Linear Equations - Uplift Education



1. Solve the following problems:

a. 42 = b. 32 = c. 52 =

e.[pic] f. [pic] g. [pic]

h. [pic] i. [pic] j. 1001

2. Solve for x.

a. [pic]

b. [pic]

c. [pic]

d. [pic]

3. The square root is between which two whole numbers? Circle the best answer.

√18 √54

a. 2 and 3 a. 6 and 7

b. 3 and 4 b. 7 and 8

c. 4 and 5 c. 8 and 9

d. 5 and 6 d. 9 and 10

4. Circle the shapes with rotational symmetry?

5. Which set of ordered pairs below best represents the 4 vertices of the parallelogram?

[pic]

a) (-3,-4), (3,-1), (-3,6), (3,9) b) (-4,-3), (3,-1), (6,-3), (3,9)

c) (-4,-3), (-1, 3), (6,-3), (9,3) d) (-3,-4), (-1,3), (-3,6), (9,3)

6. What is the measure of the missing angle below?

[pic]

a) 79° b) 90°

c) 11° d) 101°

7. What is the measure of the missing angle below?

[pic]

a) 115° b) 65°

c) 25° d) 180°

Calculator Portion

1. Fred learned from his teacher that one way he could save money is to buy a savings bond. Fred buys a $50 savings-bond with money he saved up, but he won’t be allowed to cash the savings bond for 5 years. If the savings bond earns 5% compound interest annually (5% each year), how much will it be worth at that time?

a) 52.50

b) 55.13

c) 62.50

d) 63.82

2. What is the approximate length of the missing side of this triangle?

a) 13.00

b) 8.06

c) 9.85

d) 97.00

3. What is the approximate length of the missing side of this triangle?

a) 10.39 b) 240.00

c) 13.42 d) 18.00

4. A rectangular shaped box has a length of 3 feet and a width of 4 feet. Every box needs to have a strip of tape placed across the diagonal of the box. What is the length of this strip of tape?

a) 2.0 feet b)12.0 feet

c) 7.0 feet d) 5.0 feet

5. What line gives the correct line of symmetry for the image below.

a) The x-axis

b) The y-axis

c) The x- and y-axis

d) There is no line of symmetry

6. In the diagram below, which transformation would move the shape 1 to exactly match shape 2?

a) Rotation

b) Reflection

c) Dilation

d) Translation

7. In the diagram below, which transformation would move the shape 1 to exactly match shape 2?

a) Rotation 90 degrees counter-clockwise

b) Rotation 180 degrees counter-clockwise

c) Rotation 270 degrees counter-clockwise

d) Rotation 270 degrees clockwise

8. In the diagram below, which transformations would move shape 1 exactly to match shape 2?

a) a reflection over the x-axis

b) a reflection over the y-axis

c) a reflection over the x-axis, followed by a translation to the right by 7 units

d) a 180-degree rotation about the point (0,0)

For questions 9 and 10, use the equation and substitute the value for x in order to solve for y

9. y = 3x – 2, if [pic]what is the value of y?

a. [pic]

b. [pic]

c. [pic]

d. [pic]

10. y = 36 – 9x, if [pic]what is the value of y?

a. [pic]58

b. [pic]

c. [pic]

d. [pic]

11. Which equation is represented by the graph below?

a) y = x + 3

b) y = -3x + 3

c) y = 3x + 1

d) y = 2x + 3

12. How can you tell that a table represents a linear relationship?

a. The x values form a constant pattern

b. The y values form a constant pattern

c. The x and y values each form patterns

d. The x and y values each form constant patterns

13. Teddy and Julia are driving at a steady pace on their way to Philadelphia. They stop in Cherry Hill to get gas, and then speed to Philadelphia because they are running late to meet their friends at the museum. Which graph below models the situation best?

a. b.

d.

c.

