E  Hughes  2013  

 A*    

I  can  manipulate  algebraic  fractions.  

I  can  use  the  equation  of  a  circle.  

I  can  solve  simultaneous  equations  algebraically,  

where  one  is  quadratic  and  one  is  linear.  

I  can  transform  graphs,  including  trig  

graphs.  

I  can  draw  and  recognise  an  exponential  graph.  

 A    

I  can  simplify  algebra  involving  

powers.    

I  can  rearrange  formulae  with  the  

subject  in  more  than  once.  

I  can  solve  quadratics  by  using  the  formula,  

completing  the  square,  and  factorising.  

I  can  solve  trigonometry:  cos  x  =  0.5  

and  recognise  trig  graphs.  

I  can  prove  things  using  algebra.  

 I  can  find  the  equation  of  a  line  that  goes  

through  a  point,  and  is  perpendicular  to  another  line.  

   B  

I  can  factorise  and  expand  complex  expressions.  

   

I  can  solve  simultaneous  equations  

algebraically  and  graphically.  

   

I  can  solve  inequalities  algebraically  

and  graphically.  

  I  can  use  my  knowledge  of  y  =  mx  +  c  to  work  out  the  equation  of  a  

line.  

I  can  solve  cubic  and  quadratic  graphs  

graphically.  

I  can  factorise  Quadratics    I  can  use  y  =  mx  +  c  to  find  the  gradient  

of  a  line.  

I  can  recognise  cubic  and  reciprocal  graphs,  and  match  equations  to  

graphs.  I  can  recognise  the  Difference  of  Two  

Squares  (D.O.T.S)  

 C  

     

 I  can  substitute  into  complex  formulae.  

I  can  solve  equations  with  unknowns  on  both  sides:      

2x  +  3  =  3x  -­‐  2  

 I  can  solve  inequalities.  

 I  can  interpret  

real-­‐life  graphs.  

 I  can  find  the  nth  

term  of  a  sequence.  

 I  can  draw  quadratic  

graphs  using  the  rule  to  find  the  co-­‐ordinates.  I  can  rearrange  

formulae  

 D  

I  can  expand  brackets  and  simplify  

my  answer.  

 I  can  substitute  in  

negative  numbers  to  formulae.  

 I  can  solve  and  rearrange  equations  

 

   

ALGEBRA  I  can  factorise  simple  

expressions.  

 

You can collect terms together if they are the same letter, with the same power. 7x + 3x = 10x 4x + 2y = 4x + 2y (different letters) 5x + 2 + 3x = 8x + 2 (letters and numbers are separate)4y + 2y² + 3y = 7y + 2y² (y and y² are different powers, so can’t be put together) 10x²y + 2xy²

5 2 2 x x y x y y

To factorise - underline the expression. List underneath all the things that multiply to give each part.eg - 10y = 2 x 5 x yCircle anything in both lists. These go outside the bracket.Anything left goes inside the bracket, on the correct side.

2xy (5x + y)

To solve equations, you must always do the same to both sides. To get rid of something, you do the opposite - eg - to get rid of a +3, you -3. to get rid of a x2, you ÷2

Keep going until you have what you want on its own.

You can leave answers as fractions, like above, if it doesn’t give a whole number answer. Remember, one step at a time, trying to get the x on its own.

This also works when rearranging formulae - use the same steps - it’s just that you’ll end up with a different letter on its

own than you started with.

5 miles = 8km

Sequences 3, 7, 11, 15Goes up by 4 each time, so we write 4n as the first part of your rule. To find the second part, follow the pattern back from the first term. You get -1, so you write that on the end of your rule. 4n -1This means it is one less than the 4 times table each time.

