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Bindley: Foundation GCSE Mathematics Revision and Practice Bindley: Foundation GCSE Mathematics Revision and Practice AQA GCSE Mathematics Specification B Foundation Tier Module 1 Ma4: Handling Data 1 Using and applying handling data Problem solving Pupils should be taught to: 4F1a carry out each of the four aspects of the handling General data data cycle to solve problems: handling units1,2,3,4 i) specify the problem and plan: formulate questions in General data terms of the data needed, and consider what handling inferences can be drawn from the data; decide what units1,2,3,4 data to collect (including sample size and data format) and what statistical analysis is needed. ii) collect data from a variety of suitable sources, General data including experiments and surveys, and primary and handling secondary sources units1,2,3,4 iii) process and represent the data: turn the raw data into General data usable information that gives insight into the handling problem units1,2,3,4 iv) interpret and discuss: answer the initial question by General data drawing conclusions from the data handling units1,2,3,4 4F1b identify what further information is needed to pursue General a particular line of enquiry 4F1c select and organise the appropriate mathematics and General resources to use for a task 4F1d review progress while working; check and evaluate General solutions Communicating 4F1e interpret, discuss and synthesise information General presented in a variety of forms - 1- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice 4F1f communicate mathematically, including using ICT, General making use of diagrams and relating explanatory text Reasoning 4F1h apply mathematical reasoning, explaining inferences General and deductions 4F1I explore connections in mathematics and look for General cause and effect when analysing data 2 Specifying the problem and planning Pupils should be taught to: 4F2a see that random processes are unpredictable 406-424 4F2b identify questions that can be addressed by statistical 57-58 methods 4F2c discuss how data relate to a problem 57-58 4F2d identify which primary data they need to collect and 57-59, 333-337 in what format, including grouped data, considering appropriate equal class intervals 4F2e design an experiment or survey; decide what 57-58 secondary data to use 3 Collecting data 4F3a design and use data-collection sheets for grouped 57-58, 333-335 discrete and continuous data; collect data using various methods, including observation, controlled experiment, data logging, questionnaires and surveys 4F3b gather data from secondary sources, including Provided in the printed tables and lists from ICT-based sources text 4F3c design and use two-way tables for discrete and 141 grouped data 4 Processing and representing data - 2- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice 4F4a draw and produce, using paper and ICT, pie charts 141, 333-346, for categorical data and diagrams for continuous 377-381 data, including line graphs (time series), scatter graphs, frequency diagrams and stem-and-leaf diagrams 4F4b calculate mean, range and median of small data sets 135-154 with discrete and then continuous data; identify the modal class for grouped data 4F4c understand and use the probability scale 412-413 4F4d understand and use estimates or measures of 406-424 probability from theoretical models (including equally likely outcomes) 4F4e list all outcomes for single events, and for two 406-424 successive events, in a systematic way 4F4f identify different mutually exclusive outcomes and 410-411 know that the sum of the probabilities of all these outcomes is 1 4F4h draw lines of best fit by eye, understanding what 381 these represent 5 Interpreting and discussing results Pupils should be taught to: 4F5a relate summarised data to the initial questions General to all data handling units 4F5b interpret a wide range of graphs and diagrams and General to all draw conclusions data handling units 4F5c look at data to find patterns and exceptions General to all data handling units 4F5d compare distributions and make inferences, using General to all the shapes of distributions and measure of average data handling and rang units 4F5e consider and check results and modify their approach if necessary 4F5f have a basic understanding of correlation as a 374-385 measure of the strength of the association between two variables; identify correlation or no correlation - 3- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice using lines of best fit 4F5g use the vocabulary of probability to interpret results 406-424 involving uncertainty and prediction 4F5h compare experimental data and theoretical Classwork possibilities 4F5i understand that if they repeat an experiment, they Classwork may – and usually will – get different outcomes, and that increasing sample size generally leads to better estimates of probability and population characteristics 4F5j discuss implications of findings in the context of the General problem 4F5k interpret social statistics including index numbers 343 Q.2 [for example, the General Index of Retail Prices]; time series [for example, population growth]; and survey data [for example, the National Census] Module 2 Ma4: Handling Data 1 Using and applying handling data Problem solving Pupils should be taught to: 4F1a carry out each of the four aspects of the handling General data data cycle to solve problems: handling units1,2,3,4 