Pre-Algebra Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. ____
____
1. A figure is dilated by a scale factor of 3. If the origin is the center of dilation, what is the image of a vertex located at ? a.
c.
b.
d.
2. The graph shows the relationship between the number of hours h Bree has been hiking and the total distance d she has traveled, in kilometers. 20
d
18 16 14 12 10 8 6 4 2
1
2
3
h
Which statement is true? a. The slope of the line is 8. b. The slope of the line is 12. c. To find the slope of the line, you could divide the total number of hours hiked by the total distance. d. To find the slope of the line, you could multiply the total number of hours hiked by the total distance.
____
3. For the line that passes through constant to derive the equation a. b. c. d.
and has a slope of
, you use the fact that the slope of a line is
. What is an equivalent form of this equation?
____
4. Carlita goes jogging, and her GPS collects the data for her distance over time. What would the rate of change for that data represent? a. Carlita’s distance from home b. Carlita’s starting point c. Carlita’s distance over time, or speed d. Carlita’s time since she left home
____
5. What equation could be written for this table?
____
a.
c.
b.
d.
6. What equation could be written for this table?
a. b.
____
7. Which equation represents the values in the table?
a. b. ____
c. d.
c. d.
8. Which equation is graphed?
a. b.
c. d.
____
9. The graph shows the relationship between a candle’s height h, in centimeters, and time t, in hours, as the candle burns. What function models this relationship? 20
h
18
Height (cm)
16 14 12 10 8 6 4 2 1
2
3 4 5 6 7 Time (hours)
8
9
t
a. b. c. d.
____ 10. The graph shows the distance d, in miles, that Joe can drive his car using rate of change in this situation? 100
d
90
Distance (miles)
80 70 60 50 40 30 20 10 1
a. b. c. d.
2 3 4 5 6 Gasoline (gallons)
7
20 miles per gallon of gasoline 25 miles per gallon of gasoline 30 miles per gallon of gasoline 35 miles per gallon of gasoline
g
gallons of gasoline. What is the
____ 11. The graph shows the relationship between the number of members in a club and the number of years after the club began. Based on the trend shown in this data, predict the year in which the club will have no members. Students 90 80 70 60 50 40 30 20 10 –1 –10
a. b. c. d.
1
2
3
4
5
6
7
8
Years
1 year 3 years 6 years 8 years
____ 12. A lawn specialist measured the average temperature during different growing periods and the amount that the grass grew during each period. The scatter plot shows the results of his study. Use the data to predict the growth that would occur if the temperature were 55°F. 20 18
Grass growth (cm)
16 14 12 10 8 6 4 2
50
60
70
80
90
Average temperature (°F)
a. 14 centimeters b. 5.6 centimeters
c. 10 centimeters d. 17.5 centimeters
____ 13. The scatter plot shows the data for the number of hours Grace jogs each week for 8 weeks and the number of miles she jogs. What is the slope of a trend line for the data? 30 27
Distance (miles)
24 21 18 15 12 9 6 3 1 2 3 4 5 6 7 8 9 Time spent jogging (hours)
a. b. c. d.
Positive Negative Zero There is no trend line for the data.
____ 14. The scatter plot shows the relationship between the number of horses and the number of pigs on 7 farms. What is the slope of a trend line for the data? 10 9 8
Pigs
7 6 5 4 3 2 1 1
a. b. c. d.
2
3
4 5 6 Horses
7
8
9
Positive Negative Zero There is no trend line for the data.
____ 15. Tracy earns a commission at the jewelry store where she works. The scatter plot shows the relationship between the time , in hours, Tracy works weekly and her weekly pay , in hundreds of dollars. The equation of the trend line is . Approximately how much does she earn per hour? p Pay (hundreds of dollars)
6 5 4 3 2 1
10
a. b. c. d.
20 30 40 Time (hours)
50
t
$0.12 $1.20 $8.33 $12.00
____ 16. The scatter plot shows the relationship between the amount of gasoline the distance traveled
, in miles, after filling the tank. The equation of a trend line is
much gas is in the car’s fuel tank when it is full? g Amount of gasoline (gallons)
20 16 12 8 4
40 80 120 160 Distance traveled (miles)
a. b. c. d.
10 gallons 15 gallons 16 gallons 30 gallons
, in gallons, in a car’s fuel tank and
d
. How
____ 17. The scatter plot shows, for 11 bowlers, the number of strikes points the bowler has. Use the equation of a trend line, made by a bowler with 140 points. 280
a bowler makes in a game and the number of , to estimate the number of strikes
p
240
Points
200 160 120 80 40 2
a. b. c. d.
4
6 8 Strikes
10
12
s
4 6 25 40
____ 18. A rainwater collection tank is shaped like a cylinder with a diameter of 4 ft and a height of 6 ft. What is its volume? Use 3.14 for . a. c. b. d.
____ 19. What is the volume of the cone with the given dimensions? Use 3.14 for tenth of a cubic inch.
4.5 in.
1.75 in.
a. b. c. d.
