ks3 revision † maths - collins › samples › ks3... · ks3 revision † maths ks3 revision †...
Post on 25-Jun-2020
229 Views
Preview:
TRANSCRIPT
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.
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
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
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
Sector
l
w
b
h
r
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.
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
h
b
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.
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
h
l
w
r
h
Edge
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.
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
Positive Negative No correlation
Sunlight in a day
Ice
crea
m s
ales
Line of best fit
32
Numerator
Denominator
Vertex
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%
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
PolygonExterior angle
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
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
d
s × t
What is the difference in
meaning between congruent
and similar?
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
36
37
38
39
40
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
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
KS3 Revision • Maths
m
d × v
O
Hsin x°
A
Hcos x°
O
Atan x°
a
b
c (hypotenuse)
top related