7, 8, 9, 8, 10, 5, 8, 7 a) Organize the data in a frequency table. b) Determine the mean, median and mode for these data. c) Decide which type of graph would be best to represent these data, and create it. d) Describe the shape of the frequency distribution. 17. Tom measured the heights, in centimetres, of 30 corn plants and created the following stem-andleaf plot. What is the median height? Stem Leaf The following circle graph represents data from 1500 people. The sector angle for category A is. Determine the frequency of category A. Hint: How many degrees are in a circle? 19. A group of high school students are surveyed to determine the number of hours of homework they complete each night. What type of graph would be most appropriate for displaying the distribution of these data? 20. A marine biologist is studying a specific species of fish in a lake. She records the masses of 15 fish, in grams: 315, 282, 400, 220, 336, 414, 278, 212, 510, 326, 407, 296, 390, 483, 356 The data are going to be represented in a histogram. Determine an appropriate spread for the class intervals.

3 21. A histogram for a data set has a smallest value of 12 and a greatest value of 50. Its bin width is 8. What is the number of intervals in this histogram? 22. When is a line graph more appropriate than a histogram? 23. What shape of distribution best describes the following data? Value Frequency Value Frequency a) What shape best describes a histogram of these data? b) What is the grouped mean of the data? c) What is the grouped standard deviation of the data? 25. The frequency for the middle interval of a set of 100 data is zero. What is a possible shape of the distribution? 26. Some of you did well, some of you did not do so well, but most of you have a mark near the middle. What shape of distribution would these marks likely have? 27. Each student in a large school was asked the day of the week of his or her last birthday. The results were displayed in a histogram. What would be the most likely shape of the histogram? 28. A histogram representing a skewed distribution has its greatest frequency on the left. In what direction is it skewed? 29. Calculate Alvin s body mass index (in kg/m 2 ) if his mass is 75 kg and he is 1.72 m tall. 30. A hockey player s Q-value is defined by Q = 2G + A + PIM 5. What is the sum of the Q-values of the following two players? G A PIM Theresa Dawn For the following distributions, calculate the required information. a) If X~N(20, 3 2 ), what percentage of the data have value x > 22? b) If X~N(50,64), what percentage of the data fall within the range 40< x <52? c) For X~N(30,16), find the percentage of the data for which x < 32. d) Given X~N(41, 25), find the value of x which represents the 60 th percentile.

4 32. Consider these data for shows for two different TV stations. Use these data to compare show times on the two stations. TV show time TVO frequency TV show time CTV frequency 15min 40 15min 2 30min 10 30min 21 1hr 5 1hr 11 2hr 2 2hr 2 TOTAL 57 shows 24 hrs TOTAL 36 shows 24 hrs 33. Let set be the set of even numbers between 1 and 20. Let be the set of all numbers divisible by three between 1 and 20. Which statement is true? a. c. b. d. 34. a) According to the Venn diagram, what is the value of? b) According to the Venn diagram, state the value of. c) What is the value of n(a D)? 35. A group of people are asked about their music preferences. The number of people who say they like rock music is 283. The number who say they like country is 189. The number who say they like both types of music is 112. State the number of people who like rock or country music. 36. A card is drawn from a regular deck of cards and replaced. Then a second card is drawn. Determine the probability that a spade is drawn and then a face card is drawn. 37. Using a standard deck of cards, find the probability of drawing (a) a face card; (b) a card that is black but not a face card; (c) a card that is a diamond or a Two people are playing rock, paper, and scissors. Determine the probability that they will both choose the same option two times in a row. 39. Two dice, one red and one green are rolled. What is the probability that the total will be an odd number given that a number less than four was rolled on the red die? 40. A spinner with three equal sections labelled A, B, and C is spun. Determine the probability that the spinner lands on A or B at least once. 41. The statistics for a sports team during a particular season show that the team won 80% of its games and 70% of the time the crowd was greater than people. These two events occur at the same time 50% of the time. Determine the probability that the team won, given that the crowd was greater than

5 42. A road has two stoplights at consecutive intersections. The probability of getting a green light at the first intersection is 0.7, and the probability of getting a green light at the second intersection, given that you got a green light at the first intersection, is 0.8. What is the probability of getting a green light at both intersections? 43. Two names are drawn out of a hat with five names in it to determine a social committee. Determine the probability that one particular candidate will be chosen. 44. State the number of ways that a committee of a president, treasurer, and secretary can be selected from a students' council with 15 members. 45. Determine the number of ways the 8 members of the Junior Jazz Band can stand in a line if Val must be first, Tim sixth, and Tricia last. 46. A captain and co-captain for a fencing team are chosen from a hat with the names of all 11 members in the hat. Determine the probability that Lauren and Isabel are chosen as captain and co-captain respectively. 47. Three cards are drawn randomly from a hat containing cards with the twenty-six letters of the alphabet on them. Determine the probability of selecting A and B. 48. Euchre is played with the 9, 10, J, Q, K, A from a standard deck of cards. Determine the probability that a player would have a 5-card hand containing only trump cards (remember that the jack of the same colour of the trump suit becomes a trump card for that round of play). 49. Let A be the keys on a regular keyboard. Let B be keys on a regular telephone. a) Determine n(b) and n(a). b) Determine the set A B and n(a B) c) Determine n(aub) 50. When can you use the Normal Distribution to approximate the Binomial Distribution? Under what circumstances would you make this approximation? This review package does not cover Units 4 or 5. Look over topics lists at the end of each unit. Try questions from previous review packages and briefly look over old evaluations.