Midyear Exam

1
Mid-year Exam

• What you need to know

2
Decimals

• Comparing and Ordering
• Adding and Subtracting
• Multiplying and Dividing

3
Comparing and Ordering Decimals

• Put a list of decimal numbers in order
• Example
• Put these decimals in order from least to
  greatest
• 2.4, 2.3, 2.17, 2.43
• 3.059, 3.64, 3.46

• Compare two decimals using greater than (gt) and
  less than (lt)
• Example
• 3.18 ___ 3.8
• 2.37 ___ 2.7
• 1.650 ___ 1.65

4
Make your own

• Make a list of 4 decimal numbers that a partner
  can put in order
• Make 3 compare two decimal problems to share

5
Adding and Subtracting Decimals

• Line up decimal points
• Write zeros so that all decimals have the same
  number of digits to the right of the decimal point

• Examples
• 3.026 4.7 1.38
• 78 74.9
• 6.2 0.444
• 8.91 6.08

6
Multiplying Decimals

• Multiply
• Add the number of decimal places in the factors
  to find the number of decimal places in the
  product.

• Examples
• 0.47 x 8
• 6 x 0.13
• 4.37 x 2.4

7
Dividing Decimals

• Dividing by whole numbers Divide as normal but
  bring the decimal up into your answer.
• Example
• 364.20 12

• Terminating or repeating decimals
• Examples
• 2 3
• 2 8

8
Dividing Decimals

• Dividing decimals by decimals multiply both the
  dividend and the divisor by the same number so
  that the divisor is a whole number

• Examples
• 2.25 0.5
• 0.248 0.04

9
Order of Operations

• PEMDAS
• Parenthesis
• Exponents
• Multiply and divide in order from left to right
• Add and subtract in order from left to right

• Examples
• 4 x 3 20 5
• 400 (44 -24)

10
Exponents

• An exponent tells you how many times a number, or
  base, is used as a factor
• Examples
• Write using an exponent, label the base and
  exponent, and solve.
• 7 x 7 x 7
• 2 x 2 x 2 x 2

11
Data and Graphs

• Mean, Median, Mode, Range
• Frequency Table and Line Plot
• Bar Graphs and Line Graphs
• Circle Graphs

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Mean, median, mode, range

• Mean the sum of the data divided by the number
  of data items
• Median middle number in a set of ordered data
• Mode the data item(s) that appear most often
• Range the difference between the least and the
  greatest values

• Find the mean, median, mode, and range of each
  data set
• 81, 77, 92, 89
• 4, 16, 20, 40
• 5, 15, 75, 105, 85

13
Frequency Tables and Line Plots

• A frequency table lists each item in a data set
  with the number of times the item occurs

• A line plot is a graph that shows the shape of a
  data set by stacking xs above each data value on
  a number line

14
Bar Graphs and Line Graphs

• A bar graph uses vertical or horizontal bars to
  display numerical information

• A line graph uses a series of line segments to
  show changes in data

15
Circle Graph

• A circle graph is a graph of data where the
  entire circle represents the whole
• Each wedge in the circle represents a part of the
  whole

16
Patterns and Variables

• Pattern rules
• Evaluating Algebraic Expressions
• Solving Equations
• Subtraction Property of Equality
• Addition Property of Equality
• Division Property of Equality
• Multiplication Property of Equality

17
Patterns

• Write number pattern from rules
• Examples Write the 1st 5 terms
• Start with 1 and multiply by 2 repeatedly
• Start with 90 and subtract by 15 repeatedly

• Write a rule for a number pattern
• Examples
• 53, 49, 45, 41,
• 1, 5, 25, 125,

18
Evaluate Algebraic Expressions

• Your replace each variable with a number
• Use the order of operations to simplify

• Examples
• Evaluate each expression for x 7
• 3x 15
• 5x 7
• 56 4x

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Use inverse operations (operations that undo each
other) to solve equations

• x 4 38
• Subtract 4 from each side to get x by itself
• Check your solution in the original equation
• Example
• w 4.3 9.1

• c - 12 43
• Add 12 to each side to get c by itself
• Check your solution in the original equation
• Example
• n - 53 28

20
Use inverse operations (operations that undo each
other) to solve equations

• 4n 68
• Divide each side by 4 to undo the multiplication
  and get n by itself
• Check your solution in the original equation
• Example
• 9x 36

• n 5 40
• multiply each side by 4 to undo the division and
  get n by itself
• Check your solution in the original equation
• Example
• q 6 4

21
Integers

• Opposites and absolute values
• Adding and Subtracting
• Multiplying and Dividing
• Graphing on a Coordinate Plane
• Graphing Functions

22
Opposites and absolute values

• 2 numbers are opposites if they are the same
  distance from 0 on the number line but in
  opposite directions
• The absolute value of a number is its distance
  from 0 on a number line

• Name the opposite
• -24 15 82 -1
• Find the absolute value
• -15 27 -11

23
Adding Integers

• The sum of 2 positive integers is positive
• The sum of 2 negative integers is negative

• To add integers with different signs, subtract
  the absolute value of the numbers and use the
  sign of the number that had the larger absolute
  value

24
Subtracting Integers

• Subtract an integer by adding its opposite
• 10 (-6)
• 10 6 16
• 11 31
• 11 (-31) - 20

• Solve by adding the opposite.
• 9 (-3)
• -6 (-2)
• -3 5

25
Multiplying and Dividing Integers

• When you multiply or divide 2 integers with the
  same sign, the answer is positive

• When you multiply or divide 2 integers with
  different signs, the answer will be negative

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Graph points using ordered pairs

• The x-coordinate tells how far to move left or
  right along the x-axis
• The y-coordinate tells how far to move up or down
  the y-axis

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Graphing functions

• Make a table and then graph on the coordinate
  plane

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Sample problems are on these pages

• Page 56 7-10, 18-21, 29-34, 37-40
• Page 112 1-6, 18-25, 28-33
• Page 366 1, 2, 5, 6, 10
• Page 540 1-6, 8-25, 28