MDM4U1
Exam Review Package
Name _______________________________
One Variable Stats
The data in the table below represent odometer readings of used cars on a usedcar lot. Use the data to answer questions 1 to 6.
56
87
102
81
69
78
95
115
57
92
84
128
128
65
43
34
155
117
102
109
98
144
137
116
76
176
102
104
73
192
113
105
128
95
223
120
1. a) Group these data into intervals and create a frequency table.
b) Produce a frequency diagram and a frequency polygon.
2. a) Determine the three measures of central tendency using the raw data..
b) Determine the three measures of central tendency using the midpoints of
the intervals.
c) Compare the results of parts a) and b). Explain the differences.
3. Use technology to determine the population standard deviation and the
interquartile range using the raw data.
4. a) Produce a box-and-whisker plot and a modified box-and-whisker plot.
b) Identify any outliers.
c) How have the outliers affected the measures of central tendency?
5. The used-car dealer uses the median to describe the average odometer
reading. Is this appropriate? Explain.
6. The dealer intends to sell the cars in the 20th percentile at premium prices.
To which odometer readings would this apply?
7. The final mark in a data management class is calculated using the weightings
shown in the table below. What was Sarah’s final mark?
Weighting
10%
Sarah’s Mark
Quizzes
Assignments
10%
102 out of 120
Tests
30%
203 out of 250
Culminating Assignment
20%
85 out of 100
Exam
30%
76 out of 90
78 out of 84
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
8. Describe the type of sample used in each scenario.
a) a telephone survey of numbers randomly selected from a store’s
database.
b) A student council asks students to comment on an issue by placing their
comments in a comment box.
c) A proportionate number of people from 10 age groups are randomly
selected from the population of a city.
d) A pollster randomly selects three streets from 10 randomly selected
towns in Ontario and interviews a resident of the street.
9. Identify the bias in each survey scenario. Suggest how to eliminate the bias.
a) A teacher asks the boys in the grade 9 health class to raise their hands for
how many dates each student has had as the teacher calls out the numbers.
b) A magazine asks readers to respond to a poll about their favourite actor
of the Academy Awards nominees, immediately following an article
about one of the actors.
c) A pollster asks pedestrians on a downtown sidewalk if they are in favour
of a new park in the suburbs.
10. Calculate your current mark in this class using a weighted mean (use marks
online to date!). The weightings for each category are shown below.
Knowledge
Application
Communication
Thinking/Inquiry
20%
15%
10%
20%
Hint: you will need to organize your marks into their respective categories!
* This question is optional
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
Two Variable Stats
1. Define or explain each of the following terms.
a) moderate positive linear correlation
b) r2
c) presumed relationship
d) correlation coefficient
e) coefficient of determination
2.
Match the correlation type with the coefficient, r.
Correlation Type
Coefficient, r
a) weak, positive, linear
0.00
b) strong, negative, linear
1.00
c) none
0.46
d) perfect, positive, linear
0.20
e) moderate, negative, linear
0.75
3. In a physics experiment, various masses were suspended from a spring. The
stretching distance of the spring is recorded for each case.
Mass (g)
Stretch Distance (cm)
a)
b)
c)
d)
50
1.2
100
2.5
150
3.2
200
5.3
300
7.0
500
11
750
16
Create a scatter plot and classify the linear correlation.
Determine the correlation coefficient.
Determine the line of best fit.
Use this model to predict the stretch length of this spring when loaded with a 625-g mass.
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
Permutations
1. Glyn has a spinner with two colours, red and black. He spins it four times in
a row.
a) Calculate the number of different orders in which the spinner could land
red or black.
b) Draw a tree diagram to illustrate all the possible results.
c) Explain how your tree diagram corresponds to your calculations in part a)?
2. Evaluate each of the following by first expressing each in terms of factorials.
a) 18P2
b) P(8, 3)
c) 15P2
d) 11P11
e) P(9, 0)
3. You and your friend are designing a method whereby you can communicate
across a crowded room with hand signals. The three signals are hand open
with palm facing the other person, hand open with back of hand facing the
other person, and closed hand.
a) How many different signals can you define using
i) 3 signals?
ii) 1, 2, or 3 signals?
b) Explain how the multiplicative and additive counting principles apply in
your calculations for part a).
4. a) How many four-digit numbers are possible with the digits 3, 4, 5, 6, 7, 8, and 9?
Assume that no digits repeat.
b) How many of these numbers in part a) are odd numbers?
c) How many of these numbers in part a) are even numbers?
