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