14. A triangle with a height of 7 inches is contained within a rectangle with a length of 15 inches and a width of 8 inches. What is the area of the shaded region in the figure to the right?

a) 28 square inches

b) 92 square inches

c) 120 square inches

d) 148 square inches

15. The high school just installed a new swimming pool which is rectangular in shape and has the following dimensions: it has a depth of 10 feet, with a length of 30 feet and a width of 15 feet. A crew is coming to paint the inside of the pool with a sealer so it holds in the water. How many square feet are there to cover?

a) 1350 square feet c) 1800 square feet

b) 1500 square feet d) 4500 square feet

16. Two students are playing a game using the spinner to the right. What is the probability that the spinner will land on red?

a) 50%

b) 33.3%

c) 25%

d) 75%

17. The chance of rain on Saturday is 80% and the chance of rain on Sunday is 60%. What is the chance that is will rain on both Saturday and Sunday?

a) 20%

b) 48%

c) 70%

d) 140%

18. Find the slope of the line below.

a. Slope:[pic]

b. . Slope: [pic]

c. . Slope: [pic]

d. . Slope: [pic]

19. Find the slope and y-intercept from the table

|X |Y |

|-2 |-7 |

|-1 |-2 |

|0 |3 |

|1 |8 |

|2 |13 |

|3 |18 |

|4 |23 |

a. Slope: 3

Y-intercept: -7

b. Slope: 5

Y-intercept: 3

c. Slope: [pic]

Y-intercept: 3

d. Slope: -2

Y-intercept: -7

20. Jeremy and Katie are competing for the highest grade in Algebra. The teacher has decided to base their grade entirely on their test scores, since participation and other categories were subjective. Below are their scores from this year’s tests. Record all answers on the answer sheet.

|Jeremy |88.9 |90 |96 |70.6 |90.2 |

|Katie |86.5 |90 |95 |80.6 |89 |

a. Find the median of the test scores of each student. Who has the highest median?

b. Find the average (mean) for the tests of each student. Who has the highest mean?

c. Which student has the highest grade in Algebra? Explain your reasoning.

In questions 26 and 27, complete the table on your answer sheet by using the equation given.

21. y = -4x +5 22. y = 3x – 4

|X |Y |

|-1.0 | |

|-0.5 | |

|0 | |

|0.5 | |

|1.0 | |

|X |Y |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

In questions 28 and 29, find the slope and y-intercept for each pair of points. Then write the equation of a line that passes through each pair of points. Record your answers on the answer sheet.

23. (-3, 5) and (4, -3) 24. (-5, 2) and (3, 10)

25. Use the scatter plot below for questions A through C. Record your answers on the answer sheet.

A) Draw a line that models the data.

B) Describe the relationship between absences and grades shown by the scatter plot.

C) Based on the scatter plot, and the line you created to model it, what grade would you expect someone who missed 10 days to get?

STUDENT ANSWER SHEET

CALCULATOR PORTION

Circle your answer choice

1. A B C D

2. A B C D

3. A B C D

4. A B C D

5. A B C D

6. A B C D

7. A B C D

8. A B C D

9. A B C D

10. A B C D

11. A B C D

12. A B C D

13. A B C D

14. A B C D

15. A B C D

16. A B C D

17. A B C D

18. A B C D

19. A B C D

Record your answer to 20 here

20.

a. Jeremy’s median: _____________

Katie’s median: ______________

Whose is the highest? __________

b. Jeremy’s mean: _______________

Katie’s mean: ________________

Whose is the highest? __________

c. Which student has the highest grade in Algebra? Explain.

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

____________________________

Record your answers to 21-24 here

|X |Y |

|-2 | |

|-1 | |

|0 | |

|1 | |

|2 | |

21.

|X |Y |

|-1.0 | |

|-0.5 | |

|0 | |

|0.5 | |

|1.0 | |

22.

23. Slope: ___________________

Y-intercept: ______________

Equation: ________________

24. Slope: ___________________

Y-intercept: _______________

Equation: _________________

Record your answers to 25 here

25.

A. Draw a straight line that models the data.

B. Describe the relationship between absences and grades shown by the scatter plot (what happens to grades as you have more absences?)

C. Based on the scatter plot, and the line you created to model it, what grade would you predict for someone who missed 10 days? Explain how you got your answer.

Do the following without a calculator:

TOPIC 1: Exponents and Roots

12 = 22 = 32 = 42 = 52 = 62 = 72 = 82 = 92 = 102 =

Know the square roots of 100, 81, 64, 49, 36, 25, 16, 9, 4, and 1

Anything to the first power is ____________ example: 5461

Anything to the zero power is ___________ example: 50

13 = 23 = 33 = 43 =

[pic] [pic] [pic] [pic]

The following square roots are between which two whole numbers?

[pic] [pic] [pic]

___ and ___ ___ and ___ ___ and ___

TOPIC 2: Solve using inverse operations

15 = X + 7, so X = 4X = 28, so X =

-3 = 2 + X, so X = 3X + 4 = 31, so X =

VOCABULARY: define each word or complete each sentence

Base is __________________________________________________________________________

An _____________________ tells you how many times to multiply the base together.

