7th-8th Accelerated Term 3 Final Review Name:______________________________ Date:___________________
Solve each equation. Name the inverse operations at each step.
1.
Solve each equation and determine whether the equation has no solutions, one solution, or an infinite number
of solutions.
2.
3.
4.
5.
Define a variable and write algebraic expressions for each of the given quantities. Then, answer the question
by writing and solving an equation.
6. Three waiters at a local restaurant earned different amounts of money the past week. Jennifer earned $40 less
than twice the amount Tony earned. Chris earned $60 more than Tony. How much did each waiter earn if they
earned a total of $900?
Solve each equation. Check your solution.
7.
Complete the table and create a graph for each given problem situation.
8. Horace begins measuring the diameter of a pumpkin in his pumpkin patch when it has a diameter of 6 inches.
After he measures the pumpkin, its diameter begins to increase at a rate of 2 inches per week.
Independent
Quantity
Dependent
Quantity
0
1
6
Quantity Name
Unit of
Measure
12
5
26
Expression
9. Carl initially had $200 in his savings account. Each week he withdraws $15.
Independent
Quantity
Dependent
Quantity
Quantity Name
Unit of Measure
1
155
125
8
50
Expression
Use the given equations to answer each question.
10. You are flying to visit some relatives in Boston. Budget Airline charges $150 for a round-trip ticket, plus an
additional $0.20 per pound of luggage, which is represented by the equation
. Let c represent
the cost, and let p represent the pounds of luggage. Cheap Air charges $75 for a round-trip ticket, plus an
additional $0.80 per pound of luggage, which is represented by the equation
. For how many
pounds of luggage will they be the same price?
Sketch a graph of each given function.
11. absolute value function
12. square or quadratic function
13. cube or cubic function
Determine whether the set of ordered pairs, mapping, table, or graph represents a function. Explain.
14.
15.
16.
Input
3
2
1
0
1
2
3
Output
10
5
2
1
2
5
10
17.
Determine the domain and range for each relation defined by the set of ordered pairs or mapping.
18.
19.
Find the slope from each linear equation.
20.
21.
22.
23. Examine the linear graph and determine the y-intercept. Write the y-intercept in coordinate form.
____ 24. Which graph is discrete and nonlinear?
a.
b.
____ 25. Which graph does NOT represent a function?
a.
b.
____ 26. What is the slope of the line
a. 0
b. 12
c. 16
d. undefined
____ 27. The equation
a.
b.
c.
d.
?
represents a linear function. What is the y-intercept of the equation?
(0, 36)
(0, 5)
(0, 18)
(0, 72)
____ 28. Which shows the following numbers in order from least to greatest?
a.
b.
c.
d.
____ 29. Which shows the square roots classified correctly?
a.
b.
c.
d.
____ 30. Which statement is false?
a.
b.
c.
d.
All natural numbers are integers.
All whole numbers are natural numbers.
All integers are rational numbers.
All whole numbers are integers.
____ 31. Which fraction is equivalent to
a.
b.
c.
d.
____ 32. Which decimal is equivalent to
a. 0.318
b.
c.
d.
33. Will the ordered pairs listed in the table form a straight line when plotted? Explain your reasoning.
x
8
2
10
20
y
1
3.5
12.5
20
Find the missing side length.
34.
35.
36. A 12-foot ladder is set up 5 feet from the base of a building. How far up the building does the ladder reach?
Round your answer to the nearest tenth of a foot.
37. Determine the distance between (3, 1) and (5, 6) by graphing and connecting the points, creating a right
triangle, and applying the Pythagorean Theorem.
Determine the slope of the line represented by the equation.
38.
39. Lila and Gil went to the autumn fair. They paid an entry fee and a per-game price. Lila played 8 games and
paid $17.75 in all. Gil played 11 games and paid $22.25 in all.
Write the y-intercept in coordinate form. Explain what the y-intercept represents in the problem situation.
Write the equation of a line (𝑦 = 𝑚𝑥 + 𝑏) using the given information.
40. The points (21, 264) and (51, 284). Both lie on the line.
41.
and the point (4, 17.2) lies on the line.
