Maths GCSE Guidelines for Success in this Subject

Transcription

1 Maths GCSE Guidelines for Success in this Subject Work without distractions, so no music or TV and don't answer any phone calls until the evening. Put any food or drink required on your desk so you re not constantly going to the kitchen. Check your syllabus so that you know what topics you need to cover. Make sure you know which tier you have been entered for - foundation or higher. Try to make your own notes and memorise important facts. You could write these on cards and stick them round your room. Find out which formulae are printed on your exam paper and which ones you have to learn. Go through your syllabus. Make a list of topics you have trouble with. Find some work on these topics - either ask your teacher, use your textbook, a GCSE revision book or a website such as the BBC Bitesize website. The mymaths website is very useful along with using calthx10 to login. The booster packs are great for revising all topics just select the level appropriate to you. Remember to use the lesson material; it is designed to help you without needing a teacher. Start with simple examples until you are sure you know what you are doing. Move on to more difficult examples. If you are doing the higher tier, use the foundation papers for some practise too. Use the revision guides, CGP or mathswatch DVDs which can be found on the year 11 maths page on the school website. Do the questions in the workbook or worksheet. It is the only way you can be really sure that you have mastered the skill. Work through past and practice papers from your teacher or website, or a revision book. Start with the school website and look at the practice papers in Maths Year 11. Some exam boards have sample papers on their websites. The best way to revise Maths is to practise!! Don't leave your revision to the last minute. Plan it well. Prepare a proper timetable. Attend the revision classes that your teachers have put in place for you. Use the revision resources that the maths teachers have put together lots of questions that are likely to come up! Break it down into sections and topics. You need strong foundations in basic Maths to build on. Make sure you have the correct equipment: 2 pens, 2 pencils, ruler (with scale visible), eraser, sharpener, compasses (that work and don't slip), protractor (360 ones are best, you can use them for measuring angles, scale drawings and bearings), scientific calculator (with new batteries in). Make sure you know how different functions like sin, cos, tan, square root work on your calculator. All calculators are slightly different, so practise with the one you plan to use rather than using, for example, the mymaths calculator. When you are allowed to start your exam, take a few minutes to settle down. Read the paper through carefully. Find a question you are comfortable with starting, even if it is near to the end of the paper. Read a question through, read it again and underline any important information, decide what calculation you need to carry out, show all your working, even if you are using a calculator; you get marks for your method if it is correct. Write your answer in the correct space and if necessary round the answer to an appropriate degree of accuracy. If questions say give reasons make sure you write a reason. Leave yourself enough time to thoroughly check your working answers.

2 Get More Marks Without Knowing Any More! 1) Write it down before it goes in your calculator. Show all stages in any calculations 2) Make sure you give the final answer as asked for in the question 3) Use the marks given to help you - if it is worth 3, as yourself if you have you done 3 marks of work 4) Don't cramp your working out, use all the space provided 5) Watch out for mixed units 6) Beware the calculator paper! (Still show your working out) 7) Make sure your calculator is in DEG mode 8) Don't measure diagrams if they are not to scale 9) Write down measuring units Conclusion If you practise and remember these nine simple steps, it is possible to prevent losing up to 10% of your exam marks needlessly. Good examination technique should be practised as part of GCSE Maths exam preparation and when revising the most essential exam questions and exam topics.

3 GCSE Maths watch clips: Can be found on the year 11 maths page on the school website Higher Tier Topics Grade A & A* Number Clip Shape Clip Recurring Decimals 155 Enlargement by negative scale factors 171 Fractional & negative indices 156 Equations of circles and loci 172 Surds 157 Sine & cosine rule 173 Rationalising the denominator 158 Pythagoras in 3D 174 Direct & indirect proportion 159 Trigonometry in 3D 175 Upper & lower bounds 160 Area of a triangle ½ ab Sin C 176 Cones & spheres 177 Segments of circles & frustums of cones 178 Algebra Congruent triangles 179 Vectors 180 Solving quadratics - formula 161 Solving quadratics completing the square 162 Data Handling Algebraic fractions 163 Rearranging complex formulae 164 Histograms 181 Simultaneous equations one linear & one non linear 165 Probability questions using And / Or questions 182 Gradients of parallel & perpendicular lines 166 Stratified sampling 183 Transformations of functions 167 Graphs of trig functions 168 Transformation of trig functions 169 Graphs of exponential functions 170

4 GCSE Maths watch clips: Can be found on the year 11 maths page on the school website Higher Tier Topics Grade B Number Clip Shape Clip Standard form calculations 135 Trigonometry SOH CAH TOA 147 % increase & decrease 136 Trigonometry & bearings 148 Compound interest & depreciation 137 Similarity 149 Reverse % 138 Circle Theorems 150 Four rules fractions 139 Algebra Data Handling Solving quadratics factorizing 140 Cumulative frequency 151 Difference of two squares 141 Boxplots 152 Simultaneous equations 142 Moving averages 153 Y = mx + c 143 Tree Diagrams 154 Regions 144 Graphs of cubics & reciprocal functions 145 Recognising the shapes of common graphs of functions 146

