Embed Size (px)
Citation preview
MDHS Mathematics Department MDM 4U - Student Goal Tracking Sheet
Name: ___________________ Unit name: Counting Goals for this unit:
1) I can apply the different counting techniques; tree diagrams, Fundamental Counting Principle, Factorials, Combinations, Permutations, etc…
2) I can apply / explain Pascal`s Triangle.
3) I can explain / understand set theory and apply it to concepts such as VENN Diagrams.
Today’s Topic Today’s Goal
Self-Assessment Self-Reflection
Did
I w
atch
the
assi
gned
vi
deo
for t
his
topi
c?
Did
I co
mpl
ete
the
hom
ewor
k fo
r thi
s to
pic?
Did
I co
mpl
ete
the
Jour
nal
for t
his
topi
c?
How
suc
cess
ful w
as I
with
th
is J
ourn
al?
(1 (n
eed
revi
ew) t
o 4
(mas
tere
d))
Did
I re
view
this
for t
he
unit
test
?
Did
I re
view
this
for t
he
exam
?
Counting Principles
I can use tree diagrams, multiplicative counting principle and indirect methods to determine the number of outcomes.
Factorial Notation and Permutations
I can explain Factorial Notation and apply factorials to simple problems and to applications like permutations.
Permutations and Clones
I can solve problems that involve arrangements using identical objects.
Pascal`s Triangle and Applying Pascal`s Method
I can explain and apply Pascal's Triangle to a variety of real - world applications.
Set Theory I can explain and apply set theory when given a set of data.
Today’s Topic Today’s Goal
Self-Assessment Self-Reflection
Did
I w
atch
the
assi
gned
vi
deo
for t
his
topi
c?
Did
I co
mpl
ete
the
hom
ewor
k fo
r thi
s to
pic?
Did
I co
mpl
ete
the
Jour
nal
for t
his
topi
c?
How
suc
cess
ful w
as I
with
th
is J
ourn
al?
(1 (n
eed
revi
ew) t
o 4
(mas
tere
d))
Did
I re
view
this
for t
he
unit
test
?
Did
I re
view
this
for t
he
exam
?
VENN Diagrams I can interpret sketch and use VENN diagrams in real-world situations.
Combinations I can explain and apply combinations to real - world applications.
Combinations and Permutations
I can identify whether the question is a combination or permutation and apply the appropriate strategy.
Pre-test reflection (How am I going to do? What am I good at? What do I need to study or improve?)
Post-test reflection (How did I do? What was I good at? What do I need to study or improve on for the exam? How am I going to do this?)
K A C T
U1J1 - Counting Principles
1) A restaurant has a daily special with soup or salad for an appetizer; fish, chicken or a veggy dish for the entree; and cake, ice cream or fruit salad for dessert. Draw a tree diagram to illustrate all the different meals.
2) A theatre company has half-price offers for students who buy tickets for at least three of the eight plays this season. Determine how many choices of three plays a student will have.
U1J2 - Factorial Notation and Permutations
1) Explain how factorials and permutations are related. 2) List three different forms for a permutation. 3) A band has recorded five songs. Determine how many different ways the songs could be played at a concert. 4) Determine how many ways first, second and third place could be awarded in a race with 7 people using: a) Factorials b) Permutations
U1J3 - Permutations and Clones
1) Determine how many different ten digit telephone numbers contain four 2's, three 3's and three 7's. 2) Determine how many arrangements there are for EXETER when: A) There are no restrictions. B) The "word" must end with the "X". C) The "T" and "R" must be side-by-side. D) The three "E"'s must stay together.
U1J4 - Pascal`s Triangle and Applying Pascal`s Method
Write out the first 6 rows of Pascal's Triangle and EXPLAIN how each row can be developed. Explain the relationship between nCr and Pascal's Triangle. (Use the triangle from above to help explain) Determine how many ways there are to get from A to B.
A
B Determine how many ways you can spell "Mitchell" as shown.
