Add/Subtract Polynomials Find like terms: same variable, same exponents Add/Subtract the coefficient (the number in front of the variable) Do NOT change the exponent ! Ex: (4p 2 + 5p) + (-2p 2 + p) = 2p 2 + 6p Ex: (7g 3 – 5g) – (-4g 3 + 4g) = 11g 3 – 9g 1

Algebraic Expression 2

Box and Whisker Plot Put the data in order Find the median, lower quartile (median of the lower half) upper quartile (median of the upper half) Graph the box using median, lower and upper quartiles. Graph the whiskers using the lower and upper extreme. Interquartile range = Upper quartile – lower quartile 3

Cube Root Is a special value that when cubed gives the original number. * Perfect Cube Numbers: 8, 27, 64, 125, 216 etc. Ex: 4

Curve of Best Fit Is a curve that best approximates the data. Ex. Determine the quadratic curve of best fit for the data. Then estimate what the value of y will be when x = Go to STAT Enter x values into List 1, y values into List 2 Press F2 (CALC) F3 (REG) F3 (xˆ2) Read the screen and write the equation: y = 0.33x x Go to Run Plug in x = x(-4) x The answer is 2.3

Direct Variation 6

Domain Are the input (x) values of a function Ex: find the domain {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} Domain {2, 3, 4, 6} Domain {x| 1≤ x ≤ 7} 7

Factor a) Factor GCF 18cd c 2 d + 9cd = 3cd(6d + 4c + 3) b) Factor trinomials x 2 + 2x – 15 5c 2 – 17cd + 14d (x – 3)(x+ 5 ） (c – 2d)(5c – 7d ） 8

Function Is a relation where one input has exactly one output. Functions pass the vertical line test. Function 9

Function Value The value of a function when x = a, is written as f(a). To solve, replace x with a. Ex. If f(x)= 3x 2 + x – 2 find f(-5) Go to Table Enter the function Press F6 (TABL) Enter -5 The answer is 68 10

Graph Equations Graph y = ½ x Plot the y intercept (0, 2) 2.From (0,2) use rise/run. Go up 1 unit, right 2 units 3.Draw a line Equation must be in y=mx+b form! 11

Inverse Variation Equation: xy = k or y = k/x In a table, x times y is constant If x increases, y decreases. Or vice versa. Ex: Does the table represent a direct or inverse variation? xy Inverse variation xy = 300 or y = 300/x 12

Law of Exponents 13

Law of Exponents 14

Linear Equation Ex. Solve 3 – 3(2x +1)=9 Go to EQUA Enter the equation Press F6(SOLV) x =

Linear Inequalities Ex. 2x – 3y > 6 Change the inequality into y = mx + b form. (change the sign when divide by a negative number) y < 2/3x – 2 Go to graph Press F3 (type) Press F6 ► Press F2 (Y<) Enter the equation: 2,a b/c, 3, x, –, 2. Enter Press F6 (Draw) The solution is any point in the shaded area. 16

Line of Best Fit A line of best fit is a straight line that best represents the data on a scatter plot. 17

Line of Best Fit xy Go to Stat Enter x values into List 1, y values into List 2 Press F2 (CALC) Press F3 (REG) Press F1 (x) Read the screen and plug into y = mx + b Y = -2.6x + 9.6

Literal Equations 19

Mean Absolute Deviation 20

Multiply Polynomials Use the box method Ex: (x + 5y)(x – 7y) X2X2 5xy -7xy-35y 2 X +5y X - 7y X 2 – 2xy – 35y 2 21

Property of Solving Equations 22

Quadratic Equation 1. Move everything to the left side. 2. Factor. 3. Set each parenthesis to zero and find x respectively 3x – 4 = 0 x = 4/3 x – 2 = 0 x = (x + 6)(5x – 2) = 0 x + 6 = 0 5x – 2 = 0 x = 6 x = 5/2 23