i) specify the problem and plan: formulate questions in General data terms of the data needed, and consider what handling inferences can be drawn from the data; decide what units1,2,3,4 data to collect (including sample size and data format) and what statistical analysis is needed. ii) collect data from a variety of suitable sources, General data including experiments and surveys, and primary and handling secondary sources units1,2,3,4 iii) process and represent the data: turn the raw data into General data usable information that gives insight into the handling problem units1,2,3,4 iv) interpret and discuss: answer the initial question by General data drawing conclusions from the data handling units1,2,3,4 - 4- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice 4F1b identify what further information is needed to pursue General a particular line of enquiry 4F1c select and organise the appropriate mathematics and General resources to use for a task 4F1d review progress while working; check and evaluate General solutions Communicating 4F1e interpret, discuss and synthesise information General presented in a variety of forms 4F1f communicate mathematically, including using ICT, General making use of diagrams and relating explanatory text Reasoning 4F1h apply mathematical reasoning, explaining inferences General and deductions 4F1I explore connections in mathematics and look for General cause and effect when analysing data Module 3 Ma2 Number and algebra 1 Using and applying number and algebra Problem solving Pupils should be taught to: 2F1a select and use suitable problem solving strategies General. All and efficient techniques to solve numerical and number and algebraic problems algebra sections plus area and volume sections 2F1b break down a complex calculation into simpler steps General as before attempting to solve it above 2F1c use algebra to formulate and solve a simple problem 226-237 – identifying the variable, setting up an equation, solving the equation and interpreting the solution in the context of the problem 2F1d make mental estimates of the answers to 12-14, 78-81, calculations; use checking procedures, including use 166-167, 169- of inverse operations; work to stated levels of 170, 206, 211, - 5- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice accuracy 212 Communicating 2F1e interpret and discuss numerical and algebraic General information presented in a variety of forms 2F1g use a range of strategies to create numerical, General algebraic or graphical representations of a problem and its solution 2F1h present and interpret solutions in the context of the General original problem 2F1f use notation and symbols correctly and consistently General within a given problem Reasoning 2F1j explore, identify, and use pattern and symmetry in algebraic contexts [for example, using simple codes that substitute numbers for letters], investigating whether particular cases can be generalised further, and understanding the importance of a counter- example 2F1k show step-by-step deduction in solving a problem General 2 Numbers and the number system Integers Pupils should be taught to 2F2a use their previous understanding of integers and 1-33, 87-89 place value to deal with arbitrarily large positive numbers and round them to a given power of 10; understand and use positive numbers, both as positions and translations on a number line; order integers; use the concepts and vocabulary of factor (divisor), multiple and common factor Powers and roots 2F2b use the terms, square, positive square root, cube; use 95, 112 index notation for squares, cubes and powers of 10 Fractions 2F2c understand equivalent fractions, simplifying a 243-249 fraction by cancelling all common factors; order fractions by rewriting them with a common denominator - 6- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice Decimals 2F2d use decimal notation and recognise that each 255 terminating decimal is a fraction [for example, 0.137 137 = 1000 ]; order decimals Percentages 2F2e understand that ‘percentage’ means ‘number of parts 252, 253-255 per 100’ and use this to compare proportions; interpret percentage as the operator ‘so many hundredths of’ [for example, 10% means 10 parts per 100, and 15% of Y means 100 × Y]; use 15 percentage in real life situations [for example, commerce and business, including rate of inflation, VAT and interest rates] Ratio 2F2f use ratio notation, including reduction to its simplest 89-95 form and its various links to fraction notation [for example, in maps and scale drawings, paper sizes and gears] 3 Calculations Number operations and the relationships between them Pupils should be taught to: 2F3a add, subtract, multiply and divide integers and then 1-33, 70-102, any number; multiply or divide any number by 206 powers of 10, and any positive number by a number between 0 and 1 2F3b use brackets and the hierarchy of operations 2F3c calculate a given fraction of a given quantity [for 241-242, 247- example, for scale drawings and construction of 249, 250, 255 models, down payments, discounts], expressing the answer as a fraction; express a given number as a fraction of another; add and subtract fractions by writing them with a common denominator; perform short division to convert a simple fraction to a decimal 2F3d understand and use unit fractions as multiplicative 250-251 inverses (for example, by thinking of multiplication by 1 as division by 5]; multiply and divide a fraction 5 by an integer, and