KS3 Revision † Maths - Collins › Samples › KS3... · KS3 Revision † Maths KS3 Revision †...

8
Number Number Number Number Sequences Give the order in which operations should be carried out. What are the first 10 square numbers? What is a factor? What is a prime number? What is a term-to-term rule? 1 2 3 4 5 Number Number Number Number Sequences 1 2 3 4 5 Order of operations: Brackets Indices Divide Multiply Add Subtract The first 10 square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 A factor is a number that divides exactly into another number, e.g. 1, 2, 3, 4, 6, 8, 12 and 24 are factors of 24. A prime number is a number with exactly two factors, itself and 1, e.g. 7. (Note: 1 is not a prime number) A term-to-term rule links each term in a sequence to the previous term, e.g. the term-to-term rule for 1, 4, 7, 10, 13,... is +3. KS3 Revision • Maths KS3 Revision • Maths KS3 Revision • Maths KS3 Revision • Maths KS3 Revision • Maths

Transcript of KS3 Revision † Maths - Collins › Samples › KS3... · KS3 Revision † Maths KS3 Revision †...

Page 1: KS3 Revision † Maths - Collins › Samples › KS3... · KS3 Revision † Maths KS3 Revision † Maths KS3 Revision † Maths KS3 Revision † Maths KS3 Revision † Maths. Sequences

Nu

mb

erN

um

ber

Nu

mb

erN

um

ber

Seq

uen

ces

Give the order in which

operations should be

carried out.

What are the first 10 square

numbers?

What is a factor?

What is a prime number?

What is a term-to-term rule?

1

2

3

4

5

Nu

mb

erN

um

ber

Nu

mb

erN

um

ber

Seq

uen

ces

1

2

3

4

5

Order of operations:

Brackets

Indices

Divide

Multiply

Add

Subtract

The first 10 square numbers are:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

A factor is a number that

divides exactly into another

number, e.g.

1, 2, 3, 4, 6, 8, 12 and 24 are

factors of 24.

A prime number is a number

with exactly two factors, itself

and 1, e.g. 7.

(Note: 1 is not a prime

number)

A term-to-term rule links each

term in a sequence to the

previous term, e.g.

the term-to-term rule for

1, 4, 7, 10, 13,... is +3.

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Seq

uen

ces

Per

imet

er a

nd

Are

aP

erim

eter

an

d A

rea

Per

imet

er a

nd

Are

aP

erim

eter

an

d A

rea

What is a position-to-term rule?

What is a sector?

What is the formula for the

area of a rectangle?

What is the formula for the

area of a triangle?

What is the formula for the

area of a circle?

6

7

8

9

10

Seq

uen

ces

Per

imet

er a

nd

Are

aP

erim

eter

an

d A

rea

Per

imet

er a

nd

Are

aP

erim

eter

an

d A

rea

6

7

8

9

10

A position-to-term rule (or

nth term) shows how to find

a term from its position in a

sequence, e.g. the position-to-

term rule for 9, 13, 17, 21, 25,...

is 4n + 5.

A sector is a section of a circle

enclosed between an arc and two

radii (a pie piece).

Rectangle:

Area = Length × Width

A = lw

Triangle:

Area = 12(Base × Perpendicular

height ) A = 12(bh)

Circle:

Area = Pi × Radius2

A = �r2

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Sector

l

w

b

h

r

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Per

imet

er a

nd

Are

aP

erim

eter

an

d A

rea

Stat

isti

cs a

nd

Dat

aSt

atis

tics

an

d D

ata

Stat

isti

cs a

nd

Dat

a

What is the formula for the

circumference of a circle?

What is the formula for the

area of a parallelogram?

What is the mean of a set of data?

What is the median of a set of data?

What is the mode of a set of data?

11

12

13

14

15

Per

imet

er a

nd

Are

aP

erim

eter

an

d A

rea

Stat

isti

cs a

nd

Dat

aSt

atis

tics

an

d D

ata

Stat

isti

cs a

nd

Dat

a

11

12

13

14

15

Circle:

Circumference = 2 × Pi × Radius

C = 2�r

or

Circumference = Pi × Diameter

C = �d

Parallelogram:

Area = Base × Perpendicular

height A = bh

The mean is the sum of all the

values divided by the number

of values.

The median is the middle value

when the data is put in order.

The mode is the most common

value in a set of data.

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h

b

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Dec

imal

sA

lgeb

ra3D

Sh

apes

: Vo

lum

e an

d

Surf

ace

Are

a3D

Sh

apes

: Vo

lum

e an

d

Surf

ace

Are

a3D

Sh

apes

: Vo

lum

e an

d

Surf

ace

Are

a

What is a power or index?

What is the

difference between

expanding brackets and

factorising?

What is the formula for the

volume of a cuboid?

What is the formula for the

volume of a cylinder?

What is an edge?

16

17

18

19

20

Dec

imal

sA

lgeb

ra3D

Sh

apes

: Vo

lum

e an

d

Surf

ace

Are

a3D

Sh

apes

: Vo

lum

e an

d

Surf

ace

Are

a3D

Sh

apes

: Vo

lum

e an

d

Surf

ace

Are

a

16

17

18

19

20

A power or index tells you

how many times a number

should be multiplied by itself,

e.g. 103 = 1000.

Expanding brackets involves

removing the brackets in an

expression by multiplying.

