Download FM20 Final Exam Review Part two 2011-2012.docx

FM20 Final Exam Review 2011-2012
Test Date: _______________, 2022
PART TWO: Chapters 5 to 8
Please note this is a selection of some review questions not a sample final exam. Exam
questions will be different. However, be aware that the final exam is much longer than any
unit test and covers the entire course. You have up to 3 hours to finish the exam.
Note: Outcome FM20.1 was our project outcome. It will not be on our final exam.
Chapter 5 Statistical Reasoning
FM20.6 Demonstrate an understanding of normal distribution, including standard deviation and z-scores.
FM20.7 Demonstrate understanding of the interpretation of statistical data, including
●
●
confidence intervals
confidence levels
margin of error
●
Ch. 5 Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Environment Canada compiled data on the number of lightning strikes per square kilometre in Alberta and
British Columbia towns from 1999 to 2008.
0.42
0.04
0.81
0.40
0.03
0.74
0.28
0.03
0.70
0.23
0.03
0.66
0.13
0.02
0.61
0.12
0.01
0.58
0.10
0.00
0.49
0.07
1.08
0.43
0.05
0.91
0.42
0.04
0.88
What value goes in the fourth row of this frequency table?
Lightning Strikes
(per square
kilometre)
Frequency
0.00–0.19
13
0.20–0.39
2
0.40–0.59
6
0.60–0.79
0.80–0.99
3
1.00–1.19
1
a. 3
____
b. 5
c. 4
d. 6
2. The range of a set of data is 122 and the minimum value is 87.
To display this data in a histogram, Nat chose intervals of 20 starting with 80–99.
How many intervals will her histogram have?
a. 10
b. 9
c. 7
d. 8
1
____
3. At the end of a bowling tournament, three friends analyzed their scores.
Erinn’s mean bowling score is 92 with a standard deviation of 14.
Declan’s mean bowling score is 130 with a standard deviation of 18.
Matt’s mean bowling score is 116 with a standard deviation of 22.
Who is the more consistent bowler?
a.
b.
c.
d.
____
4. The ages of participants in a bonspiel are normally distributed, with a mean of 40 and a standard deviation of 10
years. What percent of the curlers are between 20 and 30?
a.
b.
c.
d.
____
17.5%
13.5%
27%
32%
5. Which set is normally distributed?
Interval
0–9
10–19
Set A.
100
500
Set B.
800
750
Set C.
950
420
Set D.
400
620
a.
b.
c.
d.
____
Impossible to tell.
Declan
Matt
Erinn
20–29
850
700
180
760
30–39
820
650
220
820
40–49
450
600
460
900
Set A.
Set C.
Set D.
Set B.
6. Determine the z-score for the given value.
µ = 91.4, σ = 3.8, x = 87.6
a.
b.
c.
d.
____
–2
2
–1
1
7. Determine the percent of data to the left of the z-score: z = –1.50.
a.
b.
c.
d.
8.08%
6.68%
6.81%
7.35%
2
50–59
150
550
990
850
____
8. Determine the percent of data between the following z-scores:
z = 0.40 and z = 1.80.
a.
b.
c.
d.
____
30.87%
22.66%
15.44%
7.72%
9. Determine the percent of data between the following z-scores:
z = –2.25 and z = 1.75.
a.
b.
c.
d.
95.99%
94.77%
93.55%
97.23%
____ 10. A poll was conducted about an upcoming election. The result that 71% of people intend to vote for one of the
candidates is considered accurate within ±3.0 percent points, 9 times out of 10.
State the confidence interval.
a.
b.
c.
d.
69.5%–72.5%
71%–77%
74%–77%
71%–74%
____ 11. Which sample size will have the least margin of error?
a.
b.
c.
d.
3000
1000
2000
It is impossible to tell.
Ch. 5 Short Answer
12. Joel researched the average daily temperature in his town.
Average Daily Temperature in Lloydminster, SK
Month
Jan. Feb. Mar. Apr. May Jun.
average daily –10.0 –17.5 –5.0
3.7
10.7 14.3
temperature
(°C)
Determine the range of the data.
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Jul.
20.1
Aug.
14.0
Sep.
9.8
Oct.
4.8
Nov.
–5.8
Dec.
