- number of elements - complement linear, simple quadratic and cubic sequences - exponential sequences and - simple combinations of these

Transcription

1 IGCSE Mathematics Revision checklist Syllabus 1 Numbers, set notation and language 1 Identify and use: - natural s - prime s - square s - common factors (HCF) - common multiples (LCM) - rational s - irrational s - real s 1 Sequences 15 - Continue a sequence - Find the nth term of an arithmetic sequence 2 Squares and cubes 1 Calculate: - squares / square roots - cubes / cube roots 3 Directed s 1 - Use directed s in practical situations 4 Fractions and percentages 4 - Use the language and notation of simple vulgar and decimal fractions - convert between simple vulgar and decimal fractions 5 Ordering 3 - ordering quantities by magnitude - know and use symbols =,, <, >,, 6 Standard form 7 - Use the standard form A x 10 n 7 The four rules 4 - Use the four rules for calculations including: - ordering of operations - use of brackets 8 Estimation 2 Makes estimates of: - s - quantities - lengths 8 Approximations and rounding 2 - Give approximations to specified of: - significant figures - decimal places 9 Limits of accuracy 2 - Give appropriate upper and lower bounds of data given to a specified accuracy (e. g. measured length) 10 Ratio 6 - Understand elementary idea and notation of ratio - Divide a quantity in a given ratio 10 Represent sets using - language - Venn diagrams - set notation,,, U,,,,, - of elements - complement 15 - linear, simple quadratic and cubic sequences - exponential sequences and - simple combinations of these 4 - convert recurring decimals to fractions 2 - Obtain appropriate upper and lower bouds to solutions of simple problems (area, perimeter) 1

2 10 Proportion, rate 6 - Understand: - direct proportion - inverse proportion - common measures of rate - map scales - Calculate average speed 11 Percentages 5 - Calculate percentage of a quantity - Express one quantity as a percentage of another - Calculate percentage increase/ decrease 12 Use of a calculator - Use an electronic calculator efficiently - apply appropriate checks of accuracy 13 Measures 26 Use (in practical situations) units of - mass - length - area - volume - capacity Express quantities in terms of larger or smaller units 14 Time 9 Calculate times in terms of the - 24-hour clock - 12-hour clock Read - clocks - dials - timetables 15 Money 8 - Calculate using money 16 Personal and household finance 17 Graphs in practical situations - Convert from one currency to another 8 - simple interest - compound interest - discount - profit and loss 17 - Cartesian co-ordinates - travel graphs - conversion graphs - drawing graphs from given data 18 Linear functions 18 - construct tables of values - draw graphs - interpret graphs - find the gradient of a straight line graph - solve linear equations approximately by graphical method 16 - Express, in algebraic terms: - direct variation - inverse variation - Increase/ decrease a quantity by a given ratio 5 - reverse percentages (finding the cost price given the selling price and percentage profit) 8 - knowledge of compound interest formula 17 - distance-time graphs - speed-time graphs - acceleration - deceleration - distance travelled (as an area under a graph) 2

3 18 Quadratic functions 18 Exponential functions 19 Straight line graphs 18 - construct tables of values - draw graphs - interpret graphs - solve quadratic equations approximately by graphical method 28 - obtain the equation of a straight line graph in the form y = mx + c - determine the equation of a straight line parallel to a given line 18 - construct tables of values and draw graphs for functions ax n, aєr, n є { 2, 1, 0, 1, 2, 3} - draw tangent to estimate gradient of curve - solve associated equations approximately by graphical method - growth and decay (related to population and finance) 28 - calculate the gradient from the 2 points on a straight line - calculate the length of a segment - calculate the co-ordinates of midpoints - find the gradient of parallel and perpendicular lines 20 Algebraic representation 11 - use letters to express generalised s - express basic arithmetic processes algebraically 11 Construct and transform more complicated equations 20 Formulae 11 - substitute s for words and letters in formulae 11 Construct and transform more complicated formulae 21 Algebraic manipulation 11 - manipulate directed s - use brackets - extract common factors 11 - expand products of algebraic expressions - factorise more complicated expressions - manipulate algebraic fractions - factorise and simplify expressions 22 Functions 19 - Use function notation - describe inverse function - form composite functions 23 Indices 7 Use and interpret - positive indices - negative indices - zero indices 24 Solutions of equations and inequalities 25 Linear programming 13 Solve - simple linear equations - simultaneous equations (two unknowns) 12 - Use and interpret fractional indices - Solve simple exponential equation - The rules of indices 13 Solve quadratic equations by: - factorisation - completing the square - use of the formula Solve simple linear inequalities 14 Represent inequalities graphically Solve simple linear programming problems - broken line for strict inequalities - shading unwanted region 3