M
I I
T
C C
H H H
E E
L L L
U1J5 - Set Theory
Given the universal set S = a, b, c, d, e, g, i, n, o, t, u and sets X = a, e, i, o, u and Y = a, c, g answer the following: A) Determine X'
B) Determine Y'
C) Determine X U Y
D) Determine X ∩ Y
E) Determine X' ∩ Y
E) Determine n(X)
F) Create a set that is disjoint from both set X and Y.
UJ6 - VENN Diagrams
A survey of households in a major city found that: 96% have televisions, 65% have computers, 51% have dishwashers, 63% have a television and computer, 49% have a television and dishwasher, 31% have a computer and dishwasher and 30% have all three. A) Use a VENN diagram to sort the data. B) What percentage of households ONLY had a dishwasher? C) What percentage of households had a television and computer? D) What percentage of households had none of the three items? Draw a VENN diagram for the following: A) (A U B) U C' B) (A ∩ B') U (C ∩ A’∩ B’)
U1J7 - Combinations
1) A track and field club has 12 members who are runners and 10 members who specialize in field events. The club has been invited to send a team of 3 runners and 2 field athletes to a meet. Determine how many different teams could be sent. 2) A bridge hand consists of 13 cards. Determine how many hands include 5 cards of one suit, 6 cards of a second suit and 2 cards of a third suit. 3) Explain why combination locks should really be called permutation locks.
U1J8 - Combinations and Permutations
1) The camera club has 5 members and the math club has 8. Determine how many different 4 member committees can be formed with at least one member from each club. 2) A baseball team has 15 players. Only 9 players can be placed in the batting lineup. Determine how many different batting orders are available to the coach. 3) For the given letters g, h, i, j, k, l, m, n, o, p, q determine: A) How many 4 letter permutations exist. B) How many 4 letter combinations exist. C) How many 4 letter permutations exist with h as the first letter. D) How many 4 letter combinations exist with h as the first letter.
1) Without expanding (x + y)5, determine:
A) the number of terms in the expansion.
B) The value of k in the term 10xky2.
2) Expand.
A) (2x + 5y)4
B) (4x y)6
3) Write the following in (a + b)n form.
1024x10 3840x8 + 5760x6 4320x4 + 1620x2 243
1) A bag of marbles contains seven whites, five blacks and eight cat'seyes. Determine the probability of:A) Picking a white marble.
B) Picking a marble that is not black.
2) When a die was rolled 20 times, 4 came up five times.A) Determine the experimental probability of rolling a 4.
B) Determine the theoretical probability of rolling a 4.
C) How can you account for the difference between the results.
3) Estimate the subjective probability of the following. Explain your answer.
A) All classes being cancelled next week.
B) At least one severe snow storm will occur in your area next winter.
1) Determine the odds in favour of flipping three coins and having them all turn up heads.
2) A restaurant conducts a study the measures the frequency of customer visits in a given month. The results are:
Number of visits Number of Customers1 42 63 7
4 or more 3
Based on the above survey, determine:A) The odds that a customer visited the restaurant exactly 3 times.B) The odds in favour of a customer having visited the restaurant fewer than 3 times.C) The odds against a customer having visited the restaurant more than three times.
Journal13.notebook September 20, 2012
Sep 2010:50 AM
1) Shannon has a job interview with two companies. She estimates that she has a 40% chance of recieving a job from company A and a 75% chance of receiving a job from company B. Determine the probability that:A) She will receive an offer from both companies.B) She will receive an offer from company B but not A.C) Is Shannon applying the theory of theoretical, empirical or subjective probability?
Sep 2010:53 AM
2) Stacie and Mariah are sorting washed hockey equipment from themselves and 3 other teammates (Haley, Suzi and Betty). If each person has 2 jerseys in the dryer. If a shirt is pulled out of the dryer at random, determine the probability that the shirt belongs to:A) Stacie, if it is known the shirt pulled belongs to either Stacie or Mariah.B) Betty, if it is known the shirt pulled belongs to one of the 3 teammates.C) Stacie or Mariah.
Journal14.notebook September 20, 2012
Sep 2011:32 AM
1) In a class of 26 students there are 9 blondes, 7 with glasses and 4 people with both blonde hair and glasses.A) Draw a VENN diagram to illustrate this distribution.B) If a student is selected at random from the class, determine the probability that the student will have either blonde hair or glasses.