–14.8
13. Joel researched the average daily temperature in his town.
Average Daily Temperature in Lloydminster, SK
Month
Jan. Feb. Mar. Apr. May Jun.
average daily –10.0 –17.5 –5.0
3.7
10.7 14.3
temperature
(°C)
Jul.
20.1
Aug.
14.0
Sep.
9.8
Oct.
4.8
Nov.
–5.8
Dec.
–14.8
Aug.
14.0
Sep.
9.8
Oct.
4.8
Nov.
–5.8
Dec.
–14.8
Determine the mean of the data to the nearest tenth of a degree.
14. Joel researched the average daily temperature in his town.
Average Daily Temperature in Lloydminster, SK
Month
Jan. Feb. Mar. Apr. May Jun.
average daily –10.0 –17.5 –5.0
3.7
10.7 14.3
temperature
(°C)
Jul.
20.1
Determine the median of the data.
15. A teacher is analyzing the class results for a computer science test. The marks are normally distributed with a
mean (µ) of 77.4 and a standard deviation (σ) of 4.2. Determine Kathy’s mark if she scored µ – 2σ.
16. A teacher is analyzing the class results for a physics test. The marks are normally distributed with a mean (µ) of
76 and a standard deviation (σ) of 4.
Sketch the normal curve for the test.
17. The results of a survey have a confidence interval of 29% to 37%, 9 times out of 10.
Determine the margin of error.
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18. In a recent survey of high school students, 52.4% of those surveyed said they would vote for Sammie as student
council president. The survey is considered accurate to within 1.9 percent points, 19 times out of 20.
If a high school has 800 students, state the range of the number of votes Sammie should expect.
Ch. 5 Problems
19. Yumi always waits until her gas tank is nearly empty before refuelling. She keeps track of the distance she drives
on each tank of gas. The distance varies depending on the weather and the amount she drives on the highway.
The distance has a mean of 520 km and a standard deviation of 14 km.
a) What percent of the time does she drive between 534 km and 562 km on a tank of gas?
b) Between what two values will she drive 95% of the time?
20. Jackson raises Siberian husky sled dogs at his kennel. He knows, from the data he has collected over the
years, that the masses of adult male dogs are normally distributed, with a mean of 23.6 kg and a standard
deviation of 1.8 kg. Jackson has 48 puppies this year. How many of them could he expect to have a mass
greater than 20 kg when they grow up?
21. In a pre-election survey in Calgary, 18% of those surveyed said they were undecided about whom to vote for
in the mayoral election. The survey is considered accurate to within 4.3 percent points, 99 times out of 100.
a) Determine the confidence level and the confidence interval.
b) If there are 680 000 eligible voters in Calgary, state the range of the number of people who are undecided.
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Chapter 6 Systems of Linear Inequalities
FM20.8 Demonstrate understanding of systems of linear inequalities in two variables.
#1. Graph the following linear inequality: 2x + 3y < -6 Shade the solution set. Show your test point
calculation and conclusion as done in class (i.e. true or false)
#2. Graph the feasible region for the following system of linear inequalities. Remember to shade the
solution set. Show your test point calculation and conclusion as done in class (i.e. true or false).
x + 2y < 4
2x – y – 3 < 0
x – y ≥ -2
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#3. Determine the maximum and minimum value for the given objective quantity, Q, for the shaded feasible
region shown below. Use Q = 12x - 7y
#4. Draw the region given the by the system of inequalities below:
x≥0
y≥0
x + 19 ≥ 3y
3x + 2y ≤ 31
a) Name the coordinates of the vertices of the region
Do on graph paper. You must have a
page. If at home, print one off the
internet. Google “graph paper” image.
b) If Q is given by the equation Q = 2x + 4y, find the maximum realized by this equation.
#5. Read the problem below and answer the following questions. DO NOT solve the problem, but set it up
to be solved by writing the constraints and the optimization equation (the objective quantity, Q).
An 80 minute test consists of 8 questions of type A and 5 questions of type B. Each
question in part A takes 5 minutes to complete and is worth 6 points. Each question in part
B takes 10 minutes to complete and is worth 14 points. You are required to do at least two
questions from part B. How many questions from each part should you complete in order
to maximize your score? What is the maximum score you can obtain? Assume you get full
marks on each question that you attempt.
