1. Verbal Expressions: 4 less than a number: 4 is less than a number:
Sum of 3 and x:
Twice the difference of x and 4:
x-4
x<4
(x+3)
2(x-4)

2. Literal Equations

3. & Independent Variables:
Domain
& Independent Variables:
All x values (numbers from left to right)
Range
All y values (numbers from bottom to top)

4. Exponent Examples (-2a2)(3a5) (-6a7) <add exponents> (3a5)2
(64x4y8z)1/2
(125x-3)1/3
= 1251/3x-3(1/3)
= 5x-1 = 5 x

5. Rate of Change Find the rate of change between Day 6 and Day 9 3 Days
Flowers 5 12 6 15 7 14 9
3 Days
-6 flowers
-6 flowers = -2 flowers
3 days day

6. Estimate the slope of the following lines:3
-1/2 -5
0 (y= line)
Undefined (x = line)

7. Linear Equations Slope: Y-intercept: Domain: Range: Next = Now+
2x – 3y = 6
-3y = -2x + 6
y = 2/3x - 2
Linear Equations
Slope:
Y-intercept:
Domain:
Range:
Next = Now+
X – intercept:
2/3 -2
All Reals
All reals
2/3 S.A. -2 3

8. Slope Formula of (x1, y1) and (x2, y2)
Find the slope of the parallel and perpendicular of the line going through
(-2,1) and (4, -3)
-3-1
-4 = -2
6 3
4- -2
Parallel: -2/3 Perpendicular: 3/2

9. Y = 4x + 1 Next = Now+ 4 S.A. 1 Y = 1*3x Next = Now*3 S.A. 1
Next = Now Statements
Equation
Next = Now
Y = 4x + 1
Next = Now+ 4 S.A. 1
Y = 1*3x
Next = Now*3 S.A. 1
Y = -6x + 10
Next = Now- 6 S.A. 10
Y =8(1/4)x
Next = Now * ¼ S.A. 8 .

10. Slope of Parallel Lines:
 Same slope (5/6 & 5/6)
Which equation(s) is parallel to y = 3x + 2?
y = 2x + 3 B. y = 3x + 5 C. 2y = 6x + 6
(divide by 2) to get y = 3x + 3

11. Perpendicular Lines: (-1)*Reciprocal ( 5/6 & -6/5)
Which line(s) are perpendicular to y = 3x – 2
A. y = -1/3x B. y = -3x – C. 12y = -4x + 36
(divide by 12) to get y = -1/3x + 3

12. Find the slope parallel and perpendicular to 2x – 3y = 6
– 3y = -2x + 6
-3y = -2x + 6
y = 2/3x – 2
Slope parallel: 2/3
Slope perpendicular: -3/2

13. System of Equations 5( )  10x + 15y = 55 -2( ) -10x + 14y = -26
_______________
29y = 29
y = 1
2x + 3(1) = 11
2x + 3 = 11
2x = 8
x = 4
System of Equations

14. Jack is three times as old as Mary.
Their combined age is 48. How old is Mary?
J = 3M
J + M = 48
3M + M = 48
4M = 48
M = 12

15. % & % Increase/Decrease
7% increase (tax)
   (1.07)x
20% decrease (off)
(0.80)x = (0.8)x
Depreciate (Decrease) 5%
(.95)x
&Appreciate (Increase) 13.5%
(1.135)x

16. 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 
                          

17. Meaning of Exponential Equations
Explain meaning of P = 20(1.03)t where P is the population (in thousands) and t is the time in years since 2005
Population was 20,000 in 2005 and it grows by 3%
Explain meaning of P = 15(.93)t where P is the price (in thousands) and t is the time in years since 2009
Price was 15,000 in 2009 and it depreciates by 7%

18. Exponentials y = 2(3)x Multiplier: 3 Y-intercept: 2 All Reals Domain:
Range:
Next = Now
X – intercept: 3 2
All Reals
y>0
*3 S.A. 2
None

19. Greatest Common Factor (GCF):
Largest integer divides in, smallest of each exponent
(Calculator: Math Num GCD (#1,#2) )
Find GCF of 42x2yz4 and 28x5 y3
Factor 25x3 – 5x2
GCF: 5x x x2
5x2(5x – 1)
Solution: 14x2 y
____ ____

20. Quadratics y = -x2 + 3x + 4 Opening: Down Y-intercept: 4
X – intercept:
Domain:
Range:
Down 4
-(x2-3x-4)
-(x-4)(x+1)
4 & -1
All reals
y<6.25

21. Find area of the trapezoid (A = ½h(b1 + b2) ½ (6) ( x + 3 + 3x + 5)
Simplify (2x – 3)(x + 4)
2x(x + 4) – 3(x+4)
2x2 + 8x – 3x – 12
2x2 + 5x - 12
Simplify (2x – 3)-(x + 4)
2x-3 – x - 4
x - 7
Find area of the trapezoid (A = ½h(b1 + b2)
½ (6) ( x x + 5)
3(4x + 8)
12x + 24
x + 3 6
3x + 5

22. Midpoint Formula of (x1, x2) and (y1, y2)
Midpoint:  Mx =     My =
Find the center of the
circle with endpoints of
(-2,1) and (4, -3)
The midpoint is (-3,4) and an endpoint is (1,2). Find the other endpoint.
A M B X Y
-2+4,
= (1, -1) -4 -4 -7
So (-7,6) +2 6 +2 M M M

23. Distance between (3,2) &(-3,6)
    -4 6

24. Error on calculator:
If you have an error that you can’t fix immediately then reset your memory by:   2nd    +     7   

25. & Coefficient of Correlation
Regressions
& Coefficient of Correlation
STAT   EDIT     Enter x’s into L1 Enter y’s into L2
   STAT   CALC    Choose Linreg or Expregr ENTER
Go to y= and type in the equation
Look at the table
   
Coefficient of Correlation:  
~1 Positive      ~ -1 Negative
                 
   Find:   2nd 0 Scroll to DiagnosticON Enter then do regression