edexcelb colouredn by w1F535

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									    Foundation Tier : Stage 1
    Ma2 Number and Algebra
    2    Using and applying number and algebra
    2    Numbers and the number system
         Integers
    a    Use their previous understanding of integers and 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.                                                             4AB; 14BC; 17F; 21ABCDG
         Fractions
    c
         Understand equivalent fractions, simplifying a fraction by cancelling all common
         factors; order fractions by rewriting them with a common denominator.                   24ABC; 53AB; 60ABDF
         Decimals
    d    Use decimal notation and recognise that each terminating decimal is a fraction;
         order decimals.                                                                         7ACD; 28C
         Percentages
    e    Understand that ‘percentage’ means ‘number of parts per 100’ and use this to
         compare proportions; interpret percentage as the operator ‘so many hundredths
         of’.                                                                                    28BEF; 47ABC; 69A
         Ratio
    f    Use ratio notation, including reduction to its simplest form and its various links to
         fraction notation.                                                                      39EF
    3    Calculations
         Number operations and the relationships between them
    a    Add, subtract, multiply and divide integers and then any number.; multiply or
         divide any number by powers of 10, and any positive number by a number                  2A; 4CD; 14D; 19ABC; 22;
         between 0 and 1.                                                                        26ABCDE; 27ABCD; 37C; 44ABCD
    b    Use brackets and the hierarchy of operations.                                           15A
    c    Calculate a given fraction of a given quantity, expressing the answer as a fraction;
         perform short division to convert a simple fraction to a decimal.                       24E; 28C; 52A; 67ABC; 69D
    d    Understand and use unit fractions as multiplicative inverses; multiply a fraction by
         an integer; multiply a fraction by a unit fraction.                                     60C; 67AF
         Mental methods
    g
         Recall all positive integer complements to 100. Recall all multiplication facts to 10
         x 10, and use them to derive quickly the corresponding division facts; recall the
         fraction-to-decimal conversion of familiar simple fractions.                            22; 28CF
    h    Round to the nearest integer.                                                           14A
    I    Develop a range of strategies for mental calculation; derive unknown facts from
         those they know; mentally add and subtract numbers with up to two decimal
         places; multiply and divide numbers with no more than one decimal digit, using
         the commutative, associative, and distributive laws and factorisation where
         possible, or place value adjustments.                                                   19ABC; 22; 26ABCDE; 37C; 65A
         Written methods
    j    Use standard column procedures for addition and subtraction and subtraction of
         integers and decimals.                                                                  19ABC; 65A
    5    Equations, formulae and identities
         Use of symbols
    a
         Distinguish the different roles played by letter symbols in algebra, knowing that
         letter symbols represent definite unknown numbers in equations.                         3B
    b    Understand that the transformation of algebraic expressions obeys and
         generalises the rules of arithmetic; manipulate algebraic expressions by collecting
         like terms, by multiplying a single term over a bracket.                                32ABC; 46C; 50ABDEFG
    6    Sequences, functions and graphs
         Graphs of linear functions
    b
         Use the conventions for coordinates in the plane; plot points in all four quadrants     8D; 48A
    Ma3 Shape, space and measures



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    1        Using and applying shape, space and measures
    2        Geometrical reasoning
             Angles
    b        Distinguish between acute, obtuse, reflex and right angles; estimate the size of an
             angle in degrees.                                                                     23B; 38A; 53D
             Properties of triangles and other rectilinear shapes
    f        Recall the essential properties of special types of quadrilateral, including square,
             rectangle, parallelogram, trapezium and rhombus; classify quadrilaterals by their
             geometric properties.                                                                 8AC; 23A; 38A
             Proportions of circles
    i        Recall the definition of a circle and the meaning of related terms, including centre,
             radius, diameter, circumference.                                                      29A
    3        Transformations and coordinates
             Specifying transformations
    a
             Understand that rotations are specified by a centre and an (anticlockwise) angle;
             rotate a shape about the origin; measure the angle of rotation using right angles,
             simple fractions of a turn; understand that reflections rate specified by a mirror
             line, at first using a line parallel to an axis.                                   8D; 64ABD
             Properties of transformations
    b        Recognise and visualise rotations and reflections including reflection symmetry
             and rotation symmetry of 2-D shape; transform triangles and other 2-D shapes by
             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.                                                                   8BCD; 53C; 64ABDG
             Coordinates
    e
             Understand that one coordinate identifies a point on a 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.                   8D; 48AC
    4        Measures and construction
             Measures
    a        Interpret scales on a range of measuring instruments, including those for time and
             mass; convert measurements from one unit to another; make sensible estimates
             of a range of measures in everyday settings.                                          1D; 5ABC; 11AB; 14E; 45A; 54A
    b        Understand angle measure using the associated language.                               51CD
             Construction
    d        Measure and draw lines to the nearest millimetre, and angles to the nearest
             degree; draw triangles and other 2-D shapes using a ruler and protractor, given
             information about their side lengths and angles.                                      68BC
    1        Using and applying handling data
             Problem solving
    a
             Carry out each of the four aspects of the handling data cycle to solve problems:      10ABCD; 30ABCDE
    I        Specify the problem and plan; formulate questions in terms of the data needed,
             and consider what inferences can be drawn from the data, decide what data to
             collect (including sample size and data format) and what statistical analysis is
             needed.                                                                               10ABCD; 30ABCDE
    ii       Collect data from a variety of suitable sources, including experiments and
             surveys, and primary and secondary sources.                                           10ABCD; 30ABCDE
    iii      Process and represent the data; turn the raw data into usable information that
             gives insight into the problem.                                                       10ABCD; 30ABCDE
    iv       Interpret and discuss: answer the initial question by drawing conclusions from the
             data.                                                                                 10ABCD; 30ABCDE
    b
             Identify what further information is needed to pursue a particular line of enquiry.   10ABCD; 30ABCDE
    c
             Select and organise the appropriate mathematics and resources to use for a task. 10ABCD; 30ABCDE
    d        Review progress while working, check and evaluate solutions.                     10ABCD; 30ABCDE
             Communicating



