Revision List for Higher Tier Mathematics Paper 2

Transcription

1 There will be a revision session before the exam at 8.30am in M And next Tuesday 31 st May Revision List for Higher Tier Mathematics Paper Below is a list of all the topics that have not yet been tested or that could be tested further to help you prepare for your next exam. Good luck * Percentages There will be lots of these!! Use your calculator don t work out 10% etc! e.g. Find 45% of 60 = 45 x 60 = e.g. Find percentage increase or decrease = increase/decrease x 100 ORIGINAL value e.g. Expressing one quantity as a percentage of another e.g. 60 marks as a percentage out of 75 e.g. working out sale prices (profit/loss), prices including VAT??* Compound interest (Grade C) e.g. The value of a car is Each year its value depreciates by 10%. Find the value of the car at the end of three years. e.g. Reverse % - finding the original amount (100%) BEFORE it was increased/reduced * Upper and lower bounds Remember if it involves + or x use the least or the greatest values, but if it involves or choose carefully as you will need one of each * GRAPHS: * Drawing straight line graphs Equations of a straight line y = mx + c, midpoint * Drawing cubic graphs and solving quadratic equations from a graph by drawing an appropriate line on the graph and find where the line cuts the curve (read off the x values) (A/A*). Also: finding the gradient of a curve by drawing a tangent to the point and constructing a 90 triangle and working out y and the area under a curve by working out the areas of trapeziums and triangles.; x * Recognise a reciprocal graph y = 1 x * Distance-time graphs and conversion graphs * Ratio Sharing into a given ratio, Finding some missing info given a ratio, Map scales, scale drawings * ALGEBRA: * Collecting and simplifying terms (including multiplying and dividing with indices) * Expanding brackets e.g. (x + 3)(x 5) to give a quadratic expression * Factorising Quadratics: brackets: Harder Trinomial (A*) e.g. 3x² + x - 14

2 *ALL types of solving equations including: * Equations involving brackets *Equations with or more fractions (grade B find the LCM first) * Simultaneous Equations * Solve quadratic equations by using the formula (given on formula sheet) x = - b + b² - 4ac a (don t forget to round answers to e.g. d.p.!!) - this question could be linked to showing that the equation formed is * Solve quadratic equations by factorising into 1 or brackets first * TRIAL and IMPROVEMENT?* Simplifying algebraic fractions (A/A*) - Express terms as a single fraction AND go onto solve an equation by factorising * Regions of inequality * Compound measures: * Converting metric units * Speed = Distance Time * Density = Mass problems (may involve parallelogram or triangle and also may involve Pythagoras!) Volume *Pythagoras and 3D Pythagoras (3 sides) * Trigonometry: * 90º triangles use SOH, CAH, TOA ( sides AND 1 angle) * Non 90º triangles use SINE rule ( sides and angles) and COSINE rule (3 sides and 1 angle) (A/A*) * Area of non 90º triangle = 1 absinc (A/A*) * Arc length = θ π D (A/A*) 360 * Area of sector = θ π r ² (A/A*) 360 * Remember: Area of segment = Area of sector Area of Triangle * 3D Trigonometry (A/A*)

3 * Rules of Indices e.g. 3a² x 5a³d as well as (A/A*) rules * Shapes and their properties including: * Nets of 3D shapes * Congruence of triangles (SSS, RHS, AAS, SAS) (A/A*) * Perimeter, Area and Volume: * Perimeter and area of shapes: rectangle ( Area = l x w), triangle (Area = 1 b x h ), compound shapes, trapezium (Area = 1 (a + b) x h ), parallelogram (Area = b x h), circle (Area = Π x r²) * Circumference (C = Π x D) * Volume of cuboid = l x w x h * Volume of prism = Area cross-section x length (Some formulae written in front of exam paper) Might link this with Density question * Converting metric measures e.g. km to m and also e.g. from m² to cm² ( x 10,000 ), cm² to mm² ( x 100) * Volume of spheres (and hemi-spheres), pyramids, cones etc. using formulae at front of exam paper * Similar triangles * Similar area and volume - Remember Area = scale factor² Volume = scale factor³ * Translations and Rotations * Loci * Angles * on a straight line = 180, at a point = 360, in a quadrilateral = 360, in a triangle = 180, in a parallelogram, kite etc. * in polygons: Sum of interior = (n-) x 180 where n = no. of sides, Exterior angles in ANY shape add up to 360 * Bearings * Probability: * Working out probabilities from a table of values or just simple probability (Total probability adds to 1) * Probability sample space diagram and EXPECTED number; relative frequency from graph * P(not happening) = 1 P(happening) * Independent events e.g. P(getting a 5 and a 6 when a die is rolled twice) = 1 x 1 = * Experimental probability (relative frequency) from a graph * Probability without replacement remember the denominator decreases by 1 each time

4 * Statistics: * Finding the mean (or estimate of the mean), median and mode from: raw data, data in a table (fx) or grouped data in a table (find midpoint then work out fx). Finding the modal class, median class interval from grouped data use f+1 th value * Frequency polygons heart beat monitor (Plot the MIDPOINTS) * Frequency diagrams bar chart with no gaps * Pie charts * Histograms drawing and interpreting * Questionnaires * Number work: * Currency conversions and exchange rates * Money problems * Electricity Bills and other household bills * Proportion e.g. 6 pens cost.70, how much do 10 pens cost? (First work out how much 1 costs then x by how many you need) * Reciprocals * Rounding numbers to nearest 10, 100, 1000 or to? significant figures or to? decimal places * Ordering/comparing numbers e.g fractions, decimals, percentages * ESTIMATION ALWAYS means you round to 1 significant figure first e.g. Estimate: 57 x 8 60 x 80 = 4800 = e.g. Estimate:.8 x x 4 = 1 = ?* Standard Form maybe a wordy question? * Using the calculator don t forget to press = before working out the bottom line! * Rounding the answer on the calculator display correct to a given number of decimal places?* Using word formulae e.g. Wage earned = hours worked x rate per hour. Find the wage earned if a man worked for 30 hours and was paid at a rate of 4.50 per hour. * Direct and Indirect Proportion (The fish sign!!) (A/A*) * Velocity graphs Acceleration = Gradient, Distance = Area under curve (Trapezium Rule)

5 EXAM TIPS Always write down any formulae used (several are written in the front of the exam paper!) and SHOW YOUR WORKINGS. Read each question TWICE and underline any key pieces of information Make sure you answer what the question asks watch UNITS (e.g. area, volume) and ACCURACY (when rounding). Money must have a OR p and be to decimal places Work out the scale on both axes of graphs BEFORE you start the question Write all angles or measurements you find on the diagram as you go along If there is no diagram drawn for a question about shapes, draw one Check if diagram drawn to scale, if not DO NOT use a protractor QWC question set out answer in a clear orderly way, watch your maths, spelling and grammar Remember the paper will be scanned by computer write all workings in the spaces provided only, do drawings in pencil and make sure minus signs and numbers are clear to read. Mistakes must be crossed or rubbed out so your final answer is clear Lastly.. BRING A CALCULATOR we do NOT have enough calculators to lend out for the whole exam, they will be shared out and you will lose valuable time in waiting your turn. Also you will NOT be shown how to use it!