Name: Due: January 27, 2015Math 80__ OWNCS

Midterm Review SheetMath 8

Unit 1: Operations with Rational Numbers (Prerequisites Skills) Operations with integers Operations with decimals Operations with fractions Operations with percents Two-Way Frequency Table

Operations with Integers

Adding & Subtracting Integers Examples

Same sign:

Different signs:

Double negatives:

Multiply and Dividing Integers Examples

Same sign:

Different signs:

Operations with Decimals

Adding and Subtracting Decimals Examples

Line up the ________________.

Add or Subtract

Be careful of the positive and

negative signs! (Refer to adding

and subtracting integers when

dealing with positive and negative

decimals!!!)

Multiplying Decimals Examples

Multiply the Numbers

Count the decimals places from

the ________________.

Move that many places in your

final answer.

Dividing Decimals Examples

Make the ________ a whole number.

Move the same number of decimal

places in the __________________.

Divide.

Operations with Fractions

Adding and Subtracting Fractions Examples

Find the _________________.

Create equivalent fractions

Add or subtract the ____________.

Keep the ________________.

Multiplying and Dividing Fractions Examples

Change mixed numbers to

_____________.

If dividing, changing to multiplying and

use the _________________ of the 2nd

fraction.

Cancel common ___________________

Multiply across

Operations with Percents

Changing Ratios to Percents Examples

Create a ____________________.

Cross multiply and solve

OR

Use equivalent fractions

Two-Way Frequency Table

Frequency Table Examples Shows how often each item occurs

in a set of categorical data

Read each question carefully

Look for relationships

How many friends did you survey?

What percent of kids who like bowling were female?

What type of party would please the most people? Explain.

Practice for Unit 1 – Create work boxes and show all work on separate piece of graph paper!!!A survey was done to determine what type of special class students liked.

1) Complete the table.

2) How many students were surveyed?

3) How many students chose music?

4) What percent of students chose music?

5) How many students were surveyed in the 8th grade?

6) How many students in 8th grade chose art?

7) What percent of students in 8th grade chose art?

8) How many students were surveyed in the 6th grade?

9) How many students in the 6th grade chose art?

10) What percent of students in the 6th grade chose art?

11) Using the table, is there a relationship between the grade and the class chose? Justify your answer.

Unit 2: Exponents Exponential Form vs. Expanded Form Evaluating a Number to a Power Negative Exponents Zero Exponents

Music Art Film Total6th Grade 42 31 227th Grade 15 12 418th Grade 24 41 18Total

Laws of Exponents Product Rule Quotient Rule Power Rule Extended Power Rule

Writing in Scientific Notation Operations with Scientific Notation

Exponential Form vs. Expanded Form

Exponential Form Examples

Expanded Form Examples

Exponents

Evaluating a Number to a Power Examples

Write in ______________________.

_______________ the base n times.

Negative Exponents Examples

Use the _______________________.

Make the exponent positive.

Zero Exponents Examples

Any number to the zero power is _____.

Laws of Exponents

Product Rule Examples

______________ the exponents.

______________change the base.

Quotient Rule Examples

______________ the exponents.

______________change the base.

Power Rule Examples

______________ the exponents.

______________change the base.

Extended Power Rule Examples

______________ the exponents.

______________change the base.

Scientific Notation

Writing in Scientific Notation Examples

a x 10b

a: ____ digit in front of decimal

b: the number of places the decimal

point is moved

______ exponent of 10: very big number

______ exponent of 10: very small number

Operations with Scientific Notation

Multiplying with Scientific Notation Examples

______________ the coefficients.

______________the exponents.

Rewrite in _______________________.

Dividing with Scientific Notation Examples

______________ the coefficients.

______________the exponents.

Rewrite in _______________________.

Adding with Scientific Notation Examples

Rewrite the numbers with the same

______________________.

Add the ______________________.

Subtracting with Scientific Notation Examples

Rewrite the numbers with the same

______________________.

Add the ______________________.

Practice for Unit 2 – Create work boxes and show all work on separate piece of graph paper!!!

Directions: Evaluate.

12) (-2)5 13) ( 14 )

3

14) 7-2 15) 80 =

Directions: Simplify.

16) 54 53 17) 79 7-6 18) (34)7

19) (22)-3 20)

48

45 21)

73

75

22)

35⋅34

32 23)

(85 )2⋅84

814 24)

(65 )2⋅64

620

Directions: Perform the indicated operation.

25) (8 x 10-6) + (4 x 10-5) 26) (9 x 108) - (6 x 106)

27) (5 x 10-3)(4 x 10-2) 28) (2.1 x 10-8) (7 x 10-9)

Unit 3: Solving Equations Simplifying Expressions

o Distributive Propertyo Combining Like Termso Isolate the Variable

Properties

o Inverse Operationso Identities

Solving One-Step Equations Solving Two-Step Equations Distributive Property Combining Like Terms Variables on Each Side Solving Equations with Decimals and Fractions

Simplifying Expressions

Distributive Property Examples

Combine the ______________.

Keep the _____________.

Combining Like Terms Examples

__________________ the coefficient to

each ___________________ inside the

______________________.

Solving Equations

Inverse Operations

______________ ________________

_______________ ________________

Steps to Solve Equations Examples

______________ Property

Combine _________________

______________ Operations

__________________________

__________________________

No Solution Examples

___________________ cancel

___________________ statement

a b

Infinite Solution Examples

___________________ cancel

___________________ statement

a = a

How to Check Examples

___________________ the value for

the ___________________ on each side

of the ___________________ .