Sep 2011:34 AM
2) Of 150 students at a dance, 110 like pop songs and 70 like heavymetal songs. A third of the students like both pop and heavymetal songs.A) If a pop song is played, determine the odds in favour of a randomly selected student liking the song.B) Determine the odds in favour of a student disliking both pop and heavymetal songs.C) Discuss any assumptions you made in part A and B to complete the questions.
The following data show monthly sales of houses by a real-estate agency. Answer the following:
A. Determine the measures of central tendency. B. Which measure of central tendency best describes the data? Explain.
Angela is applying to university for an engineering program that will weigh her eight best grade – 12 marks, as shown in table A. Angela’s grade – 12 marks are shown in table B. Answer the following:
A. Calculate Angela’s weighted average. B. Calculate Angela’s unweighted average. C. Explain why an engineering program would use
this weighting system.
Describe two situations where the mode would be the most appropriate measure of central tendency.
6 5 7 6 8 3 5 4
6 7 5 9 5 6 6 7
Table A
Course Weight
Math, Science 3 Computers, English 2 Other 1 Table B
Course Mark
Calculus 95 English 89 Functions 94 Phys. Ed. 80 Computer Programming 84 Chemistry 90 Data Management 87 Physic 92
The following data show monthly sales of houses by a real-estate agency. Answer the following:
A. Determine the standard deviation, interquartile and semi-interquartile range. B. Create a box-and-whisker plot for these data. C. Are there any outliers in the data? Justify your answer. D. Determine the 10th and 90th percentile.
Mr. Agar’s MDM 4U has 14 students. Their scores on the midterm are shown in the table. Answer the following:
A. Calculate mean and median. B. Calculate the standard deviation. C. Determine the z-score for the mark of 65. D. Determine the mark for a z-score of 1.75.
6 5 7 6 8 3 5 4
6 7 5 9 5 6 6 7
50 71 65 54 84 69 82
67 52 52 86 85 94 72
Sketch and classify 5 – different types of linear correlations. Provide an approximate correlation coefficient for each relationship.
A survey of a group of randomly selected students compared the number of hours of television they watched per week with their grade averages. Answer the following using the given table:
A. Create a scatter plot for this data. Sketch it on this page.
B. Determine the correlation coefficient. C. What conclusions can be made about the effect of
watching television has on academic achievement. Explain.
Hours per week 12 10 5 3 15 16 8 Grade average 70 85 82 88 65 75 68
The scores for players’ first and second games at a bowling tournament are shown in the table. Answer the following:
A. Create a scatter plot for these data. B. Determine the correlation coefficient. C. Determine an equation to model the data. D. Identify any outliers. E. If there are any outliers, remove them and repeat parts B and C. F. A player scores 250 in the first game. Use both models (from part C and E) to
determine this players score in the second game. How far apart are the two predictions?
G. Explain why identifying outliers is important when determine relationships in data.
First Game Second Game 169 175 150 162 202 195 230 241 187 185 177 235 164 171
An object is thrown straight up into the air. The table below shows the approximate height as it goes upward. Use the data to complete the following:
A. Create a scatter plot. B. Determine an appropriate equation to model this situation. Include the corresponding
coefficient of determination. C. Use the model from part B to predict how long the object will be in the air (When will
it hit the ground?). D. Use the model from part B to predict the maximum height the object will reach before
starting to fall. E. Do you think you model is accurate. Explain your reasoning.
Time (s) Height (m) 0 0
0.1 1 0.2 1.8 0.3 2.6 0.4 3.2 0.5 3.8 0.6 4.2
A teacher is trying to determine whether a new spelling game enhances learning. In his grade 4 “gifted” class, he finds a strong positive correlation between use of the game and spelling-test scores. Should the teacher recommend the use of the game in all English classes at his school and throughout the board? Explain your answer.
Explain what is meant by the “hidden variable”. Outline a strategy or process that might help detect the presence of a hidden variable within a set of data.
