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formulas Flashcards

1
Q

Exterior Angles Theorem

A

a + b + c= 180
x= a + b
c= 180 - x
-exterior angles is equal to sum of opp interior angles

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2
Q

formula of exterior angles of regular polygons

A

360 / n
n = no. sides

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3
Q

formula of interior angles of regular polygons

A

180 ( n -2 )
n = no. sides

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4
Q

how to find sum of interior angles in a polygon

A

-from 1 point draw lines to other points inside the polygon
-180 x no. triangles found

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5
Q

formula for sector angle size of pie chart

A

-sector angle size = fraction x 360
-find fraction by measuring

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6
Q

formula for sector no. side of pie chart

A

-sector no. = fraction x total no.
-find fraction by measuring

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7
Q

formula for no. % in pie chart

A

-no. % = fraction x 100%
-find fraction by measuring

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8
Q

formula for mean

A

add all / no. of things

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9
Q

how to find mode/ modal

A

most occurring value

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10
Q

how to find median

A

rearrange from lowest to highest and find middle value

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11
Q

formula for range

A

highest value - lowest value

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12
Q

formula to find % of a no.

A

a/100 x b

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13
Q

formula to find no. from %

A

% x no.

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14
Q

formula for theoretical probability

A

P(x) = what should happen x no. trials

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15
Q

formula for probability

A

P(x) = no. times happens x no. trials

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16
Q

Perimeter of square

A

4b

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17
Q

Perimeter of react.

A

2( L + b )

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18
Q

Perimeter of circle (circumference)

A

πd

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19
Q

Perimeter of circle arc (circumference)

A

angle/ 360 x πd

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20
Q

Area of square

A

b^2

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21
Q

Area of react

A

Lb

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22
Q

Area of triangle

A

1/2 x bh

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23
Q

Area of trap.

A

h( a+b )/ 2
a & b are parrel sides
h = hieght btw a & b

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24
Q

Area of circle

A

πr^2

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25
Q

Area of rhombus

A

Lb

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26
Q

Area of parallelogram

A

Lb

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27
Q

Area of circle sector

A

angle/ 360 x πr^2

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28
Q

Area of curved surface area of cone

A

πrL
L = length from bottom to tip

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29
Q

Area of surface of Sphere

A

4πr^2

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30
Q

Volume of cube

A

b^3

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31
Q

Volume of cuboid

A

Lbh

32
Q

Volume of prism

A

1/2 x bh x h
(cross-section x h)

32
Q

Volume of cylinder

A

πr^2 h

33
Q

volume of pyramid

A

1/3 x base area x perpendicular height

34
Q

Volume of cone

A

1/3 x πr^2 h

35
Q

Volume of Sphere

A

4/3 x πr^3

36
Q

How to find no. in set

A

make a equation with total

37
Q

how to do set builder notation?

A
  • ” (set letter) = {x: x ____} “
  • x = all values in set
  • : = such that
  • ______ = add the rule
38
Q

Formula for straight lines

A
  • y = mx + c
    -m = gradient
    -c = y-intercept
    -y & x = not fixed values
39
Q

formula for gradient of straight line

A

-rise/ run
-without graph: need 2 points
y2 - y1/ x2 - x1
-always make fraction

40
Q

formula for y-intercept of straight line

A

-need 1 point & gradient
y - y1 = m (x - x1)

41
Q

How to find equation of parallel straight line

A

-m is same
-change c only

42
Q

how to find gradient of perpendicular straight line (has to intersect at 90)

A

-m for perpendicular is inverse
- flip fraction & make ( - )

43
Q

formula for midpoint of straight line

A
  • x1 + x2/ 2 (for x)
  • y1 + y2/ 2 (for y)
  • (x, y)
44
Q

formula for length of straight line

A

-use Pythagoras
-√ (x2 - x1)^2 + (y2 - y1)^2

45
Q

What is DOPS

A

-diff of perfect squares
- a^2 - b^2 = (a + b)(a - b)
-eg. x^2 - 9 = (x + 3)(x - 3)

46
Q

Cheats method for linear equations

A

-only use if no no. before letter
- x^2 _ (no.s [ + ] [letter]) _ (no.s [x])
-eg. (x - 2)^2 = (x - 2)(x - 2)
= x^2 - 4x + 4