6, 11, 16, 21 = 5n + 1 (goes up in 5s, back 5 would be +1)-2, 0, 2, 4 = 2n - 4 (goes up in 2s, back 2 would be -4)10, 7, 4, 1 = - 3n + 13 (goes up in -3’s, back 3 would be 13)

Factorising quadratics

y=2x+1‘The y value is double the x value, plus 1’.eg - (0,1), (1,3), (2,5)

With the general y=mx+c, the line cuts

the y-axis at c, and for every 1 you go across (right), you go ‘m’ up.

Straight line (linear) graphs

Facto

rising

Linear Quadratic Cubic

 A*    

   

I  can  manipulate  complex  indices  and  surds.  

   

I  can  find  upper  and  lower  bounds  in  area  and  volume.  

 A    

   I  can  rationalise  

surds.  

I  can  calculate  with  fractional  

indices.   NUMBER  

   

I  can  find  upper  and  lower  bounds  of  numbers.    

 B  

   

I  can  calculate  using  standard  form.  

   

I  can  calculate  with  negative  indices.  

 

I  can  do  fraction  calculations  starting  with  mixed  numbers.  

I  can  calculate  compound  interest.  

I  can  change  between  recurring  decimals  and  fractions.  

I  can  do  reverse  percentages.  

 C  

   

I  can  x  &  ÷  by  10,  100,  1000  and  0.1,  

0.01  etc.  

I  can  break  down  a  number  into  prime  

factors.  

I  can  solve  equations  with  

trial  and  improvement.  

I  can  multiply  and  divide  by  numbers  less  

than  1.  

   

I  can  multiply  and  divide  by  decimals.  

   

I  can  calculate  with  fractions  and  

ratios.    

   

I  can  work  out  simple  compound  interest.  

 I  can  use  index  laws  

with  numbers.  

 I  can  use  my  calculator  to  efficiently  work  out  complex  calculations.  

 D  

     

I  can  estimate  the  answers  to  a  calculation.  

       

I  can  work  out  ratios  in  recipes.  

     

I  can  calculate  profit  and  loss.  

 I  can  work  out  simple  proportion.  

   

I  can  increase  or  decrease  by  a  percentage.      

I  can  do  simple  fraction  calculations.  

 

Significant figures:Works the same as rounding to a given decimal place etc, just a different way to describe where to round.

The first number that isn’t a zero is the first significant figure. Everything after that counts.

Eg - rounded to 1 s.f:

4753 rounds to 5000 923 rounds to 900 0.0358 rounds to 0.04

To get from 10 to 15, you need 5 more. 5 is half of 10, so just halve each ingredient and add it on...If you’re not sure, divide by the total to see how much of each ingredient you need for 1 cookie, then multiply by how many you actually need.

For 10 cookies:

120ml milk90g sugar60g flour

24g butter

For 15 cookies:

(120 + 60) ml milk(90 + 45) g sugar(60 + 30) g flour

(24 + 12) g butter

Prime factorisation (prime factor trees)

Easy %For 17.5% (used for VAT)

Divide total by 10 = 10%Halve it = 5%Halve it = 2.5%Add them up = 17.5%

Division79 ÷ 5 = 15.8

First, how many 5’s go into 7?1, remainder 2. The 1 goes on top, the 2 carries over in front of the 9 to make it 29.

Now how many 5’s go into 29?5, remainder 4. The 5 goes on top, the 4 carries over. We can always add a ‘.0’ (and then as many 0’s as we want) after a number, to deal with remainders.

We finally do: how many 5’s go into 40? 8 with no remainder. The 8 goes on top, making the answer 15.8. We can stop now, as there is no remainder left.Don’t forget to put the decimal in the answer too!

To estimate, round each number to 1 s.f, and do the sum. This will give you a rough answer (an estimate!)

73 x 356Multiplication(grid method)

Remember, you only needed to do 7 x 3 for the first bit, then add on the three 0’s from the 300 and the 70 to make 21000.

 A*    A    

I  can  prove  circle  theorems  

   I  know  construction  proofs.  

I  can  solve  3D  trigonometry  problems.  

I  can  use  the  sine  and  cosine  rules  to  find  triangle  measurements.  