multiply a fraction by a unit - 7- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice fraction 2F3e convert simple fractions of a whole to percentages of 256-257 the whole and vice versa [for example, analysing diets, budgets or the costs of running, maintaining and owning a car] 2F3f divide a quantity in a given ratio [for example, share 93-95 £15 in the ratio of 1:2] Mental methods 2F3g recall all positive integer complements to 100 [for 1-33, 70-102 example, 37 + 63 = 100]; recall all multiplication facts to 10×10, and use them to derive quickly the corresponding division facts; recall the cubes of 2, 3, 4, 5 and 10, and the fraction-to-decimal conversion of familiar fractions [for example, 1 1 1 1 , , , , 1 , 1, 2, 1 ] 2 4 5 10 100 3 3 8 2F3h round to the nearest integer and to one significant 10, 163 figure; estimate answers to problems involving decimals 2F3i develop a range of strategies for mental calculation; 1-33, 70-102, derive unknown facts from those they know [for 155-175, 198- example, estimate 85 ]; add and subtract mentally 219 numbers with up to two decimal places [for example, 13.76 – 5.21, 20-08 + 12.4]; multiply and divide numbers with no more than one decimal digit [for example, 14.3 × 4, 56.7 ÷ 7] using the commutative, associative, and distributive laws and factorisation where possible, or place value adjustments Written methods 2F3j use standard column procedures for addition and 17-19, 168, 170 subtraction of integers and decimals 2F3k use standard column procedures for multiplication of 82-83, 207 integers and decimals, understanding where to position the decimal point by considering what happens if they multiply equivalent fractions 2F3l use efficient methods to calculate with fractions, 246-250 including cancelling common factors before carrying out the calculation, recognising that, in many cases, only a fraction can express the exact answer 2F3m solve simple percentage problems, including 253-258 percentage increase and decrease [for example, - 8- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice VAT, annual rate of inflation, income tax, discounts] 2F3n solve word problems about ratio and proportion, 91-95 including using informal strategies and unitary method of solution [for example, given that m y identical items cost £y, then one item costs £ m and n ( items cost £ n× y m ) , the number of items that can be bought for £z is z × m y ] Calculator methods 2F3o use calculators effectively; know how to enter complex calculations and use function keys for reciprocals, squares and powers 2F3p enter a range of calculations, including those involving measures [for example, time calculations in which fractions of an hour must be entered as fractions or as decimals] 2F3q understand the calculator display, interpreting it 211-212 correctly [for example, in money calculations, or when the display has been rounded by the calculator] and knowing not to round during the intermediate steps of a calculation 4 Solving numerical problems 2F4a draw on their knowledge of the operations and the Number relationships between them, and of simple integer sections 1-5 powers and their corresponding roots, to solve problems involving ratio and proportion, a range of measures including speed, metric units, and conversion between metric and common imperial units, set in a variety of contexts 2F4b select appropriate operations, methods and strategies 96 to solve number problems, including trial and improvement where a more efficient method to find the solution is not obvious 2F4c use a variety of checking procedures, including working the problem backwards, and considering whether a result is of the right order of magnitude 2F4d give solutions in the context of the problem to an 211-212 appropriate degree of accuracy, interpreting the solution shown on a calculator display, and recognising limitations on the accuracy of data and - 9- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice measurements 5 Equations, formulae and identities Use of symbols Pupils should be taught to: 2F5a distinguish the different roles played by letter Algebra 1 103- symbols in algebra, knowing that letter symbols 124 represent definite unknown numbers in equations [for example, 5x + 1 = 16], defined quantities or variables in formulae [for example, V = IR], general, unspecified and independent numbers in identities [for example, 3x + 2x = 5x, for all values of x] and in functions they define new expression or quantities by referring to known quantities [for example, y = 2x] 2F5b understand that the transformation of algebraic Algebra 2 220- expressions obeys and generalises the rules of 240 arithmetic; manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out single term common factors [for example, x + 5 – 2x – 1 = 4 – x; 5(2x + 3) = 10x + 15; x2 + 3x = x(x +3)] Module 4 Ma2 Number and algebra 1 Using and applying number and algebra Problem solving Pupils should be taught to: 2F1a select and use suitable problem solving strategies General. All and efficient techniques to solve numerical and number and algebraic problems algebra sections plus area and volume sections 2F1b break down a complex calculation into simpler steps General as before attempting to solve it above 2F1c use algebra to formulate and solve a simple problem 226-237 – identifying the variable, setting up an equation, solving the equation and interpreting the solution in - 10- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice the