SAT MATH (copy)

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discriminant = 0

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SAT

Math

11th

168 Terms

1

discriminant = 0

1 solution

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2

discriminant

b2 minus 4 ac

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3

in vertex formula, h =

b/2a

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4

in vertex formula k =

c - b^2/4a

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5

discriminant is negative

no solution

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6

discriminant is positive

2 solutions

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7

standard form shows

where parabola opens; c = y int

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8

positive a in parabolic formulas

parabola opens up

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9

negative a in parabolic formulas

parabola opens down

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10

factored form shows

x intercepts

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11

vertex form shows

vertex

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12

standard formula

ax^2 + bx + c

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13

vertex formula

a(x-h)^2 + k, where (h, k) are the vertex coordinates

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14

factored formula

a(x-b)(x-c)

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15

f(x-c) shifts the function

right c units

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16

f(x+c) shifts the function

left c units

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17

f(x) + c shifts the function

up c units

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18

f(x) - c shifts the function

down c units

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19

-f(x) causes a change in…

y-value

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20

f(-x) causes a change in…

x-value

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21

linear equation

y=mx+b

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22

30-60-90 triangle side rules

x, xroot3, 2x

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23

45-45-90 triangle side rules

x, x, xroot2

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24

distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

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25

Quadratic Formula

x = -b ± √(b² - 4ac)/2a

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26

Sum of Perfect Squares Addition (a+b)(a+b)

(a^2 + 2ab +b^2)

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27

Sum of Perfect Squares Subtraction (a-b)(a-b)

a^2 -2ab +b^2

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28

difference of perfect square (x2-y2)

(x+ y) (x-y)

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29

x^22/x^10

x^12 (sutbract exponents when dividing w/ same base)

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30

x^3 * x^4

x^7 (sum exponents when multiplying with same base)

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31

(x^3)^4

x^12 (multiply exponents when one is outside the parentheses)

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32

x^-n NEGATIVE EXP RULE

1/x^n (negative exponent is same as 1/x to that exponent’s abs value)

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33

x^(2/3)

cube root of x^2 (numerator is power x is raised to, denominator is root)

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34

every number over 1/3

cube root rulez

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35

compound interest formula

current balance = principal * (1 + (interest rate/number of times compounded)^(time)(# times copounded)

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36

compound interest

Interest paid on interest previously earned; credited daily, monthly, quarterly or semiannually

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37

interest

A sum paid or charged for the use of money or for borrowing money

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38

simple interest formula

SI = P × R × T, where P = Principal, R = Rate of Interest, and T = Time period

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39

right trig?

sohcahtoa

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40

circle formula

(x-h)^2 + (y-k)^2 = r^2

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41

circle area

A=πr²

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42

Circle Circumference

C=2πr

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43

radians to degrees conversion

radians x 180/π

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44

degrees to radians

multiply by pi/180

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45

same slope, different y-intercept

parallel lines/ no solution

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46

Same slope, same y-intercept

infinite solutions same line

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47

Different slope, different y-intercept

one solution

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48

flip over x axis

(x,y) -> (x,-y)

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49

flip over y axis

(x,y) -> (-x,y) (reflection)

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50

volume of a cylinder

V = πr2h

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51

geometry?

1- pithagoras- r triangles 2- sohcatoa - r triangles 3- circles: remember formulas and rules, apply x/2x strat equalling to total same with any shape^^

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52

every linear equation is

a modification of y=x

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53

PERCENT CHANGE

old-new/old x 100

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54

geometry strat 2 congruence

check for what the problem is telling u: equilateral, isosceles

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55

similar triangles

same ratios! --corresponding angles,etc

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56

congruent triangles

2 triangles are congruent if and only if all pairs of corresponding sides and angles are congruent / equals. rotate and match to find angle

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57

inequality solution?

dot inside both shaded regions (desmos)

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58

equal equations

all terms===

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59

ax2 plus bx plus c sum of solution???

-b/a

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60

ax2 plus bx plus c multiplication of solutions??

c/a

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61

no solution in standard form

same m dif b // A/D=B/E=// C/F

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62

infinite solutions in standarf form

same everything A/D=B/E

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63

1 solution in standard form

dif m's A/Ddoesnt= B/E

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64

roots?

square every term

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65

squares?

root every term

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66

f(-9)=f(3)

parabolas are symmetrical// vertex is in middle of 2 numbers //h=-3 beware of signs

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67

parabolic wp?

-b/2a or discriminant

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68

inequality?

variable on the left== flip sign

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69

estimates solution?

wrong usually; redo

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70

ez problem

slow down to get #'s right

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71

divide or multiply by a negative number in inequality

flip signs

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72

at least in inequality

same or greater than symbol

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73

proportion setup

part of whole times total

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74

similar triangles

Two pairs of corresponding angles are equal. : Three pairs of corresponding sides are proportional. : Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.

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75

x inequality

always on left side of equation, if switched = swap signn means less than or greater than

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76

no less than c

≥c

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77

"No more than c"

≤c

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78

Less than or equal to c or "at most c"

≤c

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79

greater than or equal to or "at least c"

≥c

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80

system of linear ineq WP

set up an annotate (SIMPLY AND UNDERSTAND) totals signs- equations signs totals!!-- annotate which units are beingg x2 identify well!! LOCATE/CREATE IS** solve if necessary

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81

usually but not always systems of inequalities will solve for two units:

money amount *usually identified when given 2 or even more totals!

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82

beware if WP is asking for total distance or average distance

apply formulas accordingly eg sum/amt

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83

distance

speed x time set proportions accordingly

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84

syst of linear inequalites

plug in values in equation till u reach max based of data

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85

max or minimum value in a WP?

SOLVE FOR 1 PLUG IN EG X= (Y-2) use results and plug in maximixing one value and minimizing the other or vice versa

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86

rate

A comparison of two quantities by division part to part part to whole

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87

proportion

comparison of 2 ratios usually for an unknown value

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88

ratio

result of the division of a ratio 15m/3s = 5m/s!! it combines 2 units

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89

unit price

total price/ units

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90

speed

distance/time

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91

ratio problems

find ratios unit conversion total? estequiometria set up lin equations sometimes careful of square units

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92

linear function problems

plug in to make it 0!!

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93

formula of area of circular sector

A=21​θr2 in radians no degrees

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94

formula of circular arc

s=rθ in radians ofc!

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95

when a problem is given in 0.2

the answers might be divided by 100 dont get confused what do these numbers mean?? leave those time consuming questions for end

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96

break even point

solutions of a factored form equation

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97

common mistake

not 2x checking for a few secs leaving time consuming questions for beginning thinking and mentalizing there is not enough time== there is== not checking all at the end and just running out of time

solution: do mocks and mini sections ! ! ! !

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98

units

usally complex units are ratios instead// total unitsx average makes no sense

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99

proportion in wp pattern

total/unit times measurement

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100

circular proportion

central angle/circular angle= sector area/circular area orrr circumference (ratio of 1 = ratio of other, ratio of other=) also central angle is same as its arc

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