1. P → Parentheses (Grouping Symbols) E → Exponents (Powers)
An easy way to remember the order of operations is to use the mnemonic device: PEMDAS.
P → Parentheses (Grouping Symbols)
E → Exponents (Powers)
MD → Multiplication or Division (Left to Right)
AS → Addition or Subtraction (Left to Right)
Example: – 5(2 + 7)
= 3 – 5(9)
Unit 2: slides 5-
= 3 – 45
= -42
Order of Operations

2. Steps to creating equations from context:
1. Read the problem statement first.
2. Reread the scenario and make a list or table of the known quantities.
3. Read the statement again, identifying the unknown quantity or variable.
4. Create expressions and inequalities from the known quantities and variables(s).
5. Solve the problem.
Interpret the solution of the equation in terms of the context of the problem and convert units when appropriate, multiplying by a unit rate.
Solving word problems

3. Expressions, coefficients, constants
The number of terms are separated by a + or –.
The coefficients are the numbers that are multiplied by the variable in the expression.
The constant is the quantity that does not change.
EX. 36x3 + 27x2 – 182x – 9
terms: 36x3 27x2 – 182x – 9
coefficients: 36,27, -182
constant: -9
Expressions, coefficients, constants

4. Exponential Equations
a= initial value
b = base
x = time
If b is a whole number then it is a growth, if b is a decimal or fraction then it is a decay.
a= initial value
r = rate
t = time
a= initial value where n is the number
r = rate of times compounded
t = time
Unit 2: slides 5-
If r is + then it is a growth, if r is – then it is a decay.
Exponential Equations

5. Slope is:
To find the slope of a line that passes
through the points A and B where
A = (x1, y1) and B = (x2, y2) is:
m =
The slope of a horizontal line is zero.
The slope of a vertical line is undefined.
Slope

6. Positive Negative Zero Undefined (Horizontal) (Vertical)
Slope Formula:
Positive Negative Zero Undefined
(Horizontal) (Vertical)
Examples:
y = x y = 2 – x y = x = 2
Slope examples

7. Slope- Intercept Form of a Line
Slope-Intercept Form of a Line: y = mx + b
b is the y-intercept m is the slope
Example: Write the equation of the line with slope 2 and y-intercept 3.
Answer: y = 2x + 3
Slope- Intercept Form of a Line

8. Point – Slope Form of a Line
Point-Slope Form of a Line: y – y1 = m(x - x1)
(x1, y1) is the point on the line
m is the slope
Example: Write the equation of the line with slope 2 and through the point (2 -1).
Answer: y + 1 = 2(x – 2)
Point – Slope Form of a Line

9. 8 pints = 1 gallon 1 mile = 5280 feet
10mm = 1 cm pints = 1 quart
12 in. = 1 ft quarts = 1 gallon
3 ft = 1 yd ton = 2000 pounds
8 pints = 1 gallon 1 mile = 5280 feet
Example: 6 pints=__________quarts 3
6 pints
Conversions

10. Properties of Exponents

11. To solve an exponential equation, make the bases
the same, then set the exponents equal to each
other and solve.
Example:
2nd card Exponential Equations

12. Properties of Operations
Commutative property of addition
a+ b = b + a 3+8=8+3
Associative property of addition
(a+b)+c=a+(b+c) (3+8)+2=3+(8+2)
Commutative property of multiplication
ab=ba 3(8)=8(3)
Associative property of multiplication
(ab)c=a(bc) (3∙8)2=3(8∙2)
Distributive property of multiplication over addition
a(b+c)=ab+ac 3(8+2)=(3)(8) + (3)(2)
Properties of Operations

13. Intercepts:
To find the x-intercept, let y = 0 and solve for x.
To find the y-intercept, let x = 0 and solve for y.
Example: Find the intercepts for 2x + 3y = 6
x-intercept: 2x + 3y = y-intercept: 2x + 3y = 6
2x + 3(0) = (0) + 3y = x = y = x = y = 2
(3, 0) (0, 2)
Intercepts

