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

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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