5. How many ways are there to roll either a 4 or a 9 with a pair of dice?
6. How many different ‘words’ can you form with the letters in each of the following words:
a) MATH
b) CAREER
c) EXTINCT
7. How many 4-digit numbers less than 8000 have at least one 9, if repetition is
allowed?
8. On the checkerboard shown, the piece can travel only diagonally upward. It can’t
move through the squares containing an explosion, but can jump over them!
Determine the number of paths from the checker’s current position to the top of the board.
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
Combinations
1.
Evaluate each of the following expressions. List any calculations that
would require a calculator.
a)
15C15
b)
21C12
c)
54C53
d)
54C2
2. Rewrite each of the following expressions as a single combination.
a)
18C2
+ 18C3
b)
25C14
– 24C13
3. Find the simplified 3rd term for each of the following expansions.
a) (4x – y)5
b) (2x – 3y)8
4. Use the binomial theorem to expand each expression fully.
a) (7x + y)3
b) (3a – 5b)4
5. Loyalist CVI is about to have a reunion of all the previous graduating
classes. There are 20 members of the current alumni association. Of
these, eight members are recent graduates. In how many ways can a subcommittee of four members be struck to provide memorabilia if
a) there are no restrictions
b) the sub-committee must be all recent graduates
c) the sub-committee must have only two recent graduates
d) the sub-committee must have no more than three recent graduates
6. There are 15 part-time workers at a local grocery store.
a) In how many ways can the general manager choose three part-time
workers to attend a seminar?
b) In how many ways can the general manager choose a clerk, a stock
person, and a bakery clerk?
c) Should the answers to parts a) and b) be the same? Explain.
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
7. A school athletics department fields a number of teams.







15 students play on the volleyball team
18 students play on the basketball team
21 student play on the soccer team
8 students play both volleyball and basketball
6 students play both volleyball and soccer
7 students play both basketball and soccer
4 students play on all three teams
a) Use a Venn diagram to determine the minimum number of trophies
that must be ordered if each student is to receive a commemorative
trophy?
b) How many students played volleyball but neither basketball nor soccer?
8. A soccer team played eight games and won five of them. There were no
ties. How many arrangements of the five wins and three losses are
possible?
9. Every Friday a downtown restaurant has an all-you-can-eat buffet with
the following items:






soup, garden salad
bread, rolls, crackers
popcorn shrimp, shrimp and dip
lasagna, chicken wraps, beef stew
snow peas, carrots, mixed vegetables
fresh fruit, apple pie, custard
a) How many different combinations of items could you choose for
your meal?
b) The restaurant also has a lunch special featuring any one item from
each group. How many choices do you have in this special?
10. There are 55 students who take Data Management this term and 24 who take Calculus. Only
5 students take both courses. A committee of 4 students is to be formed to represent this
group. In how many ways can this committee be formed if there must be at least one student
from Data Management?
11. The game of euchre uses just the 9s, 10s, jacks, queens, kings, and aces from a standard deck
of 52 cards. How many five-card euchre hands have at least one spade?
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
Probability
1. A pencil case contains three blue pens, two red pens, and five pencils. If you reach in
and randomly select a writing instrument, what is the probability that it is
a) a red pen?
b) a pen?
c) not a blue pen?
2. Lena programs her graphing calculator to generate a random number between 1 and 10, and
conducts 20 trials. Let E be the event that an even number is generated, and that she observes
that this occurs seven times.
a) What is the experimental probability that E occurs?
b) What is the theoretical probability that E occurs?
c) Lena explains that the random number generator on her graphing calculator is flawed.
What is Lena’s reasoning?
d) What might you suggest to Lena as an alternate explanation for her observations?
3. Suppose that the weather forecast calls for a 30% chance of rain on each of the three days of a
long weekend. What are the odds in favour of no rain throughout the entire long weekend?
4. Claudia and Ally are the two favourites to win an upcoming golf tournament. If Claudia is
given 1:9 odds of winning, and Ally is given 2:17 odds of winning,
a) who is favoured to win? Explain.
b) determine the probability of each player winning.
5. A box contains 48 tickets for six door prizes. Six tickets are drawn, and not replaced, to
declare the winners. If Serge purchases 8 tickets, determine the probability that he wins
a) the first prize
b) the first and second prizes
c) all six prizes
6. Elvira has three caps: one red, one green, and one blue. She also has two green T-shirts, one
blue T-shirt, and three black T-shirts. Elvira considers it a fashion faux pas to ever be seen
wearing blue and green at the same time. What is the probability that Elvira will commit a
fashion faux pas, if she randomly reaches into her dresser and selects a cap and T-shirt?