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    e
             Interpret, discuss and synthesise information presented in a variety of forms.        10ABCD; 30ABCDE
    f        Communicate mathematically, including using ICT, making use of diagrams and
             related explanatory text.                                                             10ABCD; 30ABCDE
             Reasoning
    h        Apply mathematical reasoning, explaining inferences and deductions.                   10ABCD; 30ABCDE
    I        Explore connections in mathematics and look for cause and effect when
             analysing data.                                                                       10ABCD; 30ABCDE
    3        Collecting data
    a        Design and use data-collection sheets for grouped discrete data; collect data
             using various methods, including observation, controlled experiment, data-
             logging, questionnaires and surveys.                                                  20D; 30AB
    b        Gather discrete data from secondary sources, including printed tables and lists
             from ICT-based sources.                                                               43AB
    4        Processing and representing data
    a        Draw and produce, using paper and ICT, pie charts for categorical data and            2C; 16C; 17D; 20D; 30D; 52DEF;
             frequency diagrams.                                                                   57BC
    b        Calculate mean, range and median of small data sets with discrete data; identify
             the modal class for grouped discrete data.                                            2CD; 20D; 30D; 57ABC
    c        Understand and use the probability scale.                                             62A
    e        List all outcomes for single events, and for two successive events, in a systematic
             way.                                                                                  36BCD; 62C
    5        Interpreting and discussing results
    b                                                                                              2B; 7B; 16ABD; 17E; 20D; 43CDE;
         Interpret a wide range of graphs and diagrams and draw conclusions.                       52BC
    g    Use the vocabulary of probability to interpret results involving uncertainty and
         prediction.                                                                               36A
    j    Discuss implications of findings in the context of the problem.                           30E
    Foundation Tier : Stage 2
    Ma2 Number and Algebra
    2    Numbers and the number system
         Powers and roots
    b    Use the terms square, positive square root, cube; use index notation for squares
         and cubes and powers of 10.                                                               21EF; 41C
    3    Calculations
         Number operations and the relationships between them
    c    Express a given number as a fraction of another.                                          24D
    e
         Convert simple fractions of a whole to percentages of the whole and vice versa.           28AD; 47ADE; 52A
         Mental methods
    g    Recall the cubes of 2, 3, 4, 5 and 10                                                     21F; 41C
         Calculator methods
    o    Use calculators effectively: know how to enter complex calculations and use
         function keys for reciprocals, squares and powers.                                        63BCDEFGH
    4    Solving numerical problems
    a    Draw on their knowledge of the operations and the relationships between them,
         and of simple integer 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.                                                                                 37F; 39AB; 49CD; 54ADFG; 65BC
    5    Equations, formulae and identities
         Index notation
    c    Use index notation for simple integer powers.                                             46CD
         Linear equations
    e    Solve linear equations, with integer coefficients, in which the unknown appears on
         either side or both sides of the equation.                                                3CD; 9E; 42ABCDEFG; 66A
         Formulae
    f
         Use formulae from mathematics and other subjects expressed initially in words             9ABC; 15BCD; 27E; 46ABD;
         and then using letters and symbols; substitute numbers into a formula.                    61ACD
    6    Sequences, functions and graphs


