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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
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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
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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.
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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
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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
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______________ 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
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______________ 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.
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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
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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
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__________________________
__________________________
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.
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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.
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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.
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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
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Pyramid
Cone
Sphere
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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)
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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
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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
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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 ________________________.
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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
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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 ____________________
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Zero Slope
o x ____________________ as
y ____________________
Undefined Slope
o x ____________________ as
y ____________________
Slope – Intercept Form