Intermediate 2Mind Maps
•Fractions •Volume
•Straight Line•Circle
•Simultaneous Equations•Trigonometry
•Trig Functions & Equations•Comparing Data
•Standard Deviation•Quadratic Functions
1 11 1
2 4
Multiplication
15
1 1
2 3
Adding
Basic Rules of Fraction
Simple fractions
2 1
3 2
Subtracting
1 3
2 5
Multiplication
1 4
2 5
Division
1 5
2 4
61
65 3
10
58
Flip and change
the sign
Harder fractions1 1
2 12 3
Subtracting
61
Deal with whole numbers
first
12 1
3 2 1
Same idea for addition
1 21 1
2 3
Division
3 3
2 5 9
10
Top-heavy first 3 5
2 3
Flip and change
the sign
8
Top-heavy first 3 5
2 4 8
71
Area & Volume
of a Prism
Simple Areas
Simple Volume
Composite Areas
Composite Volume
Volume = Area x Height
V = L x B x H
A = L x B A = πr2 A = ½bh
A = B x h
h
A = ½(a + b) h
h
h
V = πr2h
made up of basic areasA = L x B +
h
V = (LxBxH) +
h
LB
H
B
L
a
b
B
Lr
made up of basic
volumes
LB
Hh
(½BhL) ½bh
Straight Line
y = mx + c
m = gradient
c = y intercept
2 1
2 1
y yVm
H x x
Possible values for gradient
m > 0
m < 0m = 0
m = undefined
Parallel lines have
same gradient
m > 0
Two points needed (x1,y1) and (x2,y2) to
calculate gradient
Graph ofy = mx + c
(0,c)
2 1
2 1
y yVm
H x x
(0,c)
Note : 2y + 4x = 8
rearrange into correct form y = -2x + 4
Area is2A r
Summary of Circle Summary of Circle TopicTopic
Circumference is
C D
Sector area
2 angleSector =
360
o
o
centrer
Arc length is
length
angleArc =
360
o
o
centreD
Diameter
2D rRadiu
s12
r D
line that bisects a chord
1. Splits the chord into 2 equal halves.
2. Makes right-angle with the chord.
3. Passes through centre of the circle
Pythagoras TheoremSOHCAHTOA
Semi-circle angle is always 90
o
Tangent touches circle at one pointand make angle 90
o with point of
contact radius
www.mathsrevision.com
Simultaneous Equations
Graphically
Where two linesintersect (crossover)
Algebraically
y = -2x + 6
y = 0.5x + 1
y = -2x + 62y = x + 2
-x + 2y = 22x + y = 6
(A)(B)
1. Rearrange &
Label
2. Scale and
Eliminate
-2x + 4y = 42x + y = 6
(C)(D)
2x(A) thenadded
5y = 10y = 2
Sub y = 2 into (A) -x + 2x2 = 2
-x = -2x = 2
(2,2)
(2,2)Remember to use the check
Right - Angle TriangleONLY !
2 2 2a b c 2 2 2b c a 2 2 2a c b
a
b
c
sinopp
xhyp
cosadj
xhyp
tanopp
xadj
Ratio values for sin and cos
are between 0 and 1
Used for lengths onlyPythagoras Theorem
Used for finding length and angles
SOHCAHTOA Converse is also true !
Isosceles
2 sides&
2 angles equal
Equilateral
All lengths&
Angles equal (60o)
Special Triangles
1Area = ×a×b ×sin(C)
21
or = ×b ×c ×sin(A)21
or = ×a×c ×sin(B)2
For Any triangle
Angles in a triangleadd up to 180o
Triangle & Trig.
sin( ) sin( ) sin( )
a b c
A B C
Sine Rule
Cosine Rule
1Area = ×bh
2
2 2 2
2 2 2
2 2 2
a =b +c -2bc×cos(A)
b =a +c -2ac×cos(B)
c =a +b -2ab×cos(C)
Right - Angle
90o
Scalene
No angle the same
0 90 180 270 360
4
2.5
1
0.5
2cos(x)
cos x deg( )
3cos x deg( ) 1
x
0 90 180 270 360
1
0.5
0.5
1
Max / Mini values for
sin and cos
are 1 and -1
SGAny triangle
a
b
c
A
B
C
opp
adj
hyp
xo
a
a
sin( x)+
c
b
bos(
c
x)+c
a = stretches / squashes graph in y direction
b = how times it repeats in 360
o
c = moves graph up / down
SAS
Trig Functions and Solving Trig
Equations
Basic Strategy for Solving
Trig Equations
Basic Graphs
360o
1
-1
0
1
-1
0360o
1
-1
0180o90o
sin x
cos x
undefined
0 1 0
1 3 1
2 2 31 1
12 2
3 1 3
2 2
1 0
o
o
o
o
o
sin cos tan
0
30
45
60
90
1. Rearrange into sin = 2. Find solution in the Quads
Amplitude
Period
Amplitude
Period
Complex Graph
2
-1
1
090o 180o 270o 360o
3
y = 2sin4x + 1
Max. Value = 2 + 1 = 3
Mini. Value = -2 + 1 = -1
Period = 360 ÷ 4 = 90o
Amplitude = 2
C
AS
T
0o180o
270o
90o
Period
tan x
Period
Amplitude
180o - xo
180o + xo
xo
360o + xo
Things to note
Things to note
Q1 = 25% of dataQ2 =Median = 50% of data
Q3 = 75% of dataInterquartile range Q3- Q1
Semi – Interquartile ÷2
Ways of comparing
dataBoxplots
0123
3804
9
27 8
927
63 0
4
0
15
5
Key 1|9 = 19
n = 11
37
5
MedianModeMeanRange
Q1 Q2 Q3L H3 38
2218 37Q1 Q2 Q3L H
4 351310 30
Mean and standard deviation
See separate mindmap
Order data
Back to back stem
leaf
x x2
2
5
3
5
Standard Deviation“a measure of spread only ”
2
2
1dev
xx
nSn
22563
4 1.83devS
S = standard deviationn = number of data points
(Σx)2 = Sum of data squared
Σx2 = Sum of squared data
Σx = 15(Σx)2 = 225
Σx2 = 63
4
259
25
153.75
4
xmean
n Note
Quadratic Functions
y = ax2 + bx + c
SACe.g. (x+1)(x-
2)=0
Graphs
Evaluating
Decimal places
Factorisationax2 + bx + c
= 0
Cannot Factorise
Rootsx = -1 and x =
2
2( 4 )
2
b b acx
a
Rootsx = -1.2 and x =
0.7
Roots
Mini. Point
(0, )
(0, )
Max. Point
Line of Symmetryhalf way
between roots
Line of Symmetryhalf way
between roots
a > 0
a < 0
f(x) = x2 + 4x + 3f(-2) =(-2)2 + 4x(-2) + 3 = -1
x=
x=
cc