equations Flashcards
compound growth and decay
N = N0 x (multiplier)^n
Amount after = initial amount x (percentage change multiplier)^number of days/hours/years
area of trapezium
1/2 (a+b)hv
quadratic equation (solution to ax²+bx+c=0
x= -b ±√(b²-4ac)
—————–
2a
Pythagoras’ theorem (right-angled triangle)
a² + b² = c²
trigonometry ratios (right-angled triangle)
SOH, CAH, TOA
compound measures
distance=speed x time
mass=volume x density
force=pressure x area
sine rule (any triangle)
a over sinA = b over sinB = c over sinC
or
sinA over a = sinB over b = sinC over c
cosine rule (any triangle)
a² = b² + c² - 2bc cos A.
area of triangle (any triangle)
1/2 ab sin C
first rule on circle geometry
tangent and radius meet at 90 °
second rule of circle geometry
two radii from an isosceles triangle
third rule of circle geometry
perpendicular bisector of chord passes through centre of circle
fourth rule of circle geometry
angle at centre of circle is twice angle at circumference
fifth rule of circle geometry
angle in semicircle is 90 °
sixth rule of circle geometry
angles in same segment are equal
seventh rule of circle geometry
opposite angles in a cyclic quadrilateral add up to 180 °
eighth rule of circle geometry
tangents from same point are same length
ninth rule of circle geometry
alternate segment theorem, angle between tangent and chord always equal to angle in opposite segment
how to work out LCM
-list all prime factors that appear in either number
-if factor appears more than once
in one of numbers, list it that many times
-multiply these together
how to work out HCF
- list all prime factors that appear in both numbers
- multiply all numbers
what is difference of two squares (D.O.T.S) (factorising)
a²- b² = (a+b)(a-b)
rules for surds
- √a x √b = √a x b
- √a/√b = √a/b
- √a + √b = √a + √b
- (a+√b)²=(a+√b)(a+√b)= a²+2a√b +b
- (a+√b)(a-√b)= a²-b
- a/√b=a√b/b
first method for drawing straight-line graphs; table of 3 values
- draw up table with 3 suitable values of x
- find y-values by putting each x-values into equation
- plot points + draw line
second method of drawing straight-line graph; =mx+c
- put equation in form y=mx+c
- put dot on y-axis at value of c
- using m,go across and up or down certain number of units. make another dot and repeat until can draw line
third method of drawing straight line graph; x=0, y=0
- set x=0 in equation, and find y where it crosses y axis
- then set y=0 and find x where it crosses x-axis
- mark on 2 points and join with line
how to find midpoint on a graph
add x-coordinates and divide by 2 then do same for y-coordinates
y is proportional to x
y=kx
y is inversely proportional to x
y=k/x
how to find position of the median
(n+1)/2 (n=total frequency)
how to work out lower quartile Q1
(n+1)/4 (n=number of values)
median Q2
(n+1)/2 (n=number of values)
upper quartile Q3
3(n+1)/4 (n=number of values)
interquartile range
difference between upper quartile and lower quartile
median on cumulative frequency graph
go halfway up side, across curve, down and read off bottom scale
lower quartile on cumulative frequency graph
go 1/4 up, across to line , down read value
upper quartile on cumulative frequency graph
go 3/4 up, across to line , down to value
frequency density
frequency / class width
frequency
frequency density x class width = area of bar
the AND RULE
gives P(both events happening P(A) x P(B)
the OR RULE
gives P(at least one event happens )
P(A) + P(B) - P(A and B)
or if events cannot happen together, mutually exclusive
P(AorB)=P(A) + P(B)
