8th Grade GOFAR

Transcription

8th Grade GOFAR

Georgia Online Formative Assessment Resource (GOFAR)
8th Grade VMath Algebra Review
Name:____________________________
Date: ____________________________
Copyright © 2014 by Georgia Department of Education. Items shall not be used in a third party system or displayed publicly. Page: (1 of 28 )
1. A biology teacher gave three students in his class a different plant. He asked the students to record the
heights of their plants, in centimeters (cm), everyday for one week. The students reported their results in
different displays. Their results are shown in a graph, an equation, and a table.
Part A
List the plants in order from the slowest rate of growth per day to the greatest rate of growth per day.
Explain how you got your answer.
Part B
If the growth rate for Plant 1 remains the same, on what day number will it be 24 cm tall? Explain how you
got your answer.
Part C
If the growth rate for each plant remains the same, when will Plant 2 and Plant 3 be the same height?
Show work or give an explanation to justify your answer.
Be sure to complete ALL parts of the task.
Write your answer and show your work on the paper provided.
Do NOT type your answer in the text box below.
2. Parts A, B, and C each present a pair of linear equations. Without graphing the equations, determine
whether the graphs of each pair of lines would intersect. Explain how you know whether the lines would
intersect or not.
Part A
Do the graphs of Line 1 and Line 2 intersect? Explain how you know without graphing the lines.
Part B
Part C
3. The graph shows the relationship between the volume of Liquid 1 and its mass.
Part A
Write the equation of the line that represents the graph of Liquid 1. Explain the meaning of the coefficient
in the equation you wrote to the graph of Liquid 1.
Part B
The equation
is used to represent the relationship between the volume of Liquid 2 and its mass.
Explain how the graph of Liquid 1 is similar to the graph of Liquid 2. How are the graphs different?
Part C
Using the graph for Liquid 1, explain how you can use the point
point
What is the value of g ?
to determine the value of gin the
4. Triangle EGH is graphed on a coordinate grid.
Part A
Using the Pythagorean theorem, determine the length of side
Show your work.
Part B
What is the slope of the line containing
What is the slope of the line containing
relationship between the slopes of
and
Explain the
Part C
Write an equation to represent the line that passes through points E and G .
If
in the equation you wrote, what is the value of y ? Show your work.
5. Use the coordinate grid shown to answer Parts A and B.
Part A
List three ordered pairs that are part of the same linear function. Explain your answer.
Write the equation for the function which contains these points.
Part B
Graph the points
Explain your answer.
and
on the coordinate grid. Are the points linear or nonlinear?
6. Which of the following is the graph of a line with a slope of 1?
A)
B)
C)
D)
7. The slope of the line through points (1, 1) and (1, 2) is:
A)zero
B)negative
C)positive
D)undefined
8. A city has set up a committee to estimate the area's population growth. Below is a graph of the
population increase in recent years.
What will be the population in 2005 if this growth rate continues?
A)290,000
B)300,000
C)320,000
D)340,000
9.
What is the slope of the line on the graph below?
A)-
B)-
C)
D)
10.
Which algebraic expression corresponds to “half of the sum of 3x and 4”?
A)6x
B)3x + 2
C)
(3x) + 4
D)
(3x + 4)
11. Which of these sets of ordered pairs would define a line with a negative slope?
A)(5, 5) (0, 1)
B)(2 ,3) (-4, -1)
C)(3, 6) (5, 1)
D)(2, 3) (7, 6)
12.
Michael runs 3.5 miles in 30 minutes. If he continues at this rate for 2 hours, determine his rate of change.
A)3.5 miles/hour
B)7 miles/hour
C)14 miles/hour
D)10 miles/hour
13. Use this figure to answer the question.
Which line in the figure above has a y-intercept of 3 and a slope of
?
A)j
B)k
C)l
D)m
14. The balance below shows the equation
. What is the value of x?
A)
B)2
C)
D)3
15.
Simplify:
A)
B)
C)
D)
16. If the equations y = 3x + 5 and y = 3x – 5 were graphed, which statement below would be true?
A)The two lines will be parallel.
B)The two lines would intersect at the origin.
C)The two lines would intersect at right angles.
D)The two lines would intersect at the point (5,-5).
17. What value of x satisfies the system of equations below?
A)9
B)6
C)3
D)–2
18. In a game, the two players scored a total of 121 points. One player had 13 more points than
the other player. How many points did the player with the fewer points score?
A)52
B)54
C)67
D)108
19.
Given the system of the following two linear equations:
x + 2y =
7
3x-y = 2
What would be the first step in eliminating the variable y?
