A* I can manipulate algebraic fractions. I can use the equation of a circle. 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. quadratics by using the formula, completing the square, and factorising. 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 factorise Quadratics I can recognise the Difference of Two Squares (D.O.T.S) simultaneous equations algebraically and graphically. inequalities algebraically and graphically. I can use my knowledge of y = mx + c to work out the equation of a line. I can use y = mx + c to find the gradient of a line. cubic and quadratic graphs graphically. I can recognise cubic and reciprocal graphs, and match equations to graphs. C I can substitute into complex formulae. I can rearrange formulae equations with unknowns on both sides: 2x + 3 = 3x - 2 inequalities. I can interpret real- life graphs. I can find the n th term of a sequence. I can draw quadratic graphs using the rule to find the co- ordinates. D I can expand brackets and simplify my answer. I can factorise simple expressions. I can substitute in negative numbers to formulae. and rearrange equations ALGEBRA E Hughes 2013
You can collect terms together if they are the same letter, with the same power. 7x + 3x = 10x 4x + 2y = 4x + 2y 5x + 2 + 3x = 8x + 2 4y + 2y² + 3y = 7y + 2y² (different letters) (letters and numbers are separate) (y and y² are different powers, so can t be put together) 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. Sequences 3, 7, 11, 15 Goes 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 -1 This 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 To factorise - underline the expression. List underneath all the things that multiply to give each part. eg - 10y = 2 x 5 x y Circle anything in both lists. These go outside the bracket. Anything left goes inside the bracket, on the correct side. Factorising 10x²y + 2xy² 5 2 2 x x y x y y 2xy (5x + y) 5 miles = 8km 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. Linear Quadratic Cubic Straight line (linear) graphs 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.
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 change between recurring decimals and fractions. I can calculate compound interest. 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 use index laws with numbers. equations with trial and improvement. I can multiply and divide by numbers less than 1. I can use my calculator to efficiently work out complex calculations. I can multiply and divide by decimals. I can calculate with fractions and ratios. I can work out simple compound interest. 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.
Division 79 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. For 10 cookies: 120ml milk 90g sugar 60g flour 24g butter For 15 cookies: (120 + 60) ml milk (90 + 45) g sugar (60 + 30) g flour (24 + 12) g butter 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: 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! Multiplication (grid method) 73 x 356 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. Easy % For 17.5% (used for VAT) Divide total by 10 = 10% Halve it = 5% Halve it = 2.5% Add them up = 17.5% Prime factorisation (prime factor trees) 4753 rounds to 5000 923 rounds to 900 0.0358 rounds to 0.04 To estimate, round each number to 1 s.f, and do the sum. This will give you a rough answer (an estimate!) 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 can use circle theorems I can use similarity in length, area and volumes. I can use fractional scale factors in enlargements. I can prove congruency. I know construction proofs. 3D trigonometry problems. 3D Pythagoras problems. I can use the sine and cosine rules to find triangle measurements. 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 ½absinC. B I can use some of the circle theorems. I can use interior and exterior angles to solve problems. I understand when two shapes are mathematically similar. I can describe transformations multi- stage trigonometry problems. I can work out the dimensions of formulae. C interior angle problems. I can do enlargements with negative scale factors. I can draw loci. problems with bearings. I can construct a perpendicular bisector, and accurate triangles. I can use Trigonometry to find missing sides or angles in right- angled triangles. I can use Pythagoras to find the missing side of a right- angled triangle. I can say whether a measurement in of a length, area or volume from the units. I can find the area and circumference of a circle, given the diameter. I can work out the volume of a 3D shape. D I can answer questions about polygons. I can find the area of a triangle, regular polygons, and other shapes. I can do / recognise rotations, reflections, translations and enlargements. I can do isometric drawings. I can draw plans and elevations. I can draw and measure bearings. I can find angles using parallel lines. I can find the area and circumference of a circle, given the radius. GEOMETRY I can change m 2 to cm 2 etc I can use measurements of similar triangles to find missing edges.
N Bearings always start from North and go clockwise. They always have 3 digits. Eg: 003 147 Centre Scale factor Enlargement Mirror line Centre Angle Direction Reflection Rotation Translation Vector - eg 10 mm = 1 cm 100 cm = 1 m 1000 m = 1 km 1000g = 1kg 60 seconds = 1min 60 min = 1 hr 365 days = 1yr 52 weeks = 1 yr Polygon (many sided shape) 3 = triangle 4 = quadrilateral 5 = pentagon 6 = hexagon 7 = heptagon 8 = octagon 9 = nonagon 10 = decagon Exterior Interior Exterior angles add to 360 Do 360 number of sides. Exterior + interior = 180 Angle bisector Pythagoras Perpendicular bisector Equidistant from a point (Loci) Equidistant from a line (Loci) Trigonometry a² + b² = c² Areas of shapes base x height ½ base x height ½(a+b)h r² r Circumference d d Parallel lines Alternate Corresponding Opposite
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 find the mean of a set of data. I can draw a stem- and- leaf diagram, including the key. I can draw a scatter diagram, describe a relationship or correlation from it, and use a line of best fit to estimate. I can explain what is wrong with a questionnaire. I know what makes a good sample. 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.
Scatter Diagrams 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. Stem and leaf diagrams To 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.) To find the mean of grouped data, find the midpoint of each group, and multiply by the frequency. Questionnaires The three key things to design a good question are: Give a time frame (where appropriate) Make sure your options don t overlap Allow 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? Probabilities always add up to 1. That means if the probability you pick a red ball is 0.6 P(red) = 0.6 then 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. Number of lengths Class midpoint (m) Frequency (f) F x m 1 to 5 6 to 10 11 to 15 16 to 20 21 to 25 3 8 13 18 23 12 33 27 6 2 3 x 12 = 36 8 x 33 = 264 13 x 27 = 351 18 x 6 = 108 23 x 2 = 46 Totals 80 805 The mean is now 805 80 Lowest value Box plots Lower quartile Median Upper quartile The width of the box shows the interquartile range Highest value Each set of branches adds to 1. Read the question very carefully in case the probabilities change for the second set of branches.
Histograms Upper and Lower bounds To find the upper and lower bounds, it is the rounded value ± half the unit of rounding. Learn the conditions for congruency: Frequency density = frequency class width 100cm to the nearest cm is 100 ± 0.5cm 500g to the nearest 10g is 500 ± 5g SSS ASA SAS RHS The frequency is the area of the bar. 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. Circle Theorems Stratified Sampling Work out what fraction of the total population your sample is. For each subgroup, you want that fraction of it. Eg - sample size 50, population 1000 You want 50/1000 of each subgroup If there were 700 boys and 300 girls, you would do 700 x 50/1000 = 35 boys, and 300 x 50/1000 = 15 girls. Surds To rationalise the denominator, multiply the whole fraction by the denominator again You can use the rules to simplify surds by splitting them into their factors (and looking for square factors).
Graph transformations Trig Graphs Equation of a circle Exponential graphs On formula page! Completing the square 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 3D Pythagoras d x² + bx b ( 2) 2