I  can  use  circle  theorems  

I  can  use  similarity  in  length,  area  and  volumes.    

     

I  can  solve  3D  Pythagoras  problems.  

I  can  find  arc  lengths,  and  areas  of  sectors  and  segments  of  

circles.  

 I  can  find  the  surface  area  and  volume  of  

solids.  I  can  use  fractional  scale  factors  

in  enlargements.  

   B  

I  can  prove  congruency.   I  can  use  ½absinC.  

I  can  use  some  of  the  circle  theorems.  

I  understand  when  two  shapes  are  mathematically  similar.  

   I  can  solve  multi-­‐stage  trigonometry  problems.  

   I  can  work  out  the  dimensions  of  formulae.    

 I  can  use  interior  and  exterior  angles  to  solve  problems.  

I  can  describe  transformations  

       

I  can  solve  interior  angle  problems.  

     

I  can  do  enlargements  with  negative  scale  

factors.  

 I  can  draw  loci.  

 I  can  solve  

problems  with  bearings.  

I  can  use  Trigonometry  to  find  missing  sides  or  angles  in  right-­‐angled  

triangles.  

 I  can  say  whether  a  measurement  in  of  a  length,  area  or  volume  from  the  units.  

C    I  can  construct  a  perpendicular  bisector,  and  accurate  triangles.  

I  can  use  Pythagoras  to  find  the  missing  side  of  a  right-­‐angled  triangle.  

I  can  find  the  area  and  

circumference  of  a  circle,  given  the  

diameter.  

 I  can  work  out  the  volume  of    a  3D  

shape.  

I  can  answer  questions  about  

polygons.  

I  can  do  /  recognise  rotations,  reflections,  

translations  and  enlargements.    

 I  can  do  isometric  drawings.  

 I  can  draw  

and  measure  bearings.  

  I  can  find  the  area  and  

circumference  of  a  circle,  given  the  

radius.  

   

I  can  change  m2  to  cm2  etc  

D   I  can  find  the  area  of  a  triangle,  regular  polygons,  and  other  

shapes.  

   I  can  draw  plans  and  elevations.  

I  can  find  angles  using  parallel  lines.   GEOMETRY  

I  can  use  measurements  of  similar  triangles  to  find  missing  edges.  

 

Parallel lines Parallel lines Parallel lines

Alternate Corresponding Opposite

Bearings always start from North and go clockwise. They always have 3 digits.

N

Polygon(many sided shape)

3 = triangle4 = quadrilateral5 = pentagon6 = hexagon7 = heptagon8 = octagon9 = nonagon10 = decagon

Areas of shapesAreas of shapesAreas of shapesAreas of shapes

base x height ½ base x height ½(a+b)h ∏r²

r

Circumference ∏d

d

Eg:003∘ 147∘

10 mm = 1 cm100 cm = 1 m1000 m = 1 km1000g = 1kg

60 seconds = 1min60 min = 1 hr365 days = 1yr52 weeks = 1 yr

Enlargement

CentreAngleDirection

Mirror line

Vector - egCentreScale factor

Pythagoras TrigonometryExterior angles add to 360∘

Do 360

number of sides.

Exterior + interior = 180∘

Angle bisectorPerpendicular

bisectorEquidistant from

a point (Loci)Equidistant from

a line (Loci)

a² + b² = c²

Reflection Rotation Translation

Exterior Interior

 A    

     

I  can  construct  and  interpret  histograms.  

   

I  understand  stratified  sampling.  

   

I  can  find  the  probability  of  combined  events,  using  multiplication  and  addition  of  probabilities.  

   B  

   

I  can  find  the  median  and  interquartile  range  from  cumulative  

frequency.  

     

I  can  analyse  box  plots.  

     

I  can  analyse  data  vs  theoretical  probability.  

   

I  can  use  tree  diagrams.  

 C  

 I  can  find  the  mean  and  median  from  grouped  data.  