Square root is the inverse of _______________________________.

TOPIC 3: Angles

On the coordinate grid, label quadrants 1-4:

Find the measurements of the missing angles.

[pic] [pic] [pic]

m[pic]LNV = _________ m[pic]SMZ = _________ m[pic]QFC = _________

m[pic]LNB = 31[pic] m[pic]ZMP = 42[pic] m[pic]LFC = 59[pic]

m[pic]UNV = _________

VOCABULARY: define each word

Complementary angles add up to ___________ while Supplementary angles add up to __________.

Vertical angles have the _________________ measurement.

TOPIC 4: Transformations

In each diagram below, choose the transformation that would move the black shape exactly to match the white shape

90 degree rotation clockwise Reflection over the y axis

Reflection over y axis Translation down 4 and left 6

90 degree rotation counterclockwise Rotation 180 degrees

Transformation of 10 units right and 1 unit down Reflection over y axis and translation

down 4

Choose a word from the list below to fill in the blanks. Use each word only once.

ROTATION REFLECTION TRANSLATION TRANSFORMATION

A ______________________ is a change in a geometric figure

A _______________________ is when a figure is turned around a point.

A _______________________ is when a figure is moved up, down, or over on a coordinate plane.

A ______________________ is when a figure is flipped over a line of symmetry

Do the following with a calculator:

TOPIC 1: Triangles

Find the missing measurement in each right triangle

A computer monitor is rectangular in shape and measures 13 inches across by 10 inches high. What is the length of the diagonal?

VOCABULARY: define the following words or complete the sentences

Hypotenuse is across from the ___________________________ in a right triangle.

Legs: ___________________________________________________________________________

A right triangle has one _____________ degree angle.

Scalene triangle: __________________________________________________________________

Equilateral triangle: _______________________________________________________________

Isosceles triangle: ________________________________________________________________

The Pythagorean Theorem is used to find the missing length on a ____________ triangle.

TOPIC 2: Solving equations

Substitute and solve for the variable.

Y = 4X – 6 , if x is 2, what is y? _______ Y = -2X + 5 , if y is -1, what is x? ________

When I say do the inverse operation I mean do the _______________________________________.

Using the equation Y = 2X + 5 fill in the following table

|X |-.5 |0 |.5 |1 |1.5 |

|Y | | | | | |

VOCABULARY:

Slope is found by dividing ___________ and ______________. In a table you can find slope by __

_______________________________________________________________________________.

On a graph you can find slope by _____________________________________________________

________________________________________________________________________________

The y-intercept is the place where the line crosses _______________________, or in a table it is the value of y when _______________.

Find the slope and y-intercept for each pair of points. Then write the equation of a line that passes through those points.

(-3, 5) and (2, -3) (4, 8) and (10, 12)

Slope = Slope =

Y-intercept = Y-intercept =

Equation: Equation:

Find the slope and y-intercept for each table. Then write the equation of a line that passes through those points.

|X |Y |

|-3 |17 |

|0 |11 |

|3 |5 |

|X |Y |

|4 |-4 |

|6 |0 |

|8 |4 |

Slope: Slope:

Y-intercept: Y-intercept:

Equation: Equation:

Match each graph with the correct equation below. Draw a line to connect the graphs to equations.

[pic]   [pic]   [pic]

Y = .4x – 3 Y = .44x – 7.5 Y = -x - 7

TOPIC 3: Geometry

Find the area of the shaded region:

• If you are baking a cake and using a pan with sides of 9inches by 16inches and a depth of 2.5 inches, what is the amount of cubic inches of batter needed to fill the pan?

• How many square inches need to be covered with icing if you are covering the top and sides only?

VOCABULARY:

For each word below, decide which geometry word best matches (area, perimeter, volume)

Fill : ___________________ Cover: __________________ Fence: ______________

Tile: ___________________ Surround: ________________ Water: ______________

-----------------------

x°

79°

x°

65°

9

4

6

12

1

2

1

2

1

2

Time

Speed

Time

Speed

Time

Di

s

tance

Time

Speed

8 in

15 in

7 in

green

blue

red

blue

blue

red

blue

green

ABSENCES

GRADES

A

F

0

20

ABSENCES

GRADES

A

F

0

20

10 cm

2 cm

6 cm

8 cm

4 cm

3 cm

5 in

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