5 GCSE Maths watch clips: Can be found on the year 11 maths page on the school website Higher Tier Topics Grade C Number Clip Shape Clip Overview % 92 Pythagoras theorem 118 % increase/decrease 93 Pythagoras- line on a graph 119 Ratio 94 3-D Coordinates 120 Products of prime factors 95 Surface area of cuboids 121 HCF & LCM 96 Volume of a prism 122 Standard form 97 Similar Shapes 123 Recurring decimals to fractions 98 Dimensions 124 Four rules negative numbers 99 Bounds digit division 100 Compound Measures 126 Estimation 101 Bisecting a line 127 Drawing a perpendicular to line 128 Algebra Bisecting an angle Loci Algebraic simplification 102 Bearings 131 Expanding brackets 103 Factorisation 104 Solving equations 105 Forming equations 106 Data Handling Changing subject of a formula 107 Inequalities on a number line 108 Experimental Probabilities 132 Solving inequalities 109 Averages from a table 133 Trial and improvement 110 Designing a good questionnaire 134 Indices 111 Find the n th term 112 Drawing straight line graphs 113 Finding the equation of a straight line 114 Solving simultaneous equations graphically 115 Drawing quadratic graphs 116 Real-life graphs 117

6 GCSE Maths watch clips: Can be found on the year 11 maths page on the school website Higher Tier Topics Grade D Number Clip Shape Clip Factors, Multiples and Primes 44 Alternate Angles 67 Evaluate Powers 45 Angle sum of a triangle 68 Understanding squares, cubes and roots 46 Properties of special triangles 69 Equivalent fractions 47 Angles of regular polygons 70 Simplification of fractions 48 Area of circle 71 Ordering fractions 49 Circumference of a circle 72 Value for money 50 Area of compound shapes 73 Percentage of amount with a calculator 51 Rotations 74 Percentage of amount without a calculator 52 Reflections 75 Change to a % with a calculator 53 Enlargements 76 Change to a percentage without a 54 Translations 77 calculator Find a fraction of an amount 55 Find the mid-point of a line 78 Addition and subtraction of fractions 56 Measuring and drawing angles 79 Multiplication and division of fractions 57 Drawing triangles 80 Changing fractions to decimals 58 Plans and elevations 81 BODMAS 59 Nets 82 Long multiplication of decimals 60 Symmetries 83 Ratio 61 Proportion recipe type questions 62 Data Handling Hard calculator questions 63 Real-life money questions 64 Questionnaires & data collection 84 Two-way tables 85 Algebra Pie Charts 86 Scatter graphs 87 Generate a sequence to the nth term 65 Frequency Graphs 88 Substitution 66 Stem and leaf diagrams 89 List of outcomes 90 Mutually exclusive events 91

7 EDEXCEL LINEAR GCSE HIGHER CHECKLIST NUMBER Add, subtract, multiply and divide whole numbers integers and decimals Multiply and divide fractions Order integers and decimals Order rational numbers Use the concepts and vocabulary of factor (divisor), multiple, common factor, highest common factor, least common multiple, prime number and prime factor decomposition Use the terms square, positive and negative square root, cube and cube root Use index notation for squares, cubes and powers of 10 Use index laws for multiplication and division of integer powers Use index laws for multiplication and division of integer, fractional and negative powers Interpret, order and calculate with numbers written in standard index form Understand equivalent fractions, simplify a fraction by cancelling all common factors Add and subtract fractions Use decimal notation and recognise that each terminating decimal is a fraction Recognise that recurring decimals are exact fractions, and that some exact fractions are recurring decimals Understand that percentage means number of parts per 100 and use this to compare proportions Use percentage, repeated proportional change Understand and use direct and indirect proportion Interpret fractions, decimals and percentages as operators Use ratio notation, including reduction to its simplest form and its various links to fraction notation Understand and use number operations and the relationships between them, including inverse operations and hierarchy of operations Use in an exact calculation Calculations with surds Use surds in exact calculations Calculate upper and lower bounds

8 Divide a quantity in a given ratio Approximate to specified or appropriate degrees of accuracy including a given power of ten, number of decimal places and significant figures Use a calculator efficiently and effectively