4 26 Geometrical terms and relationships 26 Geometrical terms and relationships 27 Geometrical constructions Use and interpret terms: - point - line - parallel - bearing 20 Use and interpret terms: - right/ acute/ obtuse angle - reflex angle - perpendicular - similarity Vocabulary of - triangles - quadrilaterals - circles - polygons - simple solid figures (and nets) 21 Measure - lines - angles Construct simple geometrical figures using: - ruler - pair of compasses - protractor Construct - angle bisectors - perpendicular bisectors Read and make scale drawings 28 Symmetry 23 Recognise symmetry in two dimensions: - rotational symmetry (including its order) - line symmetry 22 - relationships between: - areas of similar triangles - areas and lengths of similar figures - surface areas of similar solids - volumes of similar solids 23 Recognise symmetry properties of prism (including cylinder) Use the symmetry properties of circle: - equal chords are equidistant from the centre - perpendicular bisector of a chord passes through centre - tangents from an external point are equal in length 4

5 29 Angle properties 24 Calculate unknown angles using angle(s): - at a point - at a point on a straight line and intersecting lines - formed within parallel lines - properties of - triangles - quadrilaterals - polygons - in a semi-circle - between tangent and radius 30 Locus 25 Using the following loci: - at a given distance from - a given point - a given straight line - equidistant from - 2 given points - 2 intersecting lines 31 Mensuration 27 Calculating the perimeter and area of - triangle - rectangle - parallelogram - trapezium - circle (circumference) Calculating the volume and surface area of a: - cuboid - prism - cylinder 32 Trigonometry 30 - Pythagoras theorem - Calculate the side or an angle using ratios for acute angles: - sine - cosine - tangent (angles in degrees and decimals to 1 dp) 35 Vectors 32 Describe a translation by using vector - add and subtract vectors - multiply a vector by a scalar 24 Use the following geometrical properties: - Angle properties of irregular polygons - Angle at the centre of a circle is twice the angle at the circumference - Angles in the same segment are equal - Angles in opposite segments are supplementary - Cyclic quadrilaterals 27 Solve problems involving - the arc length - sector area - surface area and volume of a - sphere - pyramid - cone Solving problems that include: - angles of elevation - angles of depression - sine rule - cosine rule - formula for the area of a triangle - 3D: angle between a line and a plane 32 - calculate the magnitude - represent vectors by directed line segments - use position vectors - use the sum and difference of 2 vectors to express given vectors 5

6 33 Statistics Collect, classify and tabulate data - Read, interpret and draw simple inferences from tables and diagrams - Construct and use: - bar charts - pie charts - pictograms - frequency distribution - histograms (equal intervals) - scatter graphs (line of best fit) Understand correlation Calculate the: - mean - median - mode - range 34 Probability 35 Calculate the probability of a single event Use the probability scale from 0 to 1 Probability of an event not happening Construct and read - histograms with - equal intervals - unequal intervals - cumulative frequency diagrams Estimate and interpret: - the median - percentiles - quartiles - inter-quartile range - mean of the - grouped data - continuous data Identify the modal class from a grouped frequency distribution 36 Calculate the probability of combined events using: - possibility diagrams - tree diagrams 36 Matrices 33 - display information in a form of a matrix Calculate - the sum of two matrices - the product of two matrices - the product of a matrix and a scalar - the determinant - the inverse matrix 37 Transformations 34 Reflect simple plane figures in - horizontal line - vertical line Rotate simple plane figures -about: - the origin - vertices - midpoints of edges - through multiples of 90 o Construct given - translations - enlargements 34 Use the following transformations of a plane: - reflection (M) - rotation (R) - translation (T) - enlargement (E) with positive, fractional and negative scale factors - and their combinations Identify and give precise description of transformations connecting given figures Describe transformations using: - coordinates - matrices 6