14. Arithmetic Sequence Arithmetic Sequence
a1 is first term, d is common difference
Explicit Formula: Recursive Formula:
an = a1 + d(n – 1)
Example: -3, 1, 5, 9, 13, . . .
Explicit formula: Recursive formula:
an = (n – 1)
Arithmetic Sequence

15. Geometric Sequence Geometric Sequence
a1 is first term, r is common ratio
Explicit Formula: Recursive Formula:
an = a1(r)n-1 or a0(r)n
Example: -3, 6, -12, 24,
Explicit formula: Recursive formula:
an = -3 (-2)n-1 or an = (3/2)(-2)n
Geometric Sequence

16. Mode: the number that occurs most often in a set of data.
Mean: the sum of the numbers in a data set divided by the number of numbers in the set.
Median: the middle number of a data set when the numbers are arranged in numerical order.
Mode: the number that occurs most often in a set of data.
Ex: 1, 1, 3, 4, 6
Mean =
Median = 3
Mode = 1
Unit 1: slides 1-4
Measures of Center

17. Five Number Summary and IQR and Range
The Five Number Summary:
(1). The minimum value
(2). The first quartile (Q1)
(3). The second quartile (Q2 or the median)
(4). The third quartile (Q3)
(5). The maximum value
Range= Maximum value – Minimum value
IQR= Q3 – Q1
Five Number Summary and IQR and Range

18. 1, 2, 3, 5, 5, 7, 8, 9, 12, 15, 16 Box and Whiskers plot Q1 Q2 Q3
1, 2, 3, 5, 5, 7, 8, 9, 12, 15, 16
Q Q Q3
Q Q Q3
Range = 16 – 1 = 15
IQR = 12 – 3 = 9
Box and Whiskers plot

19. Mean Absolute Deviation
To compute the mean absolute deviation (MAD),
(1). Find the mean of the set.
(2). Create a table to organize the data and find each element’s absolute deviation from the mean.
(3). Compute the average of these deviations.
Ex: Find the MAD for (3,2,6,9,5,8)
mean = 5.5
MAD = 13/6 = 2.17
Mean Absolute Deviation 19

20. To find if a data set has any outliers: (1). Find IQR IQR= Q3 – Q1
(2). Multiply (IQR)(1.5)
(3). Q1 – (IQR)(1.5) any value below this is an outlier
Q3 + (IQR)(1.5) any value above this is an outlier
Example: 2,3,5,6,8,9,19
Q1 = 3, Q3 = 9
Q3 – Q1 = 9 – 3 = 6
(6)(1.5)=9
Q1 –9 = 3 – 9 = - 6
Q3 + 9 = = 18
19 is an outlier!!!
Outliers 20

21. Transformations-Horizontal and Vertical Shifts
T h,k (x,y) = (x+h, y + k)
Example: P(7,-2)
Find T 3,-2 (P) =(7+3,-2-2) = (10,-4)
Transformations-Horizontal and Vertical Shifts 21

22. Transformations-Reflections
rx-axis= (x, – y) reflects image over the x-axis
ry-axis= (– x, y) reflects image over the y-axis
ry=x = ( y,x) reflects image over the y=x line
Example: P(7,-2)
Find rx-axis= (7,2 )
ry-axis=(-7,-2 )
ry=x = ( -2,7)
Transformations-Reflections 22

23. Transformations-Rotations
Rotation of an image counter clockwise.
R90= ( – y, x)
R180 = (– x, –y )
R270 = (y, –x )
Example: P(7,-2)
Find R90 (P) = (2,7)
R180 (P) = (-7,2)
R270 (P) =(-2, -7)
Transformations-Rotations 23

24. Midpoint on a coordinate plane M is the midpoint of AB
A(x1,y1) and B(x2,y2) then the midpoint is M
Example: find the midpoint of A(3,2) and B(-2,4)
Midpoint Formula 24

25. Distance between points in a coordinate plane:
Distance of length of a segment :
Example: Find the distance between
(3,4) and (-2,5)
Distance Formula 25