Journal 21
1) James has designed a board game that uses a spinner with ten equal sectors
numbered 1 - 10. If the spinner stops on an odd number, a player moves forward
double that number of squares. However, if the spinner stops on an even number, the
player must move back half the number of squares. Answer the following:
A) Determine the “expected” move per spin.
B) Determine if this game is “fair”. Explain why.
2) Suppose the lottery sold 10 000 000 tickets at $5.00 each. The prizes are as
follows:
Prize Number of prizes
$2 000 000 1
$1 000 500
$100 10 000
$5 100 000
Determine the expected winnings on each ticket purchased.
Journal 221) Describe the key characteristics of a binomial distribution. Provide an example.
2) A factory produces computer chips with a 0.9% defect rate. In a batch of 100computer chips determine:A) The probability of only 2 being defective.B) The probability of at least 2 being defective.C) The expected number of defective computer chips in a batch of 100.
3) Cal’s Coffee prints prize coupons under the rims of 20% of it paper cups. If you buy50 cups during the promotion, answer the following:A) Determine the probability that you win 7 prizes.B) Determine the probability you win at least one prize.C) Determine the expected number of prizes you should win during the promotion.
Journal 231) Describe the key characteristics of a geometric distribution. Provide an example.
2) A factory produces computer chips with a 1.9% defect rate. An inspector randomlychooses a chip from the assembly line to test. Answer the following:A) Determine the probability that the first defective chip will be the 6 one tested.thB) Determine the probability that the first defective chip will be one of the first threetested.C) Determine the expected waiting time until the first defective chip is found.
3) In order to win a particular board game, a player must roll, with two dice, the exactnumber of spaces remaining to reach the end of the board. If a player is 2-spaces fromwinning, create a probability distribution for the number of rolls required to win, up to 10rolls.
Journal 24
1) Describe the key characteristics of a hypergeometric distribution. Provide an
example.
2) Five cards are randomly dealt from a standard deck of cards. Create a probability
distribution of the number cards dealt that are either face cards or aces.
3) One summer, conservation official caught and tagged 98 beavers in the Red River.
Later that year, 50 beavers are caught and of the 50, 32 had tags. Estimate the size of
the beaver population along the Red River.
Journal 251) Describe and sketch the 4 - types of continuous distributions discussed in class.
2) The commuting time from Georgetown to downtown Toronto varies uniformly from 30to 55 minutes, depending on traffic and weather conditions. Answer the following:A) Construct a distribution graph for this situation.B) Determine the probability that the trip takes 45 minutes or less.C) Determine the probability that the trip takes more than 48 minutes.
Journal 261) Explain how the z-score table works. Use diagrams as necessary.
2) The results from a lab test are normally distributed with and . Answer the following:A) Determine the probability that the blood test chosen randomly from this data has ascore greater than 90.B) Determine what percent of these blood scores will have a result between 50 and 80.C) Determine how low a score must be to lie in the lowest 5% of the results.
Journal 27
1) The list below gives the age in months of 32 deer tagged in an Ontario provincial
park last fall. Use the table to answer the following:
A) Determine whether the data is normally
distributed. Justify your answer.
B) Determine the mean and standard deviation for
the data.
C) Determine the probability that a deer selected
randomly from this sample will be at least 30
years old. State any assumptions you made.
47 28 31 41 39 25 21 2926 23 34 25 33 37 28 4518 36 54 40 33 47 42 2937 22 42 37 48 64 60 49
Journal 281) Explain the key characteristics to using a Normal Approximation to the BinomialDistribution. What are some of the benefits?
2) A pencil manufacturer has 60 dozen (720) pencils randomly chosen from each day’sproduction and checked for defects. A defect rate of 10% is considered acceptable. Answer the following:A) Assuming that 10% of all manufacturer’s pencils are actually defective, determinethe probability of finding 80 or more defective pencils the sample.B) Determine the probability that there will be between 20 and 30 defective pencils intoday’s sample.C) If 110 pencils are found to be defective in today’s sample, is it likely that themanufacturing process needs improvement? Explain your conclusions.