47
Q

formula for Pythagoras

A

-a^2 + b^2 = c^2
-only in right angel

48
Q

formula for median

A

-nth = no. data
-nth + 1/2 = term

49
Q

formula to find middle of class interval

A

-find middle of class range by adding the 2 no.s & dividing by 2

50
Q

formula for arithmetic sequence

A

a n = a1 + (n-1 )d
a n = nth term
a1 = first term
d = diff btw terms

51
Q

formula for geometric sequence

A

a n = a1 x r^n-1
a n = nth term
a1 = first term
r = ratio

52
Q

Formula for straight lines

A

y = mx + c
-m = gradient
-c = y-intercept
-y & x = not fixed values

53
Q

formula for gradient of straight line

A

-rise/ run
-without graph: need 2 points
y2 - y1/ x2 - x1
-always make fraction

54
Q

formula for y-intercept of straight line

A

-need 1 point & gradient
y - y1 = m (x - x1)

55
Q

formula for length of straight line

A

-use Pythagoras
-√ (x2 - x1)^2 + (y2 - y1)^2

55
Q

how to find gradient of perpendicular straight line (has to intersect at 90)

A

-m for perpendicular is inverse
- flip fraction & make ( - )

56
Q

How to find equation of parallel straight line

A

-m is same
-change c only

57
Q

formula for midpoint of straight line

A

x1 + x2/ 2 (for x)
y1 + y2/ 2 (for y)
(x, y)

58
Q

congruency tests

A

(S = side, A = angle)
-SAS
-ASA
-SSS
-AAA
-RHS = Right angle, hypotenuse, S

59
Q

formula for frequency density

A

frequency/ class width
frequency = diff btw a & b

60
Q

how to find θ for right angled triangles

A

-SOH CAH TOA
sin θ = O/ H
cos θ = A/ H
tan θ = O/ A
-O is side opposite θ
-H is longest side

60
Q

Quadratic formula

A 
         2a -put bracket in calc when (b)^2
60
Q

Pythagoras theorem

A

a^2 + b^2 = c^2

61
Q

functions for sine, cosine, tan

A

1) sine
x< 180 (x = +) __ sin x = sin (180 - x)
x> 180 (x = -) __ x - 180 = y , sin x = sin (360- y)
2) cosine
x< 90/ x> 270 (x = +) __ cos x = -cos (180 - x)
90< x< 270 (x = -) __ cos x = cos (360 - x)
3) tan
tan x = tan (180 + x)

61
Q

sine rule

A

A, B, C - angle
a, b, c - side (side has to be opposite same letter angle)
a b
——– = ——–
sin A sin B
-cross multiply
-2 sides, 1 angle/ 1 side, 2 angles

61
Q

cosine rule

A

A, B, C - angle
a, b, c - side (side has to be opposite same letter angle)
-c^2 = a^2 + b^2 - 2ab cos C
-cos C = a^2 + b^2 - c^2
————————-
2ab
-3 sides/ 2 sides, 1 angle

62
Q

area of a right angled triangle

A

1/2 x base x height

63
Q

area of non right angle triangle

A

1/2 x ab sincC

63
Q

formula for compound interest = formula for exponential graph

A

P = principle
R = rate from % in DECIMALS
t = time
A = total amount
P (1 +/ - R)^ t = A
-appreciation/ growth = ( + )
-depreciation/ decay = ( - )
*total money including compound interest

63
Q

formula for simple interest

A

P = principle
R = rate from % in DECIMALS
t = time
simple interest = PRT
* only simple interest, not total money*

64
Q

formula when writing/ solving compound interest

A
  • P ( 1+ r/ 100)^ t = A
    r/ 100 because r has to be in decimal, not %
  • 1 + r/ 100 = t^√A/P
65
Q

how to find tax from taxable income (gross income) bracket

A

eg. $23 760 (x) + 25% (%) of the amount above $132 000 (y)
x + % of the amount over y
z = gross income
formula:
x + (% x [z - y]) = tax needed to pay

66
Q

formula for % profit/ loss

A

profit/ loss
—————— X 100%
cost price

67
Q

formula for Turning point x coordinate (only used for Quadratic)

A

x = -b
———
2a

68
Q

rules for differentiation

A

-multiply coefficient of x with power, minus power by 1
-if power = 1, take only coefficient if there is or just 1
-if number without x, remove it

math (22 decks)

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