 I  can  explain  my  use  of  averages.  

   

I  can  draw  box  plots.  

 I  can  design  

questionnaires.   HANDLING  DATA  

 D  

I  can  identify  the  modal  class.  

I  can  draw  a  stem-­‐and-­‐leaf  diagram,  including  the  key.  

I  can  explain  what  is  wrong  with  a  questionnaire.  

   

I  can  find  the  relative  

frequency  of  an  event.  

   

I  can  find  missing  

probabilities  from  a  table.  

   

I  can  list  the  possible  

outcomes  of  events.  

I  can  find  the  mean  of  a  set  of  data.  

I  can  draw  a  scatter  diagram,  describe  a  relationship  or  correlation  from  it,  and  use  

a  line  of  best  fit  to  estimate.  

I  know  what  makes  a  good  sample.    

 

To find the mean of grouped data, find the midpoint of each group, and multiply by the frequency.

Number of lengths Class midpoint (m) Frequency (f) F x m

1 to 56 to 1011 to 1516 to 2021 to 25

38

131823

12332762

3 x 12 = 368 x 33 = 264

13 x 27 = 35118 x 6 = 108

23 x 2 = 46

Totals 80 805

The mean is now 805 ÷ 80

Stem and leaf diagramsTo find the median, keep crossing off the smallest and largest numbers until you find the middle. (If there are 2 numbers left in the middle, find the middle of those two numbers.)

Hey Diddle diddle, the median’s the middle, You add then divide for the mean.

The mode is the value that comes up the most,and the range is the difference between!

*modal means the same as mode. We use it when there is grouped data.

Probabilities always add up to 1.

That means if the probability you pick a red ball is 0.6 P(red) = 0.6then the probability you don’t pick a red ball is (1- 0.6) so P(not red) = 0.4

If the probability of something happening is 0.4, and you do the experiment 200 times, you’d expect it to happen 0.4 x 200 times = 80 times. This is called relative frequency.

Each set of branches adds to 1.Read the question very carefully in case the probabilities change for the second set of branches.

Scatter Diagrams

Box plots

QuestionnairesThe three key things to design a good question are:Give a time frame (where appropriate)Make sure your options don’t overlapAllow all possible choices (eg, none, other, more than)

For example:How much money do you spend on sweets each week?☐Less than £1 ☐£1 to £1.99 ☐£2 to £2.99 ☐£3 or more?

The width of the box shows the interquartile range

Lowestvalue

Lower quartile

Upper quartileMedian Highest

value

Frequency density = frequency class width

Histograms

The frequency is the area of the bar.

Stratified SamplingWork out what fraction of the total population your sample is. For each subgroup, you want that fraction of it.Eg - sample size 50, population 1000You want 50/1000 of each subgroupIf there were 700 boys and 300 girls, you would do 700 x 50/1000 = 35 boys, and 300 x 50/1000 = 15 girls.

Surds

You can use the rules to simplify surds by splitting them into their factors (and looking for square factors).

To rationalise the denominator, multiply the whole fraction by the denominator again

Upper and Lower boundsTo find the upper and lower bounds, it is the

rounded value ± half the unit of rounding.

100cm to the nearest cm is 100 ± 0.5cm500g to the nearest 10g is 500 ± 5g

Circle Theorems

Learn the conditions for congruency:

SSS SASASA RHS

For arc length, you need to work out what fraction of your circumference it is by doing θ ÷ 360. Then multiply the circumference by this fraction to get the arc length.You do the same with the area of a sector - find what fraction of the whole are you need.

3D Pythagoras

If a question is asking for a diagonal length in a cuboid, it is a 3D Pythagoras question. In a cuboid measuring a x b x c, with a 3D diagonal d, a² + b² + c² = d²

d

On formula page!

Completing the square

Exponential graphs

Graph transformations Equation of a circle

Trig Graphs

x² + bx b 2( )2