. Round your answer to the nearest
____ 20. What is the surface area of the right rectangular prism shown in the figure?
5m
7m 9m
a. b. c. d.
____ 21. Describe the difference between the two given transformations. Transformation 1: Transformation 2: a. The image in Transformation 1 has an area that is 4 times greater than the image in Transformation 2. b. The image in Transformation 2 moves the original triangle 4 units in each direction. c. All but one of the vertices in the image of Transformation 1 is different from the original. d. The image in Transformation 2 has a perimeter that is 4 times greater than the perimeter of the image in Transformation 1.
____ 22. A triangle has coordinates
,
, and
what are the new coordinates of the triangle? a.
c.
b.
d.
. If the triangle is reflected across the y-axis,
____ 23. Shay graphs an octagon in the coordinate plane. She then applies the transformation to the octagon. Ned applies the transformation to Shay’s original octagon. What is the difference in the images? a. The area of Ned’s image is 4 times greater than the area of Shay’s image. b. Shay’s image is a distance of 4 units horizontally and vertically from Ned’s image. c. Ned’s image has side lengths that are 4 times as long as the side lengths of Shay’s image. d. The perimeter of Shay’s image is 4 times greater than the perimeter of Ned’s image.
____ 24. The ages, in years, of Sharice’s family members are shown. What is the mean absolute deviation of the data set? 2, 5, 18, 20, 31, 45, 76, 54, 34, 82 a. 22.04 years b. 25.4 years c. 32.5 years d. 36.7 years
Pre-Algebra Final Exam Review Answer Section MULTIPLE CHOICE 1. ANS: STA: 2. ANS: STA: 3. ANS:
D TEKS.8.3.B C TEKS.8.5.A D
PTS: DOK: PTS: KEY:
1 NAT: NT.CCSS.MTH.10.8.8.G.3 DOK 2 1 NAT: NT.CCSS.MTH.10.8.8.EE.5 proportional relationships DOK: DOK 1
Feedback A B C D
4. 5. 6. 7. 8. 9.
This equation indicates that the line’s slope is 3 and its y-intercept is , neither of which is correct. This equation indicates that the line’s slope is 3, which is not correct. This equation indicates that the line’s y-intercept is , which is not correct. That’s correct!
PTS: KEY: ANS: STA: ANS: STA: ANS: STA: ANS: STA: ANS: STA: ANS:
1 NAT: NT.CCSS.MTH.10.8.8.EE.6 STA: TEKS.8.5.B deriving an equation of a line DOK: DOK 1 C PTS: 1 NAT: NT.CCSS.MTH.10.8.8.F.4 TEKS.8.5.B DOK: DOK 1 D PTS: 1 NAT: NT.CCSS.MTH.10.8.8.F.4 TEKS.8.5.B DOK: DOK 1 B PTS: 1 NAT: NT.CCSS.MTH.10.8.8.F.4 TEKS.8.5.B DOK: DOK 1 B PTS: 1 NAT: NT.CCSS.MTH.10.8.8.F.4 TEKS.8.5.B DOK: DOK 1 A PTS: 1 NAT: NT.CCSS.MTH.10.8.8.F.4 TEKS.8.5.B DOK: DOK 2 A
The line passes through the points
and
h-intercept is 18. So, the equation of the line is
. The slope of the line is .
Feedback A B C D
That’s correct! The slope of the line is negative. 6 is not the h-intercept. The slope of the line is negative, and 6 is not the h-intercept.
. The
PTS: STA: DOK: 10. ANS:
1 TEKS.8.5.B DOK 1 B
NAT: NT.CCSS.MTH.10.8.8.F.4 | NT.CCSS.MTH.10.K-12.MP.4 KEY: constructing functions | analyzing graphs
The line includes the points
and
, so the slope of the line is
. So, the rate of
change is 25 miles per gallon of gasoline. Feedback A B C D
To find the rate of change, determine the slope of the line. That’s correct! To find the rate of change, determine the slope of the line. To find the rate of change, determine the slope of the line.
PTS: 1 NAT: NT.CCSS.MTH.10.8.8.F.4 | NT.CCSS.MTH.10.K-12.MP.4 STA: TEKS.8.5.B KEY: linear functions | rate of change | analyzing graphs DOK: DOK 1 11. ANS: D PTS: 1 NAT: NT.CCSS.MTH.10.8.8.SP.2 STA: TEKS.8.5.D DOK: DOK 1 12. ANS: A PTS: 1 REF: 9e8bdd87-9631-11dd-8a40-001185f11039 OBJ: Using a Scatter Plot to Make Predictions NAT: NT.CCSS.MTH.10.8.8.SP.2 STA: TEKS.8.5.D TOP: Scatter Plots KEY: scatter plot | data set | prediction DOK: DOK 2 13. ANS: A There appears to be a strong linear association between the number of hours Grace jogs each week and the number of miles she jogs. So, a trend line with a positive slope will follow the general trend of the data. Feedback A B C D
That’s correct! Consider how the number of miles Grace jogged changes as the time spent jogging increases. Consider how the number of miles Grace jogged changes as the time spent jogging increases. Consider how the number of miles Grace jogged changes as the time spent jogging increases.
