11 P R O B L E M S O L V I N G A N D D ATA A N A L Y S I SPA R T 211 11
DIRECTIONS FOR MULTIPLE-CHOICE QUESTIONS: For this section, you may use the available space for your scratch work. Solve each problem, and fill in the corresponding oval for your answer on the answer sheet.
DIRECTIONS FOR GRID-IN QUESTIONS: These questions require you to solve the problems on your own and enter your answers into the corresponding grids by marking the appropriate ovals.
• Do not mark more than one oval per column.• Columns not needed should be left blank.• You will receive credit only if you fill the ovals in correctly.• Some questions may have more than one correct answer. Only grid in one of the
correct answers.• No answer will have a negative value.• Mixed numbers such as 11/2 must be entered as 1.5 or 3/2. • Decimal answers with more digits than the grid can accommodate may be either
rounded or truncated, but you must fill the entire grid. For example, 0.666... can be entered as 2/3, .666, or .667. If .66 or .67 is entered instead, it will be scored as incorrect.
The number of degrees of arc in a circle is 360.The measure in degrees of a straight angle is 180.The sum of measures in degrees of the angles of a triangle is 180.
Not
es
1. You may use a calculator for ALL of the problems in this homework assignment. 2. Only real numbers are used.3. Figures that accompany problems in this section are provided to help you solve the problem. You can assume that figures are accurately drawn to scale EXCEPT when it is noted otherwise. All figures lie in a plane unless otherwise noted.4. The domain of any function f is defined as the set of all real number x values for which f(x) is a real number, unless otherwise noted.
r
A = πr2
C = 2πr
lw
h
V = lwh Ref
eren
ce In
form
atio
n
l
r
V = πr2h
rh
V = 43 πr3 V = 1
3 πr2h
hr h
r
lw
V = lwh
h
w
V = 13 lwh
l
x2x30°
60°
x 3
45°
45°
s
s s 2
Special Right Triangles
c
ab
c2 = a2 + b2
l
wA = lw
A = 12 bh
h
b
r
A = πr2
C = 2πr
The number of degrees of arc in a circle is 360. The number of radians of arc in a circle is 2π. The sum of the measures in degrees of the angles of a triangle is 180.
P R O B L E M S O L V I N G A N D D ATA A N A L Y S I SPA R T 211 11
PART 2
Calculator Allowed
1. Which scatterplot shows a strong positive association between c and d?
d
c
d
c
d
c
d
c
y
x
1600
2000
1200
800
400
01910 1930 1950 1970 1990 2010
Census year
Clark County Population
Popu
latio
n (in
thou
sand
s)
2. The graph shows the change in the population in Clark County, Nevada according to the US Census. Based on the graph, which of the following is the best approximation of the population of Clark County in 2005?
A) 1,450,000B) 1,575,000C) 1,700,000D) 1,825,000
3. A computer scientist observed that every year the number of transistors in an integrated circuit doubles. Which of the following equations can be used to find the relation between number of transistors, n, and the number of years, t?
11 P R O B L E M S O L V I N G A N D D ATA A N A L Y S I SPA R T 211 11
Problems 4 and 5 refer to the following information:
y
x
80
100
60
40
20
0 June July August September October
A
B
C
Three candidates, A, B, and C, are running for city council. The results of five monthly polls are recorded in the chart above. The election is in November.
4. Which of the following conclusions is most supported?
A) Candidate B will win the election.B) The difference between support for
candidates B and A in October was the same as the difference between support for A and C in July.
C) The percentage change in candidate A’s support between July and August is the same as the percentage change in candidate A’s support between August and September.
D) The difference between support for candidates B and C in July was the same as the difference between support for candidates A and C in September.
5. Is it evident from the data that candidate C is likely to lose the election?
A) No, because in one of the monthly polls he received the maximum percent of votes.
B) Yes, because in one of the monthly polls he received the minimum percent of votes.
C) No, because in each subsequent monthly poll the percent of votes he receives is increasing.
D) Yes, because in most of the monthly polls he receives significantly less votes than the other two candidates.
6. A recent survey asked the opinions of voters on the provision of funds for new roads and bridges. Of the 1,000 people who were surveyed, 71% support the provision. The group who performed the survey reported a 3.1% margin of error on a 95% confidence interval. Which of the following statements best describes the results of the survey?
A) The results indicate that the true percentage of voters who support the provision is exactly 71%.
B) The results indicate that the true percentage of voters who support the provision is definitely between 67.9% and 74.1%.
C) The results indicate, with 95% confidence, that the true percentage of voters who support the provision is between 67.9% and 74.1%.
D) The population believes, with 95% confidence, that the true percentage of voters who support the provision is between 67.9% and 74.1%.
P R O B L E M S O L V I N G A N D D ATA A N A L Y S I SPA R T 211 11
7. Which of the following situations shows a decreasing linear relationship in the real incomes of people over time?
A) The people of a small country have seen their real incomes unchanged over the past 20 years.
B) The people of a small country have seen their real incomes drop by about 1.3% annually over the past 20 years.
C) The people of a small country have seen their real incomes drop by $500 more than each previous year over the past 20 years.
D) The people of a small country have seen their real incomes drop by $500 each year over the past 20 years.
8. Joey can paint a 1,012 square foot wall using 4 gallons of paint. How many 5 gallon buckets of paint does the he need to paint a wall that has an area of 2,530 square feet?