Factorising involves taking out

the highest common factor

and putting brackets into the

expression.

Cuboid:

Volume = Length × Width × Height

V = lwh

Cylinder:

Volume = Area

of circular cross-section

× Height

V = �r2h

An edge is where two faces of

a 3D shape meet.

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h

l

w

r

h

Edge

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3D S

hap

es: V

olu

me

and

Su

rfac

e A

rea

Inte

rpre

tin

g D

ata

Inte

rpre

tin

g D

ata

Frac

tio

ns

Co

ord

inat

es a

nd

G

rap

hs

What is a vertex?

What is a line of best fit?

What is meant by the correlation

between two sets of data?

What is an improper fraction?

How can you work out the

gradient of a linear graph?

21

22

23

24

25

3D S

hap

es: V

olu

me

and

Su

rfac

e A

rea

Inte

rpre

tin

g D

ata

Inte

rpre

tin

g D

ata

Frac

tio

ns

Co

ord

inat

es a

nd

G

rap

hs

21

22

23

24

25

A vertex is where the edges

of a 3D shape meet.

A line of best fit is a straight line

which shows the trend of the

relationship between two sets of

data on a scatter graph.

The correlation is the

relationship or pattern

between the data.

An improper fraction has a

numerator which is larger

than the denominator, e.g.

Using any two points on the line,

gradient = distance between y-coordinatesdistance between x-coordinates

‘Uphill’ lines have positive

gradients and ‘downhill’ lines

have negative gradients.

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Positive Negative No correlation

Sunlight in a day

Ice

crea

m s

ales

Line of best fit

32

Numerator

Denominator

Vertex

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Co

ord

inat

es a

nd

G

rap

hs

An

gle

sA

ng

les

Pro

bab

ility

Frac

tio

ns,

Dec

imal

s an

d P

erce

nta

ges

Where on a graph can the

solution to two simultaneous

equations be found?

Give the formula for working

out the sum of the interior

angles of a polygon.

What is an exterior angle?

If the probability of

an event occurring is x, what

is the probability of the event

not occurring?

If 14 = 0.25 = 25%, give 18 as a

decimal and a percentage.

26

27

28

29

30

Co

ord

inat

es a

nd

G

rap

hs

An

gle

sA

ng

les

Pro

bab

ility

Frac

tio

ns,

Dec

imal

s an

d P

erce

nta

ges

26

27

28

29

30

The solution to the simultaneous

equations is the coordinates of

the point at which the lines of

the two equations cross.

Sum of interior angles =

(Number of sides – 2) × 180

An exterior angle is the angle

formed outside a polygon

between one side and an

adjacent side extended:

Probability of event not occurring = 1 – x

As a decimal:18 = 0.125

As a percentage:18 = 12.5%

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PolygonExterior angle

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Equ

atio

ns

Sym

met

ry a

nd

En

larg

emen

tSy

mm

etry

an

d

Enla

rgem

ent

Rat

io a

nd

Pro

po

rtio

nR

eal-

Life

Gra

ph

s an

d

Rat

es

If you are asked to solve an

equation, what does this mean?

When enlarging a shape, what is

meant by the scale factor?

How can you simplify a ratio?

What is the formula for speed?

31

32

33

34

35

Equ

atio

ns

Sym

met

ry a

nd

En

larg

emen

tSy

mm

etry

an

d

Enla

rgem

ent

Rat

io a

nd

Pro

po

rtio

nR

eal-

Life

Gra

ph

s an

d

Rat

es

31

32

33

34

35

To solve an equation, you

need to find the value of the

unknown number (this may

be represented by a letter or

a symbol).

Congruent shapes are the same

shape and the same size. Similar

shapes are the same shape but

different sizes.

The scale factor indicates

how much bigger or smaller

a shape becomes, e.g. a scale

factor of 2 doubles each

length of the shape; a scale

factor of 12 halves each length.

You can simplify a ratio by

dividing the parts of the ratio

by a common factor, e.g.

10 : 6 can be simplified to 5 : 3

by dividing by 2.

Speed = Distance ÷ Time

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d

s × t

What is the difference in

meaning between congruent

and similar?

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Rea

l-Li

fe G

rap

hs

and

R

ates

Rig

ht-

An

gle

d T

rian

gle

sR

igh

t-A

ng

led

Tri

ang

les

Rig

ht-

An

gle

d T

rian

gle

sR

igh

t-A

ng

led

Tri

ang

les

What is the formula for density?

What is Pythagoras’ Theorem?

What is the formula for sin x°?

What is the formula for cos x°?

What is the formula for tan x°?

36

37

38

39

40

Rea

l-Li

fe G

rap

hs

and

R

ates

Rig

ht-

An

gle

d T

rian

gle

sR

igh

t-A

ng

led

Tri

ang

les

Rig

ht-

An

gle

d T

rian

gle

sR

igh

t-A

ng

led

Tri

ang

les

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Density = Mass ÷ Volume

Pythagoras’ Theorem:

In a right-angled triangle, the

sum of the squares of the two

shorter sides equals the square of

the hypotenuse.

a2 + b2 = c2

Sin x° = Opposite ÷ Hypotenuse

Cos x° = Adjacent ÷ Hypotenuse

Tan x° = Opposite ÷ Adjacent

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KS3 Revision • Maths

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m

d × v

O

Hsin x°

A

Hcos x°

O

Atan x°

a

b

c (hypotenuse)