A)Multiply the second equation by 2.
B)Add the two equations.
C)Add 5 to both sides of the second equation.
D)Rewrite the equations so that y is on the right side.
20. Given the system of the following linear equations:
2x – 3y =
12
5x + 4y =
7
Solve for x and y.
A)(-2, 3)
B)(-2, -3)
C)(3, 2)
D)(3, -2)
21. The solution set for a pair of equations is (3,-1). One of the equations is
2y = x – 5. Which of the following could be the other equation?
A)4y = 2x
B)y = x + 2
C)y = x – 4
D)2y = x+3
22.
What are the x and y values in this system of equations?
2x + 4y = 8
2y = x + 8
A)(-2, 1)
B)(-2, 3)
C)(-4, 2)
D)(-4, 4)
23.
Amy needed to rent a car for a day so she researched two rental companies. Company A charges a flat rate of $25 plus $0.15 for every
mile she drove the car. Company B charges a flat rate of $50 plus $0.05 for every mile she drove the car. If Amy had to drive a total of
370 miles, which rental car company would be a better deal and by how much?
A) Company A by $12
B) Company A by $80.50
C) Company B by $12
D) Company B by $68.50
24.
Sophia has 8 books in her locker. All the books are either school books or personal books. She has three
times as many school books than personal books. How many school books does Sophia have in her locker?
A)2
B)3
C)6
D)7
25. Which list of ordered pairs is NOT a function?
A){ (1, 1), (2, 3), (3, 4), (4, 5) }
B){ (1, 1), (2, 2), (3, 3), (4, 4) }
C){ (1, 1), (3, 1), (4, 2), (5, 3) }
D){ (1, 1), (1, 3), (2, 3), (3, 4) }
26. What is the equation of the line passing through the points (5, 5) and (5, 10)?
A)x= 5
B)y= 5
C)y = x+ 5
D)y = x+ 10
27.
When graphed, which situation's data would be linear?
A)The temperature of the roof of a house every hour for 24 hours.
B)A person's body temperature every hour for a year.
C)The temperature of water rising 3°F every hour.
D)The daily temperature of a city for a year.
28. Which graph shows the line that goes through the point (3,- 1) and has ay-intercept of- 4?
A)
B)
C)
D)
29.
The percentage of wheat grain eaten by mice in a farmer's field is shown below.
Which of the following is the most likely percentage in
2005?
A)0
B)14
C)25
D)45
30. Which equation describes the line through pointsAandB?
A)
B)
C)
D)3x + y = 5
31.
Jane charges $15 for each lawn she mows plus $5 per hour she works. Which graph models how much Jane
charges for any one lawn?
A)
B)
C)
D)
32. The set of graphed points shown represents a function.
Which point could be added to the graph so that the set of graphed points remains a function?
A)
B)
C)
D)
33. Amber and Michael recorded the length and weight of each catfish they caught while on vacation in 2012. The scatter plot
shows their results.
They also created the table shown below to record the number of catfish they caught while on vacation over the past five
years.
Part A
Does the scatter plot describe a function? Explain your answer.
Part B
Do the values shown in the table describe a function? Explain your answer.
Part C
Amber and Michael’s parents caught twice as many catfish during every vacation. If x represents the
number of catfish that Amber and Michael caught, and y represents the number of catfish caught by their
parents, write an equation that models this relationship.
Does this equation describe a function? Explain your answer.
34. A class is studying linear equations.
Part A
Give an example of a linear equation to represent each type of solution set:
● A linear equation with exactly one solution
● A linear equation with infinitely many solutions
● A linear equation with no solutions
For each example, explain why the equation has that number of solutions.
Part B
What is the solution set for the equation
Show your work.
35. A student is working with the two functions shown.
●
● The second function is the set of all values when the input value is multiplied by 5.
Part A
The student does not understand what a function is in terms of inputs and outputs. Write an explanation for
the student.
Part B
Which function has the greater y-intercept? Show your work and explain your answer.
36. The graph shows the temperature over a 12-hour period.
Part A
Why does this graph represent a function? Explain your answer.
Part B
This graph shows a “piecewise function” because it can be defined with different function rules over
different input intervals. What are the two input intervals of the function? What type of function rule can be
used to describe the graph in each interval?
Part C
Analyze the graph to describe where the function is increasing or decreasing. Include how the graph differs
in the two input intervals of the function in your analysis. Justify your answer.
Part D
Write an equation for a single linear function that includes both endpoints of the graph. Show your work.
