Mid-Term Study Guide

SOL 7.1• I must be able to:

– Compare ( <, >, =)

– Order (least to greatest)

• Fractions

• Decimals

• Percents

• Scientific Notation

7.1 Notes• Change all numbers to

decimals to compare and order

• To turn to decimals:– Fractions: divide top number

by bottom number (1/4 = 1 ÷4 = 0.25)

– Percents: move decimal 2 places to the left (15% = .15)

– Scientific Notation: Move decimal to the right based on the exponent

(ex: 2.67 x 104 = 26,700)

SOL 7.1 Sample Problems

SOL 7.2

• I must be able to:

Simplify expressions with exponents, using order of operations

7.2 Notes

PEMDAS

P - Parenthesis

E - Exponents

M/D - Multiplication and Division from left

to right

A/S - Addition and Subtraction from left

to right

SOL 7.2 Sample Problems

SOL 7.3

• I must be able to:

Identify and apply (use) the following properties:

Commutative (Add and Mult)

Associative (Add and Mult)

Identity (Add and Mult)

Inverse (Add and Mult)

Distributive

Multiplicative Property of Zero

SOL 7.3 Notes

* Commutative Propertyof addition: a + b = b + aof multiplication: a x b = b x

a

* Associative Propertyof addition: a + (b+c) =

(a+b) +cof multiplication: a x (b x c)

= (a x b) x c**same order**

SOL 7.3 Notes

* Identity Property:

of addition: a + 0 = a

of multiplication: a x 1 = a

* Inverse Property:

of addition: a + (-a) = 0

of multiplication: a x 1/a = 1

SOL 7.3 Notes

* Distributive Property:

a(b+c) = ab + ac

• Multiplicative Property of Zero:

a x 0 = 0

SOL 7.3 Sample Problems

SOL 7.4

• I will be able to:

– Solve problems with fractions, decimals, and percents

– Solve problems involving tips, discounts, sales tax, and simple interest

SOL 7.4 Notes

• Tips, Discounts, and Sales Tax

– Change percent to decimal (15% = .15)

– Multiply– Add or Subtract as needed

Ex: $45.00 with a 10% discount

45.00 x .10 = 4.50

45.00 - 4.50 = 40.50

SOL 7.4 Notes continued

• Interest = prt– P = principal ($)– R = rate (%)– T = time in years

Ex: $1000 in a savings account with 5% interest for 2 years

$1,000 x .05 x 2 = $100 interest

SOL 7.4 Sample Problems

SOL 7.5

• I will be able to:– Add– Subtract– Multiply– Divide

Using Integers

SOL 7.5 Notes

• Adding Integers

If signs are the same, add the numbers and keep the sign

Ex: -4 + -4 = -8

If signs are different, subtract the numbers and keep the sign of the highest numberEx: -5 + 3 = -2

SOL 7.5 Notes

• Subtracting Integers– Change to Addition– Change the sign of the second

number

Ex: 7 - (-4) = 7 + + 4 = 11

SOL 7.5 Notes

• Multiplying and Dividing Integers

– If signs are the same, the answer is positive

– If signs are different, the answer is negative

Ex: 5 x -4 = -20 -5 x -4 = -20

SOL 7.5 Sample Problems

SOL 7.12

• I will be able to:– Identify ordered pairs– Identify quadrants– Graph ordered pairs

On the coordinate plane

SOL 7.12 Notes

• The coordinate plane is divided into four quadrants

SOL 7.12 Notes

• Ordered pairs are written (3, 4) with the x-coordinate first, and then the y-coordinate.

• The x-axis is horizontal (left to right) with positive values to the right and negative values to the left

• The y-axis is vertical (up and down) with positive values up and negative values down.

SOL 7.12 Sample Problems

SOL 7.16

• I will be able to:

Create and solve problems using

Measures of Central Tendency

Mean

Median

Mode

and the range

SOL 7.16 Notes

• Mean - average - add the numbers then divide by the number of data (should not be used when there is an outlier)

• Median - middle number - must be ordered least to greatest

• Mode - number most often used

• Range - highest number minus the lowest number

SOL 7.16 Sample Problems

SOL 7.17• I will be able to:

– Collect– Analyze– Display– Interpret data using:

• Frequency tables• Line plots• Histograms• Stem-and-leaf plots• Box-and-whisker plots• Scatterplots

SOL 7.17 Sample Problems

SOL 7.18

• I will be able to:

make inferences, conjectures, and predictions based on data.

SOL 7.18 Sample Problems