Quadratic Equation Ex. Find solutions to: y=-x 2 +x Method 1: Make sure the function is in ax 2 + bx +c form Go to eqn F2 (POLY) F1 (2) Enter the coefficients -1, 1, 12 and press F1 (SOLV) Method 2: Go to Graph Enter the function F6 (Draw) F5 (G-solv) F1 (root) Wait……… Press ► to find the second root

Range Are the output (y) values of a function Ex: find the range {(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)} Domain {-3, -1, 3, 6} Range {y| 1≤ y ≤ 3} 25

Root(s) of a function Same x-intercepts, zeroes, solution. 26

Slope 27

Slope: from equation If the equation is in y = mx + b form: y = 1/3 x – 5 m = 1/3 If not, change into y = mx + b 3x – 5y = 10 -3x -3x -5y = -3x y = 3/5 x – 2 m = 3/5 28

Slope: from a graph 1.Pick two points on the line 2. Use rise/run 3. Slope = 1/3 Be careful when line goes down! 29

Slope: from two points

Square Root of Radical Expressions 31

Standard Deviation 32

Standard Deviation Find standard deviation for the set of data: 35, 38, 41, 35, 36, 55 Go to STAT Enter data into List 1 Press F2 (CALC) Press F1 (1Var) Xσn = 7.02… 33

System of linear equations Method 1: Make sure the equations are in Ax + by = C form Go to EQN Press F1 (SIML) Press F1 (2) Enter the coefficients: 3, 6, 6 and 2, - 3, 4 Press F1 (SOLV) The answer (2, 0) Method 2: Change the equations to y = mx +b form y = -1/2 x + 1 y = 2/3x – 4/3 Go to graph Enter the functions into Y1 and Y2 Press F6 (DRAW) Press F5 (Gsolv) Press F5 (ISCT) Wait………. The answer x =2 y = 0 34 Solve: 3x + 6y = 6 2x – 3y = 4

System of Linear Inequalities Same as Linear inequalities. Just enter two inequalities into y = The solution is any point in the area that overlap. 35

Values of a Function Find range of the function, given the domain f(x) = 3n 2 – 2n + 2 {-1, 0, 1} Go to Table Enter the function Press F6 (TABL) Enter -1, 0 and 1 and write down the y values The answer is {7, 2, 3} 36

Write Equations Passes through the point (4,-2) and has an x-intercept of 3 Use x intercept which is (3, 0) x mx + b y 4 (-2) (-2) m = -2 plug it in the middle column and find y-intercept Answer: y = -2x

Write Equations Passes through the point (5,1) and has a y-intercept of -3 Use y intercept which is (0, -3) x mx + b y m = 4/5 Answer: y = 4/5x –

x intercept Same as zero, solution, root of a function Is where the graph cross the x axis, written as (x, 0) In an equation, cover the y (y = 0) and solve for x. Ex. -6 = -4x – 3y Cover -3y and solve -6 = -4x x = 3/2 x intercept (3/2, 0) 39

y intercept Is where the graph cross the y axis, written as (0, y) In an equation, cover the x (x= 0) and solve for y Ex. 3x + 2y = 10 Cover 3x and solve 2y = 10 y = 5 y intercept (0, 5) 40

Zero of a Linear Function Same as x-intercepts, solutions, roots. Set f(x) = 0 and solve the x 2x + 4 = 0 x = -2 41

Zero of Quadratic Function If the function is quadratic find the roots by factoring If a graph is given, just find the x-intercepts (x -3)(x-5) = 0 x = 3 or x = 5 42

Zeros of a Quadratic Function Same as x-intercepts, solutions, roots Go to EQN F2 (POLY) F1 (2) Enter the coefficients 1, -8, 15 and press F1 (SOLV) Answer: 3 and 5 43

Z score A Z-Score is a statistical measurement of a data’s relationship to the mean. A Z-score of 0 means the score is the same as the mean. Positive Z- score indicates the data is above the mean. Negative Z-score indicates the data is below the mean. Ex. A data set has a mean of 16.5 and a standard deviation of 3. The element x has a z-score of 1.5. In which interval does the element lie? 10.5 ≤ x < ≤ x < ≤ x < ≤ x < ≤ x <