42. Will the ordered pairs listed in the table form a straight line when plotted? Explain your reasoning.
x
y
2
27
1
12
4
57
10
147
43. Calculate the rate of change of the linear function represented by the table.
Number of
Bull’s-Eyes Made
Points Displayed
0
12,000
3
36,000
5
52,000
9
84,000
44. Consider the following graphs.
a.
Tell whether the rate of change from each graph is positive or negative.
b.
Determine the rate of change shown in each graph.
c.
Restate the rate of change as a unit rate. Explain its meaning.
Determine whether the given side lengths form a right triangle.
45. 5, 8, 17
46. 16, 30, 34
7th-8th Accelerated Term 3 Final Review
Answer Section
1. ANS:
PTS: 1
REF: 1.1
NAT: 8.EE.7a | 8.EE.7b
TOP: Skills Practice
KEY: inverse operations | two-step equation | solution | coefficient | constant | Properties of Equality
2. ANS:
The equation has an infinite number of solutions.
PTS: 1
REF: 1.2
TOP: Skills Practice
3. ANS:
NAT: 8.EE.7a | 8.EE.7b
The equation has one solution.
PTS: 1
REF: 1.2
TOP: Skills Practice
4. ANS:
NAT: 8.EE.7a | 8.EE.7b
The equation has no solutions.
PTS: 1
REF: 1.2
TOP: Skills Practice
5. ANS:
NAT: 8.EE.7a | 8.EE.7b
The equation has an infinite number of solutions.
PTS: 1
REF: 1.2
NAT: 8.EE.7a | 8.EE.7b
TOP: Skills Practice
6. ANS:
Let x represent the amount of money Tony earned.
Amount of money Jennifer earned:
Amount of money Chris earned:
Amount of money Jennifer earned:
Amount of money Chris earned:
Tony earned $220, Jennifer earned $400, and Chris earned $280.
PTS: 1
REF: 1.3
TOP: Skills Practice
7. ANS:
NAT: 8.EE.7a | 8.EE.7b
PTS: 1
REF: 1.4
TOP: Skills Practice
8. ANS:
NAT: 8.EE.7a | 8.EE.7b
Independent
Quantity
Dependent
Quantity
Quantity Name
Time
Diameter
Unit of Measure
Weeks
Inches
0
6
1
8
3
12
5
16
10
26
Expression
PTS: 1
REF: 2.4
TOP: Skills Practice
9. ANS:
Quantity Name
t
NAT: 8.F.1 | 8.F.2 | 8.F.3 | 8.F.4 | 8.F.5
KEY: linear function
Independent
Quantity
Dependent
Quantity
Time
Account Balance
Unit of Measure
Expression
PTS: 1
REF: 2.4
TOP: Skills Practice
10. ANS: 125 pounds of luggage
11. ANS:
PTS: 1
REF: 2.7
TOP: Skills Practice
Weeks
Dollars
1
185
3
155
5
125
8
80
10
50
w
NAT: 8.F.1 | 8.F.2 | 8.F.3 | 8.F.4 | 8.F.5
KEY: linear function
NAT: 8.F.1 | 8.F.2 | 8.F.5
KEY: absolute value function | square or quadratic function | cube or cubic function
12. ANS:
PTS: 1
REF: 2.7
NAT: 8.F.1 | 8.F.2 | 8.F.5
TOP: Skills Practice
KEY: absolute value function | square or quadratic function | cube or cubic function
13. ANS:
PTS: 1
REF: 2.7
NAT: 8.F.1 | 8.F.2 | 8.F.5
TOP: Skills Practice
KEY: absolute value function | square or quadratic function | cube or cubic function
14. ANS:
The set of ordered pairs represents a function. Each input has one and only one output.
PTS: 1
REF: 2.3
NAT: 8.F.1 | 8.F.2 | 8.F.3 | 8.F.5
TOP: Mid Ch Test
KEY: mapping | set | relation | input | output | function | domain | range | scatter plot | vertical line test
15. ANS:
The mapping does not represent a function. The input 2 has two outputs, a and b.
PTS: 1
REF: 2.3
NAT: 8.F.1 | 8.F.2 | 8.F.3 | 8.F.5
TOP: Mid Ch Test
KEY: mapping | set | relation | input | output | function | domain | range | scatter plot | vertical line test
16. ANS:
The table represents a function. Each input has one and only one output.