context of the problem 2F1d make mental estimates of the answers to 12-14, 78-81, calculations; use checking procedures, including use 166-167, 169- of inverse operations; work to stated levels of 170, 206, 211, accuracy 212 Communicating 2F1e interpret and discuss numerical and algebraic General information presented in a variety of forms 2F1g use a range of strategies to create numerical, General algebraic or graphical representations of a problem and its solution 2F1h present and interpret solutions in the context of the General original problem 2F1f use notation and symbols correctly and consistently General within a given problem Reasoning 2F1j explore, identify, and use pattern and symmetry in algebraic contexts [for example, using simple codes that substitute numbers for letters], investigating whether particular cases can be generalised further, and understanding the importance of a counter- example 2F1k show step-by-step deduction in solving a problem General Ma3: Shape, space and measures 1 Using and applying shape, space and measures Problem solving Pupils should be taught to: 3F1a select problem-solving strategies and resources, General including ICT tools, to use in geometrical work, and monitor their effectiveness 3F1b select and combine known facts and problem- General solving strategies to solve complex problems 3F1c identify what further information is needed to solve General a geometrical problem; break complex problems down into a series of tasks Communicating - 11- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice 3F1d interpret, discuss and synthesise geometrical General information presented in a variety of forms 3F1e communicate mathematically, by presenting and General organising results and explaining geometrical design 3F1f use geometrical language appropriately General Reasoning 3F1i apply mathematical reasoning, explaining and General justifying inferences and deductions 3F1j show step-by-step deduction in solving a General geometrical problem Module 5 Ma 2: Number and Algebra 1. Using and appying number and algebra Problem solving Pupils should be taught to: 2F1a select and use suitable problem solving strategies General. All and efficient techniques to solve numerical and number and algebraic problems algebra sections plus area and volume sections 2F1b break down a complex calculation into simpler steps General as before attempting to solve it above 2F1c use algebra to formulate and solve a simple problem 226-237 – identifying the variable, setting up an equation, solving the equation and interpreting the solution in the context of the problem 2F1d make mental estimates of the answers to 12-14, 78-81, calculations; use checking procedures, including use 166-167, 169- of inverse operations; work to stated levels of 170, 206, 211, accuracy 212 Communicating 2F1e interpret and discuss numerical and algebraic General information presented in a variety of forms 2F1g use a range of strategies to create numerical, General algebraic or graphical representations of a problem and its solution - 12- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice 2F1h present and interpret solutions in the context of the General original problem 2F1f use notation and symbols correctly and consistently General within a given problem Reasoning 2F1j explore, identify, and use pattern and symmetry in algebraic contexts [for example, using simple codes that substitute numbers for letters], investigating whether particular cases can be generalised further, and understanding the importance of a counter- example 2F1k show step-by-step deduction in solving a problem General 2 Numbers and the number system Integers Pupils should be taught to 2F2a use their previous understanding of integers and 1-33, 87-89 place value to deal with arbitrarily large positive numbers and round them to a given power of 10; understand and use positive numbers, both as positions and translations on a number line; order integers; use the concepts and vocabulary of factor (divisor), multiple and common factor Powers and roots 2F2b use the terms, square, positive square root, cube; use 95, 112 index notation for squares, cubes and powers of 10 Fractions 2F2c understand equivalent fractions, simplifying a 243-249 fraction by cancelling all common factors; order fractions by rewriting them with a common denominator Decimals 2F2d use decimal notation and recognise that each 255 terminating decimal is a fraction [for example, 0.137 137 = 1000 ]; order decimals Percentages 2F2e understand that ‘percentage’ means ‘number of parts 252, 253-255 per 100’ and use this to compare proportions; - 13- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice interpret percentage as the operator ‘so many hundredths of’ [for example, 10% means 10 parts per 100, and 15% of Y means 100 × Y]; use 15 percentage in real life situations [for example, commerce and business, including rate of inflation, VAT and interest rates] 3 Calculations Number operations and the relationships between them Pupils should be taught to: 2F3a add, subtract, multiply and divide integers and then 1-33, 70-102, any number; multiply or divide any number by 206 powers of 10, and any positive number by a number between 0 and 1 2F3b use brackets and the hierarchy of operations Mental methods 2F3g recall all positive integer complements to 100 [for 1-33, 70-102 example, 37 + 63 = 100]; recall all multiplication facts to 10×10, and use them to derive quickly the corresponding