37. The diagram shows two stacks of plastic cylinders and their total heights. The diameters of the cylinders used within the
stacks are the same length.
Part A
The shaded cylinders are each x feet tall, and the unshaded cylinders are each y feet tall. Write an
equation, using x and y, to describe the height of Cylinder G and an equation, using x and y, to describe
the height of Cylinder H.
Part B
What are the values of x and y? Show your work.
Part C
Suppose that both equations you wrote in Part A are graphed on the same coordinate grid. Describe what
the graphs of the equations would look like.
Part D
What is the connection between the graphs you described in Part C and your answers in Part B?
38. The table shows the proportional amounts of cranberry juice and apple juice used to make Fruit Punch A.
Part A
Use the values shown in the table to write an equation for Fruit Punch A that represents the relationship
between y, the number of ounces of apple juice, and x, the number of ounces of cranberry juice. Show
your work or explain your answer.
Part B
What part of the equation you wrote in Part A represents the unit rate? Explain why it represents a unit
rate.
Part C
Graph the equation from Part A. How does the graph reflect what you described in Part B?
Part D
Fruit Punch B uses 2.2 ounces of apple juice for every ounce of cranberry juice. How would a graph
representing the relationship between the number of ounces of apple juice and the number of ounces of
cranberry juice in Fruit Punch B differ from your graph in Part C? Explain your answer.
39. Two relations are given in different formats.
Use these relations to answer the questions.
Part A
Determine whether or not each relation represents a function. Justify your answers.
Part B
Determine whether each function identified in Part A is linear or nonlinear. Explain how you know.
Part C
Write an equation for each linear function identified in Part B. Explain what each part of your equation(s)
represents.
40. The graph and table show the distance and time that Ravyn ran on two different days.
Part A
Graph the data for Ravyn’s Tuesday run. Be sure to label your axes and give a title for your graph.
Part B
What is Ravyn’s rate for each run? Explain how you calculated the rate of each run.
Part C
Ravyn represents Sunday’s and Tuesday’s runs as a system of linear equations. Write the system of linear
equations that represents Sunday’s and Tuesday’s runs, where x represents time and y represents
distance.
Part D
What is (are) the solution(s) to the system of linear equations you wrote in Part C? Show your work.
Explain the meaning of the solution(s).
41. Jon is going to get a job as a delivery driver. He can choose between the two plans shown for his weekly
salary. Let x represent the number of hours Jon works in a week and let y represent his weekly salary, in
dollars.
Part A
Which plan has a greater rate of change? Show or explain your work.
Part B
Which plan has the greater pay for 15 hours worked in a week? Show or explain your work.
Part C
For what number of hours worked in a week would Jon earn the same weekly salary under either plan?
How much would Jon earn during this week? Show or explain your work.
42. Students are given a pass code to access their school library accounts. The pass codes consist of 2 two-digit numbers
separated by an underscore. For example, Amy’s pass code is 30_15.
Part A
Mario gave two clues about his pass code.
● If the second number is subtracted from the first number, the difference is 15.
● The sum of the first number and the second number is 61.
What is Mario’s pass code? Show your work.
Part B
Lynne’s pass code is the point at which the lines, represented by the equations shown, intersect.
She explained that the x-coordinate was the first number of her pass code and the y-coordinate was the second number.
What is Lynne’s pass code? Show your work.
Part C
Recall that Amy’s pass code is 30_15. Create a system of two linear equations, both involving x and y, such that its solution
gives Amy’s pass code. Let
and
Show your work.
43. If
what is the value of x?
A)
B)
C)1
D)3
Answer Key :
1.
2.
3.
4.
5.
6. A)
7. D)undefined
8. B)300,000
9. A)-
10. D)
(3x + 4)
11. C)(3, 6) (5, 1)
12. B)7 miles/hour
13. C)l
14. B)2
15. D)
16. A)The two lines will be parallel.
17. A)9
18. B)54
19. A)Multiply the second equation by 2.
20. D)(3, -2)
21. C)y = x – 4
22. B)(-2, 3)
23. C) Company B by $12
24. C)6
25. D){ (1, 1), (1, 3), (2, 3), (3, 4) }
26. A)x= 5
27. C)The temperature of water rising 3°F every hour.
28. C)
29. B)14
30. C)
31. A)
32. C)
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43. A)

8th Grade GOFAR

Transcription

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