AQA GCSE Mathematics Specification A

Document Sample
AQA GCSE Mathematics Specification A Powered By Docstoc
					                                 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