9 EDEXCEL LINEAR GCSE HIGHER CHECKLIST ALGEBRA Distinguish the different roles played by letter symbols in algebra, using the correct notation Distinguish in meaning between the words equation, formula, identity and expression Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors, multiplying two linear expressions, factorise quadratic expressions including the difference of two squares and simplify rational expressions Set up and solve simple equations Set up and solve simple equations including simultaneous equations in two unknowns Solve quadratic equations Derive a formula, substitute numbers into a formula and change the subject of a formula Solve linear inequalities in one variable, and represent the solution set on a number line Solve linear inequalities in two variables, and represent the solution set on a coordinate grid Using systematic trial and improvement to find approximate solutions of equations where there is no simple analytical method of solving them Generate terms of a sequence using term-to-term and position to-term definitions of the sequence Use linear expressions to describe the NTH term of an arithmetic sequence Use the conventions for coordinates in the plane and plot points in all four quadrants, including using geometric information Recognise and plot equations that correspond to straight-line graphs in the coordinate plane, including finding gradients Understand that the form y = mx + c represents a straight line and that m is the gradient of the line and c is the value of the y - intercept Understand the gradients of parallel lines Find the intersection points of the graphs of a linear and quadratic function, knowing that these are the approximate solutions of the corresponding simultaneous equations representing the linear and quadratic functions Draw, sketch, recognise graphs of simple cubic functions, the reciprocal function y = with x 0, the function y = k for integer values of x and simple positive values of k, the trigonometric functions y = sin x and y = cos x Construct the graphs of simple LOCI Construct linear functions from real-life problems and plot their corresponding graphs

10 Construct linear, quadratic and other functions from real-life problems and plot their corresponding graphs Construct distance time graphs Discuss, plot and interpret graphs (which may be non-linear) modelling real situations Generate points and plot graphs of simple quadratic functions, and use these to find approximate solutions Direct and indirect proportion (algebraic) Transformation of functions

11 EDEXCEL LINEAR GCSE HIGHER CHECKLIST GEOMETRY Recall and use properties of angles at a point, angles on a straight line (including right angles), perpendicular lines, and opposite angles at a vertex Understand and use the angle properties of parallel lines, triangles and quadrilaterals Calculate and use the sums of the interior and exterior angles of polygons Recall the properties and definitions of special types of quadrilateral, including square, rectangle, parallelogram, trapezium, kite and rhombus Recognise reflection and rotation symmetry of 2-D shapes Understand congruence and similarity Use pythagoras theorem in 2-D and 3-D Use the trigonometric ratios and the sine and cosine rules to solve 2-D and 3-D problems Distinguish between centre, radius, chord, diameter, circumference, tangent, arc, sector and segment Understand and construct geometrical proofs using circle theorems Use 2-D representations of 3-D shapes Describe and transform 2-D shapes using single or combined rotations, reflections, translations, or enlargements by a positive, fractional or negative scale factor and distinguish properties that are preserved under particular transformations Use and interpret maps and scale drawings Understand and use the effect of enlargement for perimeter, area and volume of shapes and solids Interpret scales on a range of measuring instruments and recognise the inaccuracy of measurements Convert measurements from one unit to another Convert between volume measures, including cubic centimetres and cubic metres Make sensible estimates of a range of measures Understand and use bearing Understand and use compound measures Measure and draw lines and angles Draw triangles and other 2-D shapes using ruler and protractor Use straight edge and a pair of compasses to carry out constructions

12 Construct LOCI Calculate perimeters and areas of shapes made from triangles and rectangles or other shapes Calculate the area of a triangle using ab sin c Find circumferences and areas of circles Find surface area of a cylinder Calculate volumes of right prisms and shapes made from cubes and cuboids Solve mensuration problems involving more complex shapes and solids Use vectors to solve problems EDEXCEL LINEAR GCSE HIGHER CHECKLIST Statistics and Probability Understand and use statistical problem solving process/handling data cycle Identify possible sources of bias Design an experiment or survey Design data-collection sheets distinguishing between different types of data Extract data from printed tables and lists Design and use two-way tables for discrete and grouped data Produce charts and diagrams for various data types Calculate median, mean, range, quartiles and interquartile range, mode and modal class Interpret a wide range of graphs and diagrams and draw conclusions Look at data to find patterns and exceptions Recognise correlation and draw and/or use lines of best fit by eye, understanding what these represent Compare distributions and make inferences Understand and use the vocabulary of probability and probability scale Understand and use estimates or measures of probability from theoretical models (including equally likely outcomes), or from relative frequency List all outcomes for single events, and for two successive events, in a systematic way and derive relative probabilities Identify different mutually exclusive outcomes and know that the sum of the probabilities of all these outcomes is 1

13 Know when to add or multiply two probabilities: when A and B are mutually exclusive, then the probability of A or B occurring is P (A) + P (B), whereas when A and B are independent events, the probability of A and B occurring is P (A) + P (B), Use tree diagrams to represent outcomes of compound events, recognising when events are independent Compare experimental data and theoretical probabilities Understand that if they repeat an experiment, they may, and usually will, get different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics Use calculators efficiently and effectively, including statistical functions