SAT main concepts

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Arc length formula

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SAT

46 Terms

1

Arc length formula

2πr x (angle)/360

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2

Sector area formula

πr² x (angle) / 360

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3

Quadratic formula

(-b±√(b²-4ac))/(2a)

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4

Sum of the roots formula

-b / a

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5

Product of roots formula

c / a

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6

Discriminant formula

b² - 4ac

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7

Complementary rules

  • sin(x) = cos(90-x)

  • cos(x) = sin(90-x)

x = degree of angle

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8

Sin(x)

opposite / hypot. (SOH)

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9

Cos(x)

adjacent / hypot (CAH)

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10

Tan(x)

opposite / adjacent (TOA)

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11

probability

Target (center event happening) / total (all possibilities)

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12

total angle

180(n-2)

n = # of sides

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13

20% less than

total x 0.8

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14

20% of

total x 0.2

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15

Lines tangent to a circle:

forms a right angle

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16

Radius

r = C / 2π

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17

tangent line + radius

forms right angle

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18

Equation of a circle

(x - h)² + (y - k)² = r²

h = x cor. of center

k = y cor. of center

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19

what does the discriminant tell us?

the number of roots / solutions

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20

how many roots are there if the discriminant is less than 0?

0

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21

Formula to find the x vertex

-b / 2a

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22

What does the average of two roots tell us?

the x vertex

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23

Vertex form

y = a(x - h) ² + k

(h, k) = x, y corrdinants

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24

In vertex form, what is the (x, y)?

(h, k)

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25

Steps to finding the remainder in synthetic division (equation / equation)

  • find the number that makes the denominator 0

  • plug it into the top numerator

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26

What is 3 ^(2 / 3) in root form?

∛3²

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27

Exponent on exponent

Multiply them

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28

If there are no solutions to the system…

the ratio of coefficient for x & y must be equal

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29

Triangles: direct relationship between…

angle and the opposite side

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30

Bigger the angle…

longer the opposite side

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31

Special right triangles

  • 60, 30, 90

  • 45, 45, 90

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32

Side length rations for a 60, 30, 90 triangle

  • 60: x√3

  • 30: x

  • 90: 2x

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33

Side length ratio for a 45, 45, 90 triangle

  • 45: x

  • 45: x

  • 90: x√2

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34
<p>What is the standard deviation of a bell curve graph</p>

What is the standard deviation of a bell curve graph

low

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35
<p>What is the standard deviation of a skewed graph?</p>

What is the standard deviation of a skewed graph?

Medium

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36
<p>What is the standard deviation for a DT</p>

What is the standard deviation for a DT

high

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37

Finding a side of similar triangles

short / long

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38

Slope formula

m = (y2 - y1) / (x2 - x1)

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39

Slope of a perpendicular line

the negative reciprocal

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40

cycle of i starting at i^1

  • i

  • -1

  • -i

  • 1

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41

i^0

1

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42

i^1

i

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43

-1

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44

-i

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45

i^4

1

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46

slope intercept form

y = mx + b

m: slope

b: y-intercept when x is 0

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