PTS: 1 NAT: NT.CCSS.MTH.10.8.8.SP.2 STA: TEKS.8.5.D KEY: scatter plot | linear association | trend line DOK: DOK 1 14. ANS: D There is no association between the number of horses and the number of pigs on the farms, so there is no relationship between the two variables. So, a trend line should not be fit to the data. Feedback A B C D
Look at the association between the number of horses and the number of pigs. Look at the association between the number of horses and the number of pigs. Look at the association between the number of horses and the number of pigs. That’s correct!
PTS: 1
NAT: NT.CCSS.MTH.10.8.8.SP.2
STA: TEKS.8.5.D
KEY: scatter plot | no association 15. ANS: D The slope of the trend line is 0.12. Since
DOK: DOK 1 is in hundreds of dollars, Tracy earns about $12.00 per hour.
Feedback A B C
D
Even though the slope of the trend line is 0.12, the amount Tracy earns per hour is not $0.12. Even though the slope of the trend line is 0.12, the amount Tracy earns per hour is not $1.20. The amount Tracy earns per hour is not the reciprocal of the trend line’s slope. That’s correct!
PTS: 1 NAT: NT.CCSS.MTH.10.8.8.SP.3 | NT.CCSS.MTH.10.K-12.MP.4 STA: TEKS.8.5.D KEY: scatter plot | linear association | trend line | slope | equation of line DOK: DOK 1 16. ANS: C The g-intercept of the trend line represents the amount of gas in the car’s fuel tank when it is full. The g-intercept is 16. So, there are 16 gallons of gasoline in the car’s fuel tank when it is full. Feedback A B C D
The trend line predicts 10 gallons of gasoline left in the car’s fuel tank after driving 180 miles. The trend line predicts 15 gallons of gasoline left in the car’s fuel tank after driving 30 miles. That’s correct! The car uses about 1 gallon of gasoline for every 30 miles traveled.
PTS: 1 NAT: NT.CCSS.MTH.10.8.8.SP.3 | NT.CCSS.MTH.10.K-12.MP.4 STA: TEKS.8.5.D KEY: scatter plot | linear association | trend line | intercept | equation of line DOK: DOK 1 17. ANS: A Substitute 140 for in the equation.
A bowler with 140 points is estimated to have made about 4 strikes. Feedback A B C D
That’s correct! This is about the number of strikes made by a bowler with 190 points. This is the slope of the trend line. This is the -intercept of the trend line.
PTS: STA: DOK: 18. ANS: STA:
1 TEKS.8.5.D DOK 1 B TEKS.8.6.A
NAT: NT.CCSS.MTH.10.8.8.SP.3 | NT.CCSS.MTH.10.K-12.MP.4 KEY: scatter plot | linear association | trend line | predict values | equation of line PTS: 1 KEY: volume
NAT: NT.CCSS.MTH.10.8.8.G.9 DOK: DOK 2
19. ANS: B The volume
of a cone is given by the formula
, where
is the base radius and
is the height
of the cone. The base radius of the cone is 1.75 in. The height of the cone is 4.5 in. So, the volume of the cone is about .
Feedback A B C D
Don’t forget to square the radius. That’s correct! Don’t forgot to include the factor of
.
You need to use the base radius of the cone, not the base diameter.
PTS: 1 NAT: NT.CCSS.MTH.10.8.8.G.9 KEY: volume | cone DOK: DOK 1 20. ANS: B The formula for the surface area of a rectangular prism is the width, and is the height.
Thus, the surface area of the prism is
STA: TEKS.8.7.A
, where
.
Feedback A B C D
21. 22. 23. 24.
The prism has 6 faces, not just 3 faces. That’s correct! is the volume of the prism. This is the surface area of a cube with side length
.
PTS: 1 NAT: NT.CCSS.MTH.10.7.7.G.6 STA: TEKS.8.7.B KEY: rectangular prism | surface area DOK: DOK 1 ANS: D PTS: 1 NAT: NT.CCSS.MTH.10.8.8.G.3 STA: TEKS.8.10.C DOK: DOK 2 ANS: B PTS: 1 NAT: NT.CCSS.MTH.10.8.8.G.3 STA: TEKS.8.10.C DOK: DOK 2 ANS: D PTS: 1 NAT: NT.CCSS.MTH.10.8.8.G.3 STA: TEKS.8.10.C DOK: DOK 3 ANS: A First, find the mean of the data set.
is the length,
is
So, the mean age is 36.7 years. So, the mean absolute deviation is 22.04 years.
Feedback A B C D
That’s correct! Check the number of observations there are in the data set. This is the median of the data set. This is the mean of the data set.
PTS: STA: KEY: DOK:
1 NAT: NT.CCSS.MTH.10.6.6.SP.5.c | NT.CCSS.MTH.10.6.6.SP.2 TEKS.8.11.B mean absolute deviation | measure of spread | summary of data DOK 1