Is it _______________?

o Yes: ___________________

o No: ___________________

Practice for Unit 3 – Create work boxes and show all work on separate piece of graph paper!!!

Directions: Evaluate the expressions. Use x = -4, y = ½ , and z = 8

29) 5z 30) z – 2 31) 7xy2

Directions: Simplify the expressions.

32) 7x – 10x 33) x + x – 6 34) 8x – 4 + 7x + 9

Directions: Simplify each expression.

35) 7x – 9 + 3x + 4 36) 8h – 3 – 4h + 9

37) -3p + 7 – 6p + 4 + p 38) -5x + 9 + 3x – x – 4 + 8

Directions: Solve each equation.

39) -9x – 3x = 36 40) y – 4 – 8 = 10

41) 2k – 6 + 3k = 14 42) 2m – 7m + 6 = -4

Directions: Simplify each expression.

43) 7(x – 4) 44) -6(2x – 3)

45) 5(2x + 1) – 3x 46) -2(3x + 4) + x – 9

Directions: Solve each equation.

47) 2(x – 7) = 22 48) -4(y – 3) = 20

49) 3(2b – 1) = 57 50) 2(10 – m) = 30

Directions: Solve the equation.

51) 5x – 4 = 5x – 4 52) 3x + 7 = 3x – 2

53) 3x + 7 = 7 54) x – 8 = x + 1

55) 3(2x + 8) = 6x + 24 56) -6(x – 4) = 6x + 24

Directions: Define the variable. Set up expressions. Set up the equation. Solve the equation. Reread the question.

57) Four times a number increased by five is 29. Find the number. Three less than twice a number is -11. Find the number.

58) Teddy bought a bat for $10 and x baseballs for $4 each. If he spent $22, how many baseballs did he buy?

59) Ms Calbo has a tutoring company. She charges $20 per hour plus a $10 application fee. If someone paid him $190, how many hours did she tutor?

60) Mr. Brown buys the basketball teams pizza every month for winning. In December, he bought 4 more than twice the number of pizzas he bought in November. If he bought 22 pizzas in December, how many pizzas did he buy in November?

61) The Falcons won eight games more than they lost. If they played 78 games, how many games did they lose?

62) Jacey wants new carpet in her bedroom. Carpet Plus charges $100 plus $8 per square foot. The World of Carpet charges $75 plus $10 per square foot. Find the number of square feet for which their prices are equal.

Unit 4: Volume Cross Section of 3-D Figures Area of 2-D Figures Area of Compound Shapes Volume

o Prismo Cylindero Pyramido Sphere

Surface Area Solving for Unknown Measurement Comparing Volumes and Determining the Difference Composite Figures

Area

Rectangle

Triangle

Circle

Volume

Prism

Cylinder

Pyramid

Cone

Sphere

Practice for Unit 4 – Create work boxes and show all work on separate piece of graph paper!!!

Directions: Find the area or volume of the figure. If necessary, leave in terms of .

66) 67)

68) 69)

70) 71)

63) 64) 65)

78) What is the effect on the volume when the height is doubled? What is the effect on the volume when the radius is doubled?

Directions: Find the height of the solid.

79) V = 3,000 ft3 80) V = 162 cm3

81) V = 141.37 in3 82) V = 448 ft3

Directions: Find the radius of the cylinder.

7) V = 48 in3 8) V = 770 cm3

Height = 3 in Height = 5 cm

9) V = 150 in3 10) V = 792 cm3

Height = 6 in Height = 7 cm

Unit 5: Intro to Functions What is a Function? Identifying Functions and Non-Functions Interpreting Time-Distance Graph Sketching Graphs

What is a Function?

Functions Examples

__________ do not repeat

Every _________ has one __________.

Pass the ________________________.

Can be represented

o ____________________.

o ____________________.

o ____________________.

o ____________________.

Inputs are _______________________.

Outputs are______________________.

Interpreting Time-Distance Graphs Examples

Define and label the _____________.

You may not always need ____________.

Determine the __________ __________

should be _______ or _____________.

Sketch the function based on the information

given.

Remember the ____________ the graph, the

the greater the ________________________.

Unit 6: Linear Functions Defining and graphing linear functions Determining if a point is a solution to the linear function Defining slope when given points Slope-intercept form Determining slope and intercept from an equation

Defining and Graphing Linear Functions

Graphing Linear Functions Example

Solve for ________.

Create a ____________ _______

____________.

Plot the points on a coordinate grid.

Should yield a _____________________

line.

All points on the line are ____________

to the function.

Label graph and axes.

Special Cases

Determining if a Point is a Solution Example Solve for __________.

Create __________________________

OR _____________________________

OR _____________________________.

If yields a __________ statement then

point ________ a solution.

Defining Slope

Defining Slope Given a Graph Examples

Slope is represent by ___________.

_________

OR

_________

Defining Slope Given Points

_________

Describing Slope

Positive Slopeo x ____________________ as

y ____________________

Negative Slopeo x ____________________ as

y ____________________

Zero Slope

o x ____________________ as

y ____________________

Undefined Slope

o x ____________________ as

y ____________________

Slope – Intercept Form