division facts; recall the cubes of 2, 3, 4, 5 and 10 Calculator methods 2F3o use calculators effectively; use function keys for reciprocals, squares and powers 4 Solving numerical problems 2F4a Pupils should be taught to: Number Sections 1-5 draw on their knowledge of simple integer powers and their corresponding roots, to solve problems 5 Equations, formulae and identities Use of symbols Pupils should be taught to: 2F5a distinguish the different roles played by letter Algebra 1 103- symbols in algebra, knowing that letter symbols 124 represent definite unknown numbers in equations [for example, 5x + 1 = 16], defined quantities or variables in formulae [for example, V = IR], general, unspecified and independent numbers in identities - 14- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice [for example, 3x + 2x = 5x, for all values of x] and in functions they define new expression or quantities by referring to known quantities [for example, y = 2x] 2F5b understand that the transformation of algebraic Algebra 2 220- expressions obeys and generalises the rules of 240 arithmetic; manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out single term common factors [for example, x + 5 – 2x – 1 = 4 – x; 5(2x + 3) = 10x + 15; x2 + 3x = x(x +3)] Index notation 2F5c use index notation for simple integer powers; 112-114 substitute positive and negative numbers into expressions such as 3x2 + 4 and 2x3 Linear equations 2F5e solve linear equations, with integer coefficients, in 226-233 which the unknown appears on either side or on both sides of the equation; solve linear equations that require prior simplification of brackets, including those that have negative signs occurring anywhere in the equation, and those with a negative solution Formulae 2F5f use formulae from mathematics and other subjects 107-117 expressed initially in words and then using letters and symbols [for example, formulae for the area of a triangle, the area enclosed by a circle, wage earned = hours worked × rate per hour]; substitute numbers into a formula; derive a formula [for example, convert temperatures between degrees Fahrenheit and degrees Celsius, find the perimeter of a rectangle given its area A and the length l of one side] 6 Sequences, functions and graphs Sequences Pupils should be taught to: 2F6a generate terms of a sequence using term-to-term and 269-273 position-to-term definitions of the sequence Graphs of linear functions - 15- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice 2F6b use the conventions for coordinates in the plane; plot 276-291 points in all four quadrants; plot graphs of functions in which y is given explicitly in terms of x [for example, y = 2x + 3), or implicitly [for example, x + y = 7] 2F6c construct linear functions from real life problems 291-297 and plot their corresponding graphs; discuss and interpret graphs arising from real situations Interpret graphical information 2F6e interpret information presented in a range of linear 291-297 and non-linear graphs [for example, graphs describing trends, conversion graphs, distance-time graphs, graphs of height or weight against age, graphs of quantities that vary against time, such as employment] - 16- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice Ma3: Shape, space and measures 1 Using and applying shape, space and measures Problem solving Pupils should be taught to: 3F1a select problem-solving strategies and resources, General including ICT tools, to use in geometrical work, and monitor their effectiveness 3F1b select and combine known facts and problem- General solving strategies to solve complex problems 3F1c identify what further information is needed to solve General a geometrical problem; break complex problems down into a series of tasks Communicating 3F1d interpret, discuss and synthesise geometrical General information presented in a variety of forms 3F1e communicate mathematically, by presenting and General organising results and explaining geometrical design 3F1f use geometrical language appropriately General Reasoning 3F1i apply mathematical reasoning, explaining and General justifying inferences and deductions 3F1j show step-by-step deduction in solving a General geometrical problem 2 Geometrical reasoning Angles Pupils should be taught to: 3F2a recall and use properties of angles at a point, angles 177-179 on a straight line (including right angles), perpendicular lines, and opposite angles at a vertex 3F2b distinguish between acute, obtuse, reflex and right 38, 39 angles; estimate the size of an angle in degrees Properties of triangles and other rectilinear shapes - 17- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice 3F2c use parallel lines, alternate angles and corresponding 180-181 angles; understand the consequent properties of parallelograms and a proof that the angle sum of a triangle is 180 degrees; understand a proof that the exterior angle of a triangle is equal to the sum of the interior angles at the other two vertices 3F2d use angle properties of equilateral, isosceles and 181-184, 189- right-angled triangles; understand congruence; 190 explain why the angle sum of any quadrilateral is 360 degrees 3F2e use their knowledge of rectangles, parallelograms 363, 365 and triangles to deduce formulae for the area of a parallelogram, and a triangle, from the formula for the area of a rectangle 3F2f recall the essential properties of special types of 184-186 quadrilateral, including square, rectangle, parallelogram, trapezium