#6. Suppose that you must write a final exam in physics and in mathematics. You have at most 12 hours in
total to study for these two finals. You feel that you should study at least 2 hours for math and at
least one hour for physics. In addition, you feel that you should spend at least half as much time
studying for math as for physics. You estimate that for every hour you spend studying physics you
will increase your year’s mark by 2% and for every hour you spend studying math you will increase
your year’s mark by 1%. How many hours should you spend studying for each subject in order to
increase your combined average in the two classes by the greatest amount? What is the maximum
amount by which you can increase your combined average?
This is a full linear programming word problem. You must include graph of feasible region including
the vertices. As well, remember other aspects of a good solution to a word problem.
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Chapter 7
Quadratic Functions and Equations
FM20.9 Demonstrate an understanding of the characteristics of quadratic functions of the form
y = a(x – p)2 + q, including:
●
●
●
●
vertex
intercepts
domain and range
axis of symmetry
Ch. 7 Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which parabola opens upward?
a. y = 2x – 4x2 – 5
b. y = 2 + 4x – 5x2
c. y = 4 – 2x2 –5x
d. y = –5x + 4x2 + 2
____
2. Which set of data is correct for this graph?
A.
Axis of Symmetry
x = 4.25
Vertex
(4.25, –2.5)
Domain
Range
–8 ≤ x ≤ 4.25
2.5 ≤ y
B.
x = 2.5
(2.5, 4)
x∈R
y∈R
C.
x=4
(4, 2.5)
–6 ≤ x ≤ 2
0≤y
D.
x = –2.5
(–2.5, 4)
x∈R
4≤y
a. Set D.
b. Set A
c. Set B
d. Set C
____ 3.
What are the x- and y-intercepts for the function y =x2 –2x + 3?
a. no x-intercepts, y = 3
b. x = 0, x = 3, y = 2
c. x = –1, x = 3, y = 3
d. x = –3, x = 1, y = 3
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____
4. Which set of data is correct for the quadratic relation y = (x + 45)2 + 60?
Direction parabola opens
Vertex
Axis of Symmetry
A.
upward
(–60, –45)
x = –60
B.
downward
(60, 45)
x = 60
C.
upward
(–45, 60)
x = –45
D.
downward
(45, 60)
x = 45
a.
b.
c.
d.
____
Set A.
Set D.
Set B.
Set C.
5. Which set of data is correct for the quadratic relation y = –6(x – 18)2 – 30?
Direction parabola opens
Vertex
Axis of Symmetry
A.
upward
(30, –18)
x = 30
B.
downward
(6, 30)
x = –18
C.
upward
(–6, –18)
x = –30
D.
downward
(18, –30)
x = 18
a.
b.
c.
d.
Set B.
Set C.
Set D.
Set A.
____
6. Which function has a maximum value?
a. f(x) = 1.2(x + 3)2 + 1.5
b. f(x) = –3(x – 12)2 + 5
c. f(x) = 2(x – 15)2 – 3
d. f(x) = (x – 13)2 + 12
____
7. Which quadratic function represents this parabola?
a.
b.
c.
d.
____
f(x) = –4(x + 1.5)2 + 2
f(x) = 4(x – 1.5)2 – 2
f(x) = 4(x + 1.5)2 – 2
f(x) = 4(x + 1.5)2 + 2
8. Solve x2 + 6x + 5 = 0 using factoring.
a. x = 5, x = 1
b. x = –5, x = –1
c. x = 5, x = –1
d. x = –5, x = 1
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Ch. 7 Short Answer
1. Fill in the table for the relation y = x2 – x + 7.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
2. Determine the x-intercepts of the corresponding quadratic equation for the graph.
3. Use the graph to determine the equation of the parabola.
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4. Determine the value of a given that (7, –6) satisfies the quadratic function y = a(x – 5)2 + 6.
Ch. 7 Problem
6. For the quadratic function y = x2 + 10x + 25:
a) Determine the coordinates of the vertex.
b) Sketch the graph.
7.
Identify and correct any errors in the following solution:
8. Explain how you would graph the function y = 4(x + 1)2 – 4 without using a table of values or a graphing
calculator.