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
7. Ten boys and twelve girls decide to rent a 16-passenger van and a 6-passenger car to drive to
a rock concert in a nearby city. If the group is distributed randomly between the vehicles,
what is the probability that
a) there are no boys in the car?
b) there are no girls in the car?
c) Steve and Susan are both in the van?
d) either Steve or Susan are in the van?
8. Six friends at a dinner party are seated randomly at a round table. What is the probability that
a) Russel will be seated next to Sadia?
b) Russel, Jade, and Sadia are seated next to each other in alphabetical order, clockwise?
9. Suppose that whenever Enrico and Cliff play chess, odds are 2:1 in favour of Enrico winning
a game. Suppose a 3-game match is arranged.
a) Create a tree diagram that illustrates all the possible outcomes for the match.
b) Determine the probability of each outcome.
c) Add the probabilities determined in part b). Does this total make sense? Explain.
d) What is the probability that Enrico will not win all three games?
e) What is the probability that Cliff will win exactly two games?
f) What are the odds in favour of Cliff winning the match?
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
Probability Distributions
1. Determine if a uniform, binomial, geometric, or hypergeometric distribution would be the
best model for each of the following experiments. Explain your reasoning.
a) generating binary random numbers on a calculator until a 0 appears
b) counting the number of spades in a hand of five cards dealt from a well-shuffled deck
c) rolling a 2 on a die
d) predicting the number of tails when flipping a coin 30 times
2. A lottery ticket costs $1.00 and a total of 2 250 000 tickets were sold. The prizes and their
frequencies are given in the following table.
Prize
Number of Prizes
$250 000
1
$25 000
2
$2 500
5
$250
20
$25
100
Determine the expected winnings of each ticket.
3. Of 20 people invited to a pool party, 4 prefer vanilla ice cream, 7 prefer chocolate, and 3
prefer strawberry. The host surveys six of these people at random to determine how much ice
cream to buy.
a) What is the probability that at least 3 of the people surveyed prefer chocolate ice cream?
b) What is the probability that none prefer vanilla ice cream?
c) What is the expected number of people who prefer strawberry ice cream?
d) What is the expected number of people who do not have a preference for any of the three
flavours?
4. Suppose you randomly choose an integer, n, between 1 and 10, and then draw a circle with a
radius of n centimetres. What is the expected area of this circle to the nearest hundredth of a
square centimetre?
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
5. The probability of winning a prize in a game is 0.2.
a) Show the probability distribution for the number of prizes won in 10 games.
b) If the game will be played 1000 times during the fair, how many prizes should the game
operators keep in stock?
6. a) What is the probability that at least one double will occur within the first five rolls of two
dice?
b) What is the expected waiting time before a double?
7. A multiple-choice mathematics quiz has five questions, each with five possible answers.
Someone simply guesses at each answer.
a) What is the probability of zero or one correct guesses?
b) What is the probability of getting more than half the questions right?
c) What is the expected number of correct guesses?
8. In an experiment a tetrahedral die is rolled repeatedly until an even number shows up. What
is the probability that it takes fewer than 4 rolls for this to occur?
9. In a game of chance, a pair of dice is rolled. If the sum is 2 or 12, you win $10. If the sum is
6, 7, or 8 you win $1. You win nothing for any other sum.
a) Create a probability distribution for this situation.
b) Calculate the expected winnings for this game.
c) How much should the dealer charge to play the game so that they make an average profit
of 50 cents per game?
10. In the spring, the Ministry of the Environment caught and tagged 300 raccoons in an area in
cottage country. The raccoons were released after being vaccinated against rabies. To
estimate the raccoon population in the area, the ministry caught 25 raccoons during the
summer. Of these, 10 had tags. Estimate the raccoon population in the area.
MDM4U1 – Mr. Murray
MDM4U1
Exam Review Package
Name _______________________________
Normal Distributions
1. A cereal manufacturer finds that the mass of cereal in the 200-g packages is normally
distributed with a mean of 200 g and a standard deviation of 16.3 g.
a) What is the probability that a package chosen at random has a mass between 180 g and
220 g?
b) If a container with less than 170 g is considered below standard, what proportion of
cereal packages would be rejected?
c) Out of 500 packages, how many have a mass greater than 230 g?
2. What technique must be utilized in order to make predictions about discrete quantities using a
normal model?
3. The probability of winning a large stuffed animal in the ring-toss game at a fair is
10%.
a) Using a binomial distribution and a normal distribution, predict how the probabilities of
winning at least 5 of 50 games will differ.
b) Find the probability of winning at least 5 of 50 games using
i) a binomial distribution
ii) a normal approximation
c) Do your calculations support your predictions?
MDM4U1 – Mr. Murray