formulas Flashcards
Exterior Angles Theorem
a + b + c= 180
x= a + b
c= 180 - x
-exterior angles is equal to sum of opp interior angles
formula of exterior angles of regular polygons
360 / n
n = no. sides
formula of interior angles of regular polygons
180 ( n -2 )
n = no. sides
how to find sum of interior angles in a polygon
-from 1 point draw lines to other points inside the polygon
-180 x no. triangles found
formula for sector angle size of pie chart
-sector angle size = fraction x 360
-find fraction by measuring
formula for sector no. side of pie chart
-sector no. = fraction x total no.
-find fraction by measuring
formula for no. % in pie chart
-no. % = fraction x 100%
-find fraction by measuring
formula for mean
add all / no. of things
how to find mode/ modal
most occurring value
how to find median
rearrange from lowest to highest and find middle value
formula for range
highest value - lowest value
formula to find % of a no.
a/100 x b
formula to find no. from %
% x no.
formula for theoretical probability
P(x) = what should happen x no. trials
formula for probability
P(x) = no. times happens x no. trials
Perimeter of square
4b
Perimeter of react.
2( L + b )
Perimeter of circle (circumference)
πd
Perimeter of circle arc (circumference)
angle/ 360 x πd
Area of square
b^2
Area of react
Lb
Area of triangle
1/2 x bh
Area of trap.
h( a+b )/ 2
a & b are parrel sides
h = hieght btw a & b
Area of circle
πr^2
Area of rhombus
Lb
Area of parallelogram
Lb
Area of circle sector
angle/ 360 x πr^2
Area of curved surface area of cone
πrL
L = length from bottom to tip
Area of surface of Sphere
4πr^2
Volume of cube
b^3
Volume of cuboid
Lbh
Volume of prism
1/2 x bh x h
(cross-section x h)
Volume of cylinder
πr^2 h
volume of pyramid
1/3 x base area x perpendicular height
Volume of cone
1/3 x πr^2 h
Volume of Sphere
4/3 x πr^3
How to find no. in set
make a equation with total
how to do set builder notation?
- ” (set letter) = {x: x ____} “
- x = all values in set
- : = such that
- ______ = add the rule
Formula for straight lines
- y = mx + c
-m = gradient
-c = y-intercept
-y & x = not fixed values
formula for gradient of straight line
-rise/ run
-without graph: need 2 points
y2 - y1/ x2 - x1
-always make fraction
formula for y-intercept of straight line
-need 1 point & gradient
y - y1 = m (x - x1)
How to find equation of parallel straight line
-m is same
-change c only
how to find gradient of perpendicular straight line (has to intersect at 90)
-m for perpendicular is inverse
- flip fraction & make ( - )
formula for midpoint of straight line
- x1 + x2/ 2 (for x)
- y1 + y2/ 2 (for y)
- (x, y)
formula for length of straight line
-use Pythagoras
-√ (x2 - x1)^2 + (y2 - y1)^2
What is DOPS
-diff of perfect squares
- a^2 - b^2 = (a + b)(a - b)
-eg. x^2 - 9 = (x + 3)(x - 3)
Cheats method for linear equations
-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
formula for Pythagoras
-a^2 + b^2 = c^2
-only in right angel
formula for median
-nth = no. data
-nth + 1/2 = term
formula to find middle of class interval
-find middle of class range by adding the 2 no.s & dividing by 2
formula for arithmetic sequence
a n = a1 + (n-1 )d
a n = nth term
a1 = first term
d = diff btw terms
formula for geometric sequence
a n = a1 x r^n-1
a n = nth term
a1 = first term
r = ratio
Formula for straight lines
y = mx + c
-m = gradient
-c = y-intercept
-y & x = not fixed values
formula for gradient of straight line
-rise/ run
-without graph: need 2 points
y2 - y1/ x2 - x1
-always make fraction
formula for y-intercept of straight line
-need 1 point & gradient
y - y1 = m (x - x1)
formula for length of straight line
-use Pythagoras
-√ (x2 - x1)^2 + (y2 - y1)^2
how to find gradient of perpendicular straight line (has to intersect at 90)
-m for perpendicular is inverse
- flip fraction & make ( - )
How to find equation of parallel straight line
-m is same
-change c only
formula for midpoint of straight line
x1 + x2/ 2 (for x)
y1 + y2/ 2 (for y)
(x, y)
congruency tests
(S = side, A = angle)
-SAS
-ASA
-SSS
-AAA
-RHS = Right angle, hypotenuse, S
formula for frequency density
frequency/ class width
frequency = diff btw a & b
how to find θ for right angled triangles
-SOH CAH TOA
sin θ = O/ H
cos θ = A/ H
tan θ = O/ A
-O is side opposite θ
-H is longest side
Quadratic formula
2a -put bracket in calc when (b)^2
Pythagoras theorem
a^2 + b^2 = c^2
functions for sine, cosine, tan
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)
sine rule
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
cosine rule
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
area of a right angled triangle
1/2 x base x height
area of non right angle triangle
1/2 x ab sincC
formula for compound interest = formula for exponential graph
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
formula for simple interest
P = principle
R = rate from % in DECIMALS
t = time
simple interest = PRT
* only simple interest, not total money*
formula when writing/ solving compound interest
- P ( 1+ r/ 100)^ t = A
r/ 100 because r has to be in decimal, not % - 1 + r/ 100 = t^√A/P
how to find tax from taxable income (gross income) bracket
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
formula for % profit/ loss
profit/ loss
—————— X 100%
cost price
formula for Turning point x coordinate (only used for Quadratic)
x = -b
———
2a
rules for differentiation
-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
