methods! Flashcards
sine rule for angles
sin a/a = sin b/b = sin c/c
sine rule for sides
a/sin a = b/sin b = c/sin c
cosine rule (angles)
cos a = b^2 + c^2 - a^2/2 x b x c
need side side side
cosine rule (sides)
a^2 = b^2 + c^2−2(bc)cosA
need side angle side
gradient formula (2 coordinates)
y2 - y1/ x2 - x1
reciprocal
x/y -> y/x
cumulative frequency
previous frequency + current frequency
area of sector
θ/360 x πr^2
θ = sector angle
how to find a fraction on recurring decimals?
f = 0.xyxyxyxyxyxyxy
100f = xy.xyxyxyxyxy
100f - f = 99f
ans = 99f/99
sin30
√1/2
sin45
√2/2
sin60
√3/2
sin90
1
cos0
1
cos30
√3/2
cos45
√2/2
cos60
√1/2
cos90
0
tan30
1/√3
tan45
1
tan60
√3
tan90
infinity
area using sin
1/2absinc
frequency density
frequency/class width (ub-lb)
simultaneous equations
make y the same
+ or -, depending on the symbols (double symbols mean -, opposite means +)
plug x into the equation to find y
how do you find perpendicular gradient (two coordinates)
find gradient:
y2 - y1/ x2 - x1
find the negative reciprocal of the answer
how do you find the tangent equation (a,b)
find gradient:
y2 - y1/ x2 - x1
find the negative reciprocal of the answer (perpendicular gradient)
plug it into y = mx + c, before plugging in the original coordinate in
b = (m x a) + c
make c make sense with the equation
graph circle equation
x^2 + y^2 = r^2
● means (number line)
included (≤)
〇 means (number line)
not included (<)
what is the quadratic formula?
x = -b ± √b - 4ac/2a
(A ∪ B)
a or b
(A ∩ B)
a and b
(A ∩ B)’
not a and b
(A ∪ B)’
not a or b
RHS
right angle hypotenuse side
ASA
angle side angle
SAS
side angle side
SSS
side side side
AAA
angle angle angle
ξ
universal set - everything in the venn diagram
straight line graph
y = mx + c
quadratic graphs
ax^2 + bx + c
U shapes
how to complete the square (a=1)
rearrange into (x + p)^2 + q
ensure that the equation is in standard format (ax^2 + bx + c)
write it out (x + b/2)^2 (ignore c for now)
expand it and compare with the original equation
make c make sense with the equation (c and b can be both positive and negative)
how to complete the square (a≠1)
rearrange into (x + p)^2 + q
divide a by each term
ax^2/a + bx/a + c/a
this should simplify to standard format
x^2 + bx/a + c/a
now complete the square as usual
how do you find the turning point by square completion?
-> (x + p)^2 + q
x = -p
y = q
how do you use completed square to solve the equation/write in surd form
(x + p)^2 + q
move q to the other side
(x + p)^2 = -q
sqaure root both sides and include the ±
x + p = ± √q
get x on its own, and solve what x is
x = -p ± √q
exponential graph
y = k^x
⤴ shape
reciprocal graphs
y = 1/x
⤴⤹ shape
cubic graphs
y = x^3
k
constant
how to find quadratic sequences
write down the sequence find the nth term before finding the constant
a + b + c
3a + b
2a
how to rationalise a denominator
e.g √x/√y + 2
multiply the bottom by the denominator, and the opposite sign if necessary e.g
√x/√y + 2
cancel it out if you can
area trapezium formula
(a+b)/2 x h
area triangle formula
bxh/2
how to calculate surface area
add area of all faces
how to do direct proportionality
e.g y is direct proportionate to x^2
write this down
y ∝ kx^2
plug in the numbers, and rearrange to make k the subject
k = y/x^2
how to do inverse proportionality
e.g y is inversely proportionate to x
in inverse proportion, y = k/x
plug in the numbers and rearrange to make k the subject
a^x/y
^y√a
ans^x
a^0
1
a^y x a^x
a^y + x
(a^x)^y
a^xy
a^y ÷ a^x
a^y-x
a^-x
1/a^x
how to simplify surds (e.g √40)
find two factors, where one number is a square number
(√10x√4)
move the square number on the outside and root it
(2√10)
volume of cylinder
πr^2 x h
how to add surds
if like: add the numbers on the outside e.g
2√x + 2√x = 4√x
if unlike: keep it the same OR try and find like terms before adding
how to draw histogram graph
find class width
calculate frequency density (frequency/class width)
frequency density is the y axis
make the width as far as the intervals go.
how to find the inverse function
replace f(x) with y
swap x and y
make y the subject
median in frequency table
(n+1/2)th
mean in frequecny table
midpoint x frequency/total freq
