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 O 2 I can solve inequalities. I can interpret realOlife graphs. I can find the n th term of a sequence. I can draw quadratic graphs using the rule to find the coOordinates. 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.
Transcript
!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!O!2!
!
I!can!solve!
inequalities.!
!
I!can!interpret!
realOlife!
graphs.!
!
I!can!find!the!nth!
term!of!a!
sequence.!
!
I!can!draw!quadratic!
graphs!using!the!rule!to!
find!the!coOordinates.!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.
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.
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
