Transcript mid-term notes

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 Property
of addition: a + b = b + a
of multiplication: a x b = b x a
* Associative Property
of addition: a + (b+c) = (a+b)
+c
of 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:
ax0=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 number
Ex: -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