and rhombus; classify quadrilaterals by their geometric properties 3F2g calculate and use the sums of the interior and 187-190 exterior angles of quadrilaterals, pentagons and hexagons; calculate and use the angles of regular polygons Properties of circles 3F2i recall the definition of a circle and the meaning of 387 related terms, including centre, radius, chord, diameter, circumference, tangent and arc; understand that inscribed regular polygons can be constructed by equal division of a circle 3-D shapes 3F2j explore the geometry of cuboids (including cubes), 125-134 and shapes made from cuboids 3F2k use 2-D representations of 3-D shapes and analyse 125-134 3-D shapes through 2-D projections and cross- sections, including plain and elevation 3 Transformations and coordinates Specifying transformations Pupils should be taught to: 3F3a understand that rotations are specified by a centre Shape and and an (anticlockwise) angle; rotate a shape about - 18- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice the origin; measure the angle of rotation using right Space 4 angles or simple fractions of a turn; understand that reflections are specified by a mirror line, at first 307-331 using a line parallel to an axis; understand that translations are specified by a distance and direction, and enlargements by a centre and positive scale factor Properties of transformations 3F3b recognise and visualise rotations, reflections and Shape and translations, including reflection symmetry of 2-D Space 4 and 3-D shapes, and rotation symmetry of 2-D shapes; transform triangles and other 2-D shapes by 307-318 translation, rotation and reflection, recognising that these transformations preserve length and angle, so that any figure is congruent to its image under any of these transformations 3F3c recognise, visualise and construct enlargements of 321-324 objects using positive scale factors greater than one; understand from this that any two circles and any two squares are mathematically similar, while, in general, two rectangles are not 3F3d recognise that enlargements preserve angle but not 45-47, 321-324 length; identify the scale factor of an enlargement as the ratio of the lengths of any two corresponding line segments and apply this to triangles; understand the implications of enlargement for perimeter; use and interpret maps and scale drawings Coordinates 3F3e understand that one coordinate identifies a point on a 276-281 number line, two coordinates identify a point in a plane and three coordinates identify a point in space, using the terms ‘1-D’, ‘2-D’ and ‘3-D’; use axes and coordinates to specify points in all four quadrants; locate points with given coordinates; find the coordinates of points identified by geometrical information [for example, find the coordinates of the fourth vertex of a parallelogram with vertices at (2 1) (-7, 3) and (5, 6)]; find the coordinates of the midpoint of the line segment AB, given points A and B 4 Measures and construction Measures - 19- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice Pupils should be taught to: 3F4a interpret scales on a range of measuring instruments, Number 4 including those for time and mass; convert measurements from one unit to another; know rough 198-219 metric equivalents of pounds, feet, miles, pints and gallons; make sensible estimates of a range of measures in everyday settings 3F4b understand angle measure using the associated Shape and language [for example, use bearings to specify Space 1 direction] 34-55 3F4c understand and use speed 295-297 3F4d measure and draw lines to the nearest millimetre, 37-51, 125-128 and angles to the nearest degree; draw triangles and other 2-D shapes using a ruler and protractor, and given information about their side lengths and angles; understand, from their experience of constructing them, that triangles satisfying SSS, SAS, ASA and RHS are unique, but SSA triangles are not; construct cubes, regular tetrahedra, square- based pyramids and other 3-D shapes from given information 3F4e use a straight edge and compasses to do standard 43-51 constructions, including an equilateral triangle with a given side Mensuration 3F4f find areas of rectangles, recalling the formula, Shape and understanding the connection to counting squares Space 5 and how it extends this approach; recall and use the formulae for the area of a parallelogram and a 355-373, triangle; find the surface area of simple shapes using 393-394 the area formulae for triangles and rectangles; calculate perimeters and areas of shapes made from triangles and rectangles 3F4g find volumes of cuboids, recalling the formula and 395-400 understanding the connection to counting cubes and how it extends this approach; calculate volumes of shapes made from cubes and cuboids 3F4h find circumferences of circles and areas enclosed by 387-392 circles, recalling relevant formulae 3F4i convert between area measures, including cm2 and 361, 398 m2, and volume measures, including cm3 and m3 - 20- AQA Maths B GCSE Foundation 2003 Bindley: Foundation GCSE Mathematics Revision and Practice - 21- AQA Maths B GCSE Foundation 2003

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gcse mathematics, gcse maths, foundation tier, maths exam, mark scheme, mark schemes, gcse maths revision, exam practice, exam-style questions, practice workbook, easy learning, andrew manning, steve lomax, margaret thornton, mark willis

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