1. X-intercept Roots Zeros Hits ground/water ~=0 Crosses x-axis (~,0)
Table Method:
y1= equation    y2=0 
2nd  Trace 5 MOVE Enter Enter Enter 
The x values when y=0 (or y goes from + to -)
Graphing Method:

2. y-intercept Initial Value Start at
Equation:
Table:
Calculator:
The number without a variable
y= 3x2 +5x or y = 6(2)x
The y value when x = 0
2nd Trace 1(value) Enter

3. Exponential Growth (Equation):
y=abx or y=a(1 + r)x
y=final amount  
a=initial amount 
b=base   r=rate as a percentage  (4.5%= .045)
If b > 1 then it’s increase;  If 0<b<1 then it’s decay 
                          

4. Decimals of
Depreciate (Decrease) 5%
&Appreciate (Increase) 13.5%
(1- .05) = .95
( ) = 1.135
                          

5. % & % Increase/Decrease
50$ shirt with 7% increase (tax)
50$ shirt with 20% decrease (off)
 Final = Beginning ( 1 +  r)
                                  
50(1.07)    $53.50
50(0.8)$40

6. Linear Growth: Slope of y =3x + 2 Y-intercept of y = 3x + 2
y= mx + b 
m=slope (rate of change, change per x)
 b=y-intercept (crosses y-axis & initial value)
3 (also rate of change )
2 (also starting value)

7. The equation p(x) = .5x + 2 where x is the year since 2000 and p(x) represents the population (in thousands) of Pineboro.
What is the slope and what does it represent?
What is the y-intercept and what does it represent?
.5 thousand;
increase in population per year 2
population in 2000

8. Find rate per mile: $2 per .4 mile
Find rate per minute: $3 per 30 seconds
Find rate per foot: $12 per 10 feet
$2/ .4 = $5 per mile
$1.20/.2 = $6 per mile
3/.5 = $6 per minute
$12/10 = 1.2 per foot

9. Write equations of the following:
Balloon company charges flat-fee of $10 per delivery and $2 per mile
Taxi charges a flat-fee of $3 and $2 per 0.5 mile
Car rental charges $20 a day plus 65 cents a mile
Car rental charges $50 per day
C = 2m + 10
F= 2/.5 m + 3 Or F= 4m + 3
C=0.65m + 20
C = 50

10. & Coefficient of Correlation
Regressions
& Coefficient of Correlation
Coefficient of correlation:
STAT   EDIT   Enter x’s into L1 Enter y’s into L2
 STAT   CALC  Choose Linreg or Expregr ENTER
Write equation on paper and then type in y=
   
~1 Positive      ~ -1 Negative
                 
Find:   2nd 0 Scroll to DiagnosticON Enter  then do
regression 

11. The number of schools in Turnstown can be represented by the following table:
According to the line of best fit, how many schools are predicted for 2014? 10 30 44 50
Year
1960
1970
1990
2004
2010
Schools 20 40 80
108
120
Change 1960 to 0 and the other years (only do on year problems)
STAT EDIT Put the numbers in STAT CALC Linregression
3) Write the equation. Y = 2x + 20
4) Type Equation into Y= y = 2x + 20
5) Look at table for x=54 ( = 50)  128

12. Exponent Examples 2a2*3a5 (3a5)2 = 2aa 3aaaaa = 6a7
Multiply: Mult. Coefficients, add exponents
= (3aaaaa)(3aaaaa)= 9a10
Power: Write it out then perform rule

13. Exponent Examples Continued:
Write out the variables; reduce the coefficients; cancel letters
Negative exponents: Switch the location and make positive;
5xo
= 5
Zero power makes exponent disappear

14. Write it out twice
Move negative exponents
Write out exponents; remove
Zero exponent
Combine exponents
Subtract exponents

15. Dividing by a monomial Simplify Divide each by the bottom 6x3
Divide each by 6x3
6x3
6x3
6x3
Simplify

16. Greatest Common Factor (GCF):
42x2yz4 and 28x5 y3
Largest integer that goes into each coefficient
Smallest of each exponent
14x2 y
Calculator (for coefficient)
Math Num GCD (#1,#2) z

17. Least Common Multiple (LCM):
Example: 10x2 yz4 and 15x5 y3
Smallest integer they go into, largest of each exponent
LCM: 30x5y3z4

18. Slope of Parallel Lines:
What is the slope of the line parallel to
y = 3x + 2?
3x + 2y = 8
 Same slope (5/6 & 5/6) 3
2y = -3x + 8
y = -3/2x + 8/2 so -3/2

