methods! Flashcards
1
Q
sine rule for angles
A
sin a/a = sin b/b = sin c/c
2
Q
sine rule for sides
A
a/sin a = b/sin b = c/sin c
3
Q
cosine rule (angles)
A
cos a = b^2 + c^2 - a^2/2 x b x c
need side side side
4
Q
cosine rule (sides)
A
a^2 = b^2 + c^2−2(bc)cosA
need side angle side
5
Q
gradient formula (2 coordinates)
A
y2 - y1/ x2 - x1
6
Q
reciprocal
A
x/y -> y/x
7
Q
cumulative frequency
A
previous frequency + current frequency
8
Q
area of sector
A
θ/360 x πr^2
θ = sector angle
9
Q
how to find a fraction on recurring decimals?
A
f = 0.xyxyxyxyxyxyxy
100f = xy.xyxyxyxyxy
100f - f = 99f
ans = 99f/99
10
Q
sin30
A
√1/2
11
Q
sin45
A
√2/2
12
Q
sin60
A
√3/2
13
Q
sin90
A
1
14
Q
cos0
A
1
15
Q
cos30
A
√3/2
16
Q
cos45
A
√2/2
17
Q
cos60
A
√1/2
18
Q
cos90
A
0
19
Q
tan30
A
1/√3
20
Q
tan45
A
1
21
Q
tan60
A
√3
22
Q
tan90
A
infinity
23
Q
area using sin
A
1/2absinc
24
Q
frequency density
A
frequency/class width (ub-lb)
25
simultaneous equations
make y the same
+ or -, depending on the symbols (double symbols mean -, opposite means +)
plug x into the equation to find y
26
how do you find perpendicular gradient (two coordinates)
find gradient:
y2 - y1/ x2 - x1
find the negative reciprocal of the answer
27
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
28
graph circle equation
x^2 + y^2 = r^2
29
● means (number line)
included (≤)
30
〇 means (number line)
not included (<)
31
what is the quadratic formula?
x = -b ± √b - 4ac/2a
32
(A ∪ B)
a or b
33
(A ∩ B)
a and b
34
(A ∩ B)'
not a and b
35
(A ∪ B)'
not a or b
36
RHS
right angle hypotenuse side
37
ASA
angle side angle
38
SAS
side angle side
39
SSS
side side side
40
AAA
angle angle angle
41
ξ
universal set - everything in the venn diagram
42
straight line graph
y = mx + c
43
quadratic graphs
ax^2 + bx + c
U shapes
44
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)
45
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
46
how do you find the turning point by square completion?
-> (x + p)^2 + q
x = -p
y = q
47
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
48
exponential graph
y = k^x
⤴ shape
49
reciprocal graphs
y = 1/x
⤴⤹ shape
50
cubic graphs
y = x^3
51
k
constant
52
how to find quadratic sequences
write down the sequence find the nth term before finding the constant
a + b + c
3a + b
2a
53
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
54
area trapezium formula
(a+b)/2 x h
55
area triangle formula
bxh/2
56
how to calculate surface area
add area of all faces
57
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
58
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
59
a^x/y
^y√a
ans^x
60
a^0
1
61
a^y x a^x
a^y + x
62
(a^x)^y
a^xy
63
a^y ÷ a^x
a^y-x
64
a^-x
1/a^x
65
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)
66
volume of cylinder
πr^2 x h
67
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
68
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.
69
how to find the inverse function
replace f(x) with y
swap x and y
make y the subject
70
median in frequency table
(n+1/2)th
71
mean in frequecny table
midpoint x frequency/total freq