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12
Chapter 8
Proportional Reasoning
FM 20.3 Expand and demonstrate understanding of proportional reasoning related to:
●
●
●
●
●
●
rates
scale diagrams
scale factor
area
surface area
volume
Ch. 8 Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. A 2 L carton of milk costs $3.26. What is the unit rate?
a. $0.83/500 mL
b. $3.27/2 L
c. $0.61/L
d. $1.63/L
____
2. The graph shows how a cyclist travels over time.
When does the cyclist start to return to the starting position?
a. AB
____
c. EF
d. FG
3. Which situations could be described using the rates 15 L/min, $2.89/ft , and $3.60/100 g?
2
a.
b.
c.
d.
____
b. BC
water flow from a leaky faucet, price of fabric, price of cheese
fuel consumption, price of sod, price of gold
water flow through a hydro electric plant, price of ceramic tile, price of trail mix
water flow through a garden hose, price of carpet, price of salami
4. The distance between two towns on a map is 16.5 cm. The map was made using a scale
of 5 cm to 100 km. What is the actual distance between the two towns?
a. 135 km
b. 825 km
c. 330 km
d. 165 km
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____
5. Which of the following boxes are similar to a gift box that is 10 cm by 8 cm by 16 cm?
a.
b.
c.
d.
____
a box 20 cm by 19 cm by 30 cm
a box 6 cm by 4 cm by 8 cm
a box 15 cm by 13 cm by 21 cm
none of the above
6. A 1:7 scale model of snowmobile is 46.3 cm long , 17.0 cm wide, and 19.0 cm tall.
What are the dimensions of the actual snowmobile?
a. 330.2 cm long, 129.0 cm wide, 143.0 cm tall
b. 316.1 cm long, 121.0 cm wide, 128.0 cm tall
c. 324.1 cm long, 119.0 cm wide, 133.0 cm tall
d. 328.0 cm long, 135.0 cm wide, 143.0 cm tall
____
7. A stage director needs a large chess pawn for a scene. The pawn in her chess set is
35 mm tall and she estimates that the height of the enlarged pawn must be 700 mm.
How many times greater will the surface area of the larger pawn be
a. 800
b. 400
c. 200
d. 1600
____
8. A cylindrical oil tank has a surface area of 1800 m . A similar oil tank has dimensions that are reduced
2
by a scale factor of
a. 800 m2
b. 630 m2
c. 1200 m2
d. 533 m2
. What is the surface area of the smaller tank?
Ch. 8 Short Answer
9. The butcher shop sells a 3 lb package of chicken legs for $9.57. The supermarket sells chicken legs
for $7.68/kg. Determine the price per kilogram that each store charges. Which store has the lower
price per kilogram?
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10. A 25 m long fence has 32 fence posts. How long is a similar fence that has 105 posts?
11. The coffee mug used for this scale diagram was 9.0 cm tall.
Measure to determine what scale factor was used for this diagram.
12. The actual width of a garage door is 3 m. In a scale diagram, the width of the garage door is
20 cm. What scale factor was used? Give your answer as a percent to one decimal place.
13. The radius of a circle with an area of 8 cm2 will be enlarged by a scale factor of 4.
Determine the area of the enlarged circle.
15
14. The sides of a square with an area of 49 cm2 will be reduced by a scale factor of
Determine the area of the reduced square to the nearest square centimetre.
.
15. An orange has a diameter of 8 cm. A honeydew melon has a diameter of 18 cm.
Estimate how many times greater the volume of a melon is, compared with the volume of an orange.
Ch. 8 Problems
16. The diagram of a coffee shop and the attached parking lot was drawn with a scale of 1:300. On the
diagram, the area of the coffee shop is 15 cm2 and the area of the parking lot is 52 cm2.
a)
Determine the area of the actual coffee shop in square metres.
b) Determine the area of the actual parking lot in square metres.
16
17. Cassie made a scale model of a gorilla using 73 linking cubes.
a) How many linking cubes would she need to make a model with dimensions four times as large?
b) By what factor is the surface area of the new model greater than the surface area of the original
model?
17
18 | Page
FM 20 review questions
Ch. 5 MULTIPLE CHOICE
1. C
2. C
3. D
6. C
7. B
8.