19. Slope of Perpendicular Lines:
What is the slope of the line perpendicular to y = 3x + 2?
What is the slope of the line perpendicular to 3x + 2y = 8
 Negative Reciprocal slope (5/6 & -6/5)
-1/3
2y = -3x + 8
y = -3/2x + 8/2 so 2/3

20. Direct Variation: (Set up Proportion then solve)
Y varies directly as x. y is 8 when x is 3. Find
x when y is 40
Y = Y
X X
Write proportion
8 = 40 X
Substitute in
Cross multiply
8x = 3(40)
Solve by dividing
x = 120/8 = 15

21. The number of dolls made varies directly as the number of hours worked
The number of dolls made varies directly as the number of hours worked dolls are made in 25 hours. Find how many dolls are made in 75 hours
dolls = dolls
hours hours
Write proportion
100 = d
Substitute in
Cross multiply
25x = 75(100)
Solve by dividing
x = 7500/25 = 300

22. Systems of Equations 2x – y = 10 Find x + y x = y + 4 2x – 1y = 10
Put in matrix ready mode with
x’s and y’s together
2nd x-1   1 ENTER 2 X 3
[ ]
[ ]
Put into matrix
Solve with matrix
2nd MODE 2nd x-1  Scroll to RREF 2nd x-1 1 ENTER
You get [ ] so x = 6 and y = 2 so x + y = 8
[ ]

23. Midpoint of (x1, x2) and (y1, y2)
Midpoint:  Mx =     My =
Or Graph to find Midpoint
Midpoint is ½ way
Find midpoint of (3,2) and (-1,5)
(1, 3.5)

24. Mary’s house is (3, 1) and is the exactly halfway between Jack’s house (-1,3) and Gary’s house? Find the coordinates of Gary’s house.
Jack’s House
Down 2
Midpoint
Right 4
Down 2
Gary’s House
(5, -1)
Right 4

25. What does An+1=2An + 3 mean?
Next number = 2 * (now number) + 3

26. Describe the change in butterflies Increases by 12% every day
The number of butterflies, of a particular day, is related to the previous day’s number of butterflies, Bn by the function Bn+1 = 1.12Bn.
Describe the change in butterflies
Increases by 12% every day
(112% - 100% = 12%)
B)Find the number of butterflies on the 4th day if there was 50 butterflies on the first day
Day 1: 50
Day 2: 50(1.12) = 56
Day 3: 56(1.12) = 62.7
Day 4: 62.7(1.12) = butterflies

27. Factor trick with Calculator (only for multiple choice)
Use if given area or “Which is a factor?
37 STO X ENTER Store 37 as x
(Problem) / (Answer A) If no decimal then it could be a factor
(Problem)/(Answer B)
(Problem)/(Answer C)
(Problem)/(Answer D)
Example: Area is 10x2 – x – 2. Which could be a length?
A) 5x – B) 2x C) 10x – D) 2x - 1
37 STO X ENTER Store 37 as x
(10x2 – x – 2 ) / (5x – 2) Decimal so not a factor
(10x2 – x – 2)/(2x + 1) Decimal so not a factor
(10x2 – x – 2)/(10x – 3) Decimal so not a factor
(10x2 – x – 2)/(2x – 1) NOT A DECIMAL so it’s the answer!

28. & Independent Variables:
Domain
& Independent Variables:
All x values (numbers from left to right)
Domain of {(2,3),(5,6),(1,8)}
Domain of y = x2 + 3x
{1,2,5}
All reals

29. & Dependent Variables:
Range
& Dependent Variables:
All y values (numbers from down to up)
Range of {(2,3),(5,6),(1,8)}
Range of y = x2 + 6x
{3,6,8}
y> -9
(-3,-9)

30. Error on calculator:
If you have an error that you can’t fix immediately then reset your memory by:   2nd    +     7   
If calculator keeps saying 2nd Curve when finding intersection then make sure you have y2 = 0

31. Slope of (x1, x2)  and (y1, y2)  m=

32. Distance between (x1,x2) &(y1,y2)
   
don’t forget to close the parenthesis

33. Pythagorean Theorem 
Pythagorean Theorem:   a2 + b2 = c2       c a b

34. Area of rectangle and triangle:
Rectangle A=lw
Triangle A = ½ bh

35. Area &Circumference of Circle:
Area: A= (3.14) r2
Circumference=2(3.14)r  or  (3.14)d

36. Other Reminders: 4 less than a number: 4 is less than a number: x-4
Sum of 3 and x:
Twice the difference of x and 4:
There are twice as many cats as dogs
Quadrants:
x-4
x<4
(x+3)
2(x-4)
c = 2d
 II           I
    
III           IV