PTS: 1
REF: 2.3
NAT: 8.F.1 | 8.F.2 | 8.F.3 | 8.F.5
TOP: Mid Ch Test
KEY: mapping | set | relation | input | output | function | domain | range | scatter plot | vertical line test
17. ANS:
The graph does not represent a function. A vertical line passes through two points in all places except where
or
.
PTS: 1
REF: 2.3
NAT: 8.F.1 | 8.F.2 | 8.F.3 | 8.F.5
TOP: Mid Ch Test
KEY: mapping | set | relation | input | output | function | domain | range | scatter plot | vertical line test
18. ANS:
domain:
range:
PTS: 1
TOP: End Ch Test
19. ANS:
domain:
range:
REF: 2.4
NAT: 8.F.1 | 8.F.2 | 8.F.3 | 8.F.4 | 8.F.5
KEY: linear function
PTS: 1
REF: 2.2
NAT: 8.F.1 | 8.F.5 TOP: End Ch Test
KEY: discrete graph | continuous graph | linear graph | collinear points | non-linear graph
20. ANS:
PTS: 1
TOP: End Ch Test
21. ANS:
REF: 3.4
NAT: 8.F.1 | 8.F.3 | 8.F.4
KEY: slope | slope-intercept form
The slope is undefined.
PTS: 1
TOP: End Ch Test
22. ANS:
REF: 3.4
NAT: 8.F.1 | 8.F.3 | 8.F.4
KEY: slope | slope-intercept form
PTS: 1
REF: 3.4
NAT: 8.F.1 | 8.F.3 | 8.F.4
TOP: End Ch Test KEY: slope | slope-intercept form
23. ANS:
Because the graph is a line, it will keep increasing by 60 for every 4 units going backward, or 15 for every 1
unit going backward.
The next points to the left with integer x-values would be (2, 195), (1, 210), and (0, 225).
The y-intercept is (0, 225).
PTS:
TOP:
24. ANS:
TOP:
1
REF: 3.5
NAT: 8.EE.5 | 8.F.1 | 8.F.3 | 8.F.4
End Ch Test KEY: y-intercept | direct variation
B
PTS: 1
REF: 2.2
NAT: 8.F.1 | 8.F.5
Standardized Test
KEY:
25. ANS:
TOP:
KEY:
26. ANS:
TOP:
27. ANS:
TOP:
28. ANS:
TOP:
KEY:
29. ANS:
TOP:
KEY:
30. ANS:
TOP:
31. ANS:
TOP:
KEY:
32. ANS:
TOP:
KEY:
33. ANS:
discrete graph | continuous graph | linear graph | collinear points | non-linear graph
C
PTS: 1
REF: 2.3
NAT: 8.F.1 | 8.F.2 | 8.F.3 | 8.F.5
Standardized Test
mapping | set | relation | input | output | function | domain | range | scatter plot | vertical line test
A
PTS: 1
REF: 3.6
NAT: 8.F.1 | 8.F.3 | 8.F.4
Standardized Test
KEY: point-slope form | standard form
C
PTS: 1
REF: 3.5
NAT: 8.EE.5 | 8.F.1 | 8.F.3 | 8.F.4
Standardized Test
KEY: y-intercept | direct variation
A
PTS: 1
REF: 5.1
NAT: 7.NS.3
Standardized Test
natural numbers (counting numbers) | whole numbers | integers | closed | rational numbers
A
PTS: 1
REF: 5.2
NAT: 8.NS.1 | 8.NS.2 | 8.EE.2
Standardized Test
irrational numbers | terminating decimal | repeating decimal | bar notation
B
PTS: 1
REF: 5.3
NAT: 8.NS.1
Standardized Test
KEY: real number | Venn diagram | closure
C
PTS: 1
REF: 5.2
NAT: 8.NS.1 | 8.NS.2 | 8.EE.2
Standardized Test
irrational numbers | terminating decimal | repeating decimal | bar notation
C
PTS: 1
REF: 5.2
NAT: 8.NS.1 | 8.NS.2 | 8.EE.2
Standardized Test
irrational numbers | terminating decimal | repeating decimal | bar notation
Yes. The ordered pairs listed in the table will form a straight line when plotted because the rate of change is
the same every time.