4. B
A
Answer Section
Chapters 5 to 8
5. A
9. B
10. C
11. A
Ch. 5 SHORT ANSWER
12. 37.6°C
13. 2.0°C
14. 4.25°C
15. 69.0
16.
17. ±4%
18. 404–434
Ch. 5 PROBLEMS
19.a) 534 = 520 + 1(14)
562 = 520 + 3(14)
Since 534 km is one standard deviation above the mean and 562 is three standard deviations above the mean,
the percent of the time Judy drives between these two distance is half of 99.7% – 68%, or 15.85%.
b) She will drive 95% of the time between the two values two standard deviations from the mean.
520 – 2(14) = 492
520 + 2(14) = 548
The two distances are 492 km and 548 km.
20. 20 = 23.6 – 2(1.8)
Since 20 kg is two standard deviations below the mean, I would expect 95% plus half of the remaining 5% of
the puppies to be in this range.
95% + 0.5(5%) = 97.5%
0.975(48) = 47
I would expect 47 puppies to have a mass greater than 20 kg when they grow up.
21. a) The confidence level is 99 times out of 100 or 99%.
18% – 4.3% = 13.7%
18% + 4.3% = 22.3%
19 | Page
The confidence interval is 13.7% to 22.3%.
b) 0.137(680 000) = 93 160
0.223(680 000) = 151 640
The number of people who are undecided should be in the range of 93 160 to 151 640.
FM 20 Ch 7 review
Answer Section
Ch. 7 MULTIPLE CHOICE
1. D
2.
5. C
6.
Ch. 7 SHORT ANSWER
1.
y-intercept
x-intercept(s)
Axis of symmetry
Vertex
Domain
Range
2. x = 0, x = 4
3. y = –3(x – 1)2
4. a = –3
20 | Page
C
B
(0, 7)
none
x = 0.5
(0.5, 6.75)
x∈R
y ≥ 6.75
3.
7.
A
C
4.
8.
D
B
Ch. 7 PROBLEMS
6. a) The vertex is (–5, 0).
b)
21 | Page
7.
The first error is in line 1. The number 16 should have been factored out of the equation.
The second error is in line 5. The square root of a perfect square can be both negative and positive
values.
8. Use different forms of the equation to determine points on the graph.
From y = 4(x + 1)2 – 4, the vertex is (–1, –4) and a > 0, so the graph opens upward. The equation
for the line of symmetry is x = –1.
Then use stair case numbers and vertex to draw the graph, plot the vertex and points using
staircase, and draw a curve through the points.
22
ch 8 review questions
Ch. 8 MULTIPLE CHOICE
1. D
2. C
3. D
Answer Section
4. C
5. D
6. C
7. B
8. A
Ch. 8 SHORT ANSWER
9. Butcher shop: $7.03/kg
Supermarket: $7.68/kg
The butcher shop has the lower price.
10. 82 m
11. 0.6
12. 6.7%
13. 128 cm2
14. 19 cm2
15. e.g., about 11 times greater
Ch. 8 PROBLEM
16. a) Scale is 1 cm:300 cm.
For an enlargement, the scale factor, k, is 300.
Area of coffee shop = k2(area of coffee shop drawing)
Area of coffee shop = 3002(15 cm2)
Area of coffee shop = 90 000(15 cm2)
Area of coffee shop = 1 350 000 cm2
Area of coffee shop = 1 350 000 cm2
Area of coffee shop = 135 m2
The area of the actual coffee shop is 135 m2.
b) Scale is 1 cm:300 cm.
For an enlargement, the scale factor, k, is 300.
Area of parking lot = k2(area of parking lot drawing)
Area of parking lot = 3002(52 cm2)
Area of parking lot = 90 000(52 cm2)
Area of parking lot = 4 680 000 cm2
Area of parking lot = 4 680 000 cm2
Area of parking lot = 468 m2
The area of the actual parking lot is 468 m2.
17. a) The scale factor, k, is 4. For volume, use the cube of the scale factor.
Volume of model = k3(volume of original)
Volume of model = 43(73 cubes)
Volume of model = 64(73 cubes)
Volume of model = 4672 cubes
b) For surface area, use the square of the scale factor.
The surface area of the new model is 42 = 16 times greater than the surface area of the original.
23