A) 1B) 2C) 8D) 10
y
x
10
8
6
4
2
02 4 6 8 10
Sample A
Time (in hours)
Are
a C
over
ed (i
n sq
uare
inch
es)
y
x
10
8
6
4
2
02 4 6
Sample B
Time (in hours)
Are
a C
over
ed (i
n sq
uare
inch
es)
8 10
9. The graphs show the growth of two different cell samples. Both samples are placed in lab dishes that have an area of about 12 square inches. A lab technician measures the growth of the two cell samples every 6 minutes. The data for each dish was graphed as shown above. Which of the following is a correct statement about the data above?
A) When time = 0, Sample A is growing at a slower rate than Sample B is.
B) When time = 0, Sample A covers a greater portion of its dish than Sample B does.
C) Sample A doubles in area in less than one hour.
D) Sample B doubles in area in about two and a half hours.
11 P R O B L E M S O L V I N G A N D D ATA A N A L Y S I SPA R T 211 11
y
x
195
185
175
165
155
145
0
January
FebruaryMarch Ap
rilMayJune
July
200
Month
Num
ber
of Ic
e C
ream
Con
es S
old
10. The Java Joint ice cream shop recorded the total cones of ice cream sold per month from January to July in the scatterplot above. Based upon the line of best fit to the data shown, which of the following values is closest to the average monthly increase in cones of ice cream sold?
A) 5B) 6C) 7D) 8
11. Ethan paid a total of $488.70 to get his car repaired at an auto repair shop. This total included a state tax of 8%. What amount, rounded to the nearest cent, of the total bill was tax?
A) $36.20B) $39.10C) $40.20D) $43.42
12. Of the following four situations which option shows an increasing linear relationship in the school population?
A) Every year for the past ten years the school population has grown by 50 students.
B) Every year for the past ten years the school population has added 10 more students than it added the previous year.
C) Every year for the past ten years the school population has grown by 2% of the previous year’s population.
D) Every year for the past ten years the school population has grown by 0.5% more than it grew the previous year.
P R O B L E M S O L V I N G A N D D ATA A N A L Y S I SPA R T 211 11
y
x
50
40
30
20
10
010 20 30
Top Movies
40 50Screens (in hundreds)
Box
Off
ice
Sale
s (in
mill
ion
dolla
rs)
13. The scatterplot above shows the number of screens, in hundreds, and the total box office sales, in millions, for the top movies in the US for one weekend. The line of best fit is also shown and has the equation y = 0.3585x – 1.7356. Which of the following best explains how the number 0.3585 in the equation relates to the scatterplot?
A) Over a weekend, a top movie’s box office sales were $35.85 more for every increase of 1 in the number of screens on which the movie was shown.
B) Over a weekend, the top movie’s box office sales were $358,500 more for every increase of 1 in the number of screens on which each movie was shown.
C) Over a weekend, atop movie’s box office sales were $35.85 more for every increase of 100 in the number of screens on which the movie was shown.
D) Over a weekend, a top movie’s box office sales were $358,500 more for every increase of 100 in the number of screens on which the movie was shown.
14. From the year 2003 the number of farmer’s markets in state A has grown at a rate of 7.5% per year. Which of the following graphs best describes the situation?
11 P R O B L E M S O L V I N G A N D D ATA A N A L Y S I SPA R T 211 11
15. In a recent poll, 750 likely voters in one congressional district were asked which candidate they would support for the upcoming congressional election. Of the sample, 49% favor Candidate A, 34% favor Candidate B, and 17% are undecided but will vote in the fall election. The margin of error reported for this poll was 3.6% for a 95% confidence interval. Which of the following statements can be accurately drawn from the data?
A) The true percentage of people who support Candidate A is more than 45.4%.
B) The true percentage of people who support Candidate B is less than 37.6%.
C) The true percentage of people who are undecided is most likely between 13.4% and 20.6%.
D) The true difference in support for Candidate A and Candidate B is most likely between 13.2% and 16.8%.
16. As part of a science fair project, a student buys three packages of a particular seed. She grows seeds from all three packages under the same conditions. The table shows the numbers of seeds in each package and the percentage of the seeds that sprouted from each package.
Package Numberof Seeds
A 128
B 113
C 121
87%
81%
84%
SeedsSprouted
A local nursery buys 100 packages of each type of seed. Which of the following is a reasonable approximation of the number of seeds that sprout in the nursery under the same environmental conditions?
P R O B L E M S O L V I N G A N D D ATA A N A L Y S I SPA R T 211 11
For problems 17-20, solve the problem and enter your answer in the grid on the answer sheet.
Note : Figure not drawn to scale
Chickens 50%
Goats 20%
Cows 20%
Horses10%
17. A farm has four kinds of animals: chickens, goats, horses, and cows. The percentage of the total number of animals that each type makes up is shown in the pie chart above. What is the ratio of the number of chickens to the number of cows?
18. A concert has an attendance of 400 people. 20% of the attendees are children and the rest are adults. How many adults attended the concert?
Failed
16
28
Passed
84
72
100
Total
100
44 200156
Female
Male
Total
19. The table above shows the number of students who passed and failed a placement exam for a math class at a major university. Given these results, what is the probability that a randomly selected student who failed the exam was male?
20. John is performing an experiment with hydrogen gas. He releases 0.5 kilograms of hydrogen into a 0.9 cubic meter vessel. If he then adds an additional quantity of hydrogen that is 60% of the mass of the first quantity into the vessel, what is the resulting density of the hydrogen in kilograms per cubic meter? (Note: Density is mass divided by volume)