PTS: 1
REF: 3.2
KEY: first differences
34. ANS:
NAT: 8.F.2 | 8.F.4
TOP: Pre Test
PTS: 1
REF: 6.1
NAT: 8.NS.2 | 8.EE.2 | 8.G.6 | 8.G.7
TOP: Pre Test
KEY: right triangle | right angle | leg | hypotenuse | diagonal of a square | Pythagorean Theorem | theorem |
postulate | proof
35. ANS:
PTS: 1
REF: 6.1
NAT: 8.NS.2 | 8.EE.2 | 8.G.6 | 8.G.7
TOP: Pre Test
KEY: right triangle | right angle | leg | hypotenuse | diagonal of a square | Pythagorean Theorem | theorem |
postulate | proof
36. ANS:
The ladder reaches 10.9 feet up the side of the building.
PTS: 1
REF: 6.1
NAT: 8.NS.2 | 8.EE.2 | 8.G.6 | 8.G.7
TOP: Pre Test
KEY: right triangle | right angle | leg | hypotenuse | diagonal of a square | Pythagorean Theorem | theorem |
postulate | proof
37. ANS:
The distance between (3, 1) and (5, 6) is approximately
10.6 units.
PTS: 1
TOP: Pre Test
38. ANS:
REF: 6.4
NAT: 8.EE.2 | 8.G.7 | 8.G.8
The slope is 1.6.
PTS: 1
TOP: Pre Test
39. ANS:
REF: 3.4
NAT: 8.F.1 | 8.F.3 | 8.F.4
KEY: slope | slope-intercept form
. The cost for the 8 games Lila paid is 8 1.5  $12. The
The per-game price is
cost of the entrance fee is 17.75  12  $5.75. The y-intercept is (0, 5.75), and this means that the fee for
entering the autumn fair is $5.75 per person.
PTS: 1
TOP: Pre Test
40. ANS:
REF: 3.5
NAT: 8.EE.5 | 8.F.1 | 8.F.3 | 8.F.4
KEY: y-intercept | direct variation
PTS: 1
TOP: Pre Test
41. ANS:
REF: 3.6
NAT: 8.F.1 | 8.F.3 | 8.F.4
KEY: point-slope form | standard form
PTS: 1
TOP: Pre Test
42. ANS:
REF: 3.6
NAT: 8.F.1 | 8.F.3 | 8.F.4
KEY: point-slope form | standard form
No. The ordered pairs listed in the table will not form a straight line when plotted because the rate of change
is not the same every time.
PTS: 1
REF: 3.2
KEY: first differences
43. ANS:
NAT: 8.F.2 | 8.F.4
TOP: Post Test
(3, 36,000), (5, 52,000)
PTS: 1
REF: 3.2
NAT: 8.F.2 | 8.F.4
KEY: first differences
44. ANS:
a.
The rate of change from Graph A is negative.
TOP: Mid Ch Test
The rate of change from Graph B is positive.
b.
c.
Graph A:
This means that the rate of decrease is 30 feet per second, or an object is descending at a rate of 30
feet per second.
Graph B:
This means that it takes 2.5 cups of flour to make 1 loaf of bread.
PTS: 1
TOP: End Ch Test
45. ANS:
REF: 3.1
NAT: 8.EE.5 | 8.F.1 | 8.F.2 | 8.F.3 | 8.F.4 | 8.F.5
KEY: rate | rate of change | per | unit rate | rise | run | rise/run
No. This is not a right triangle because 89 is not equal to 289.
PTS: 1
REF: 6.2
NAT: 8.EE.2 | 8.G.6 | 8.G.7 | 8.G.8
TOP: Mid Ch Test KEY: converse | Converse of the Pythagorean Theorem | Pythagorean triple
46. ANS:
Yes. This is a right triangle.
PTS: 1
REF: 6.2
NAT: 8.EE.2 | 8.G.6 | 8.G.7 | 8.G.8
TOP: Mid Ch Test KEY: converse | Converse of the Pythagorean Theorem | Pythagorean triple