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         Sequences
    a    Generate terms of a sequence using term-to-term and positions-to-term
         definitions of the sequence.                                                           9BC; 58AB
    Ma3 Shape, space and measures
    2    Geometrical reasoning
         Angles
    a
         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.                   23AB; 53E
         Properties of triangles and other rectilinear shapes
    c    Understand that the angle sum of a triangle is 180 degrees.                            23A; 38B; 53F
    d    Use angle properties of equilateral, isosceles and right-angled triangles;
         understand congruence; explain why the angle sum of any quadrilateral is 360
         degrees.                                                                               23A; 38ABC
    e    Use their knowledge of rectangles, parallelograms and triangles to deduce
         formulae for the area of a parallelogram, and a triangle, from the formula for the
         area of a rectangle.                                                                   31BC; 40C
    g
         Calculate the use and sums of the interior and exterior angles of quadrilaterals,
         pentagons and hexagons; calculate the use and angles of regular polygons.              38CEFG
         Properties of circles
    I    Understand that inscribed regular polygons can be constructed by equal division
         of a circle.                                                                           38D
    3    Transformations and coordinates
         Specifying transformations
    a    Understand that translations are specified by a distance and direction, and
         enlargements by a centre and positive scale factor.                                    59B; 64AC
         Properties of transformations
    b
         Recognise and visualise translations; transform triangles and other 2-D shapes
         by translation, recognising that these transformations preserve length and angle,
         so that any figure is congruent to its image under this transformation.                64ACG
    c    Recognise, visualise and construct enlargements of objects using positive scale
         factors greater than one.                                                              59AB; 64E
    d    Recognise that enlargements preserve angle but not 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.                                                                         59BC
    4    Measures and construction
         Construction
    e    Use straight edge and compasses to do standard constructions including an
         equilateral triangle with a given side.                                                25C; 38G; 68AD
         Mensuration
    f
         Find areas of rectangles, recalling the formula, understanding the connection to
         counting squares and how it extends this approach; recall and use the formulae
         for the area of a parallelogram and a triangle; find the surface area of simple
         shapes using the area formulae for triangles and rectangles; calculate perimeters      1ABCD; 17CG; 31ABCDE;
         and areas of shapes made from triangles and rectangles.                                40ABCD; 55D; 56B
    g    Find volumes of cuboids, recalling the formula and understanding the connection
         to counting cubes and how it extends this approach; calculate volumes of shapes
         made from cubes and cuboids.                                                           55AB
    Ma4 Handling Data
    2    Specifying the problem and planning
    a    See that random processes are unpredictable.                                           10ABCD
    b    Identify questions that can be addressed by statistical methods.                       10ABCD; 30ABE
    c    Discuss how data relate to a problem.                                                  10ABCD
    d    Identify which primary data they need to collect and in what format, including
         grouped data, considering appropriate equal class intervals.                           10ABCD
    e    Design an experiment of survey; decide what secondary data to use.                     10ABCD; 30E
    3    Collecting data



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    a        Design and use data-collection sheets for continuous data.                         57D
    4        Processing and representing data
    a        Draw and produce, using paper and ICT, diagrams for continuous data, including
             scatter graphs and stem-and-leaf diagrams.                                         20A; 33A; 57CD
    b        Calculate mean, range and median of small data sets with continuous data;
             identify the modal class for grouped continuous data.                              20BC; 57AD
    d        Understand and use estimates or measures of probability from theoretical models
             (including equally likely outcomes).                                               36ACD; 62ABC
    f        Identify different mutually exclusive outcomes and know that the sum of the
             probabilities of all these outcomes is 1.                                          62FG
    h        Draw lines of best fit by eye, understanding what these represent.                 33C
    5        Interpreting and discussing results
    a        Relate summarised data to the initial questions.                                   10CD; 30E
    b                                                                                           2B; 7B; 16ABD; 17E; 20D;
             Interpret a wide range of graphs and diagrams and draw conclusions.                43CDEF; 52BC
    c        Look at data to find patterns and exceptions.                                      10CD; 20C; 30DE
    d        Compare distributions and make inferences, using the shapes of distributions and
             measures of average and range.                                                   2B; 20C; 57A
    e        Consider and check results and modify their approach if necessary.               10CD
    f
         Have a basic understanding of correlation as a measure of the strength of the
         association between two variables; identify correlation using lines of best fit.       33BC
    h    Compare experimental data and theoretical probabilities.                               62E
    l    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.                               62DG
    Foundation Tier : Stage 3
    Ma2 Number and Algebra
         Numbers and the number system
         Percentages
    e    Use percentage in real-life situations.                                                47F; 69BCEF
    3    Calculations
         Number operations and the relationships between them
    c    Add and subtract fractions by writing them with a common denominator.                  60CEG
    d    Divide a fraction by an integer.                                                       67DE
    f    Divide a quantity in a given ratio.                                                    39G
         Mental methods
    h
         Round to one significant figure; estimate answers to problems involving decimals.      4BE; 37ABD
         Written methods
    k    Use standard column procedures for multiplication of integers and decimals,
         understanding where to position the decimal point by considering what happens if
         they multiply equivalent fractions.                                                    26ABCDE; 34AC; 65ABC
    l    Use efficient methods to calculate with fractions, including cancelling common
         factors before carrying out the calculation, recognising that, in many cases, only a
         fraction can express the exact answer.                                                 60EG; 67BCDEF
    m    Solve simple percentage problems, including increase and decrease.                     69BCDEF
    n    Solve word problems about ratio and proportion, including using informal,
         strategies and the unitary method of solution.                                         39ABCD; 49CD
         Calculator methods
    p    Enter a range of calculations, including those involving measures.                     49ABCD; 54DFG
    q    Understand the calculator display, interpreting it correctly, and knowing not to
         round during the intermediate steps of a calculation.                                  49ABCD
    4    Solving numerical problems
    b    Select appropriate operations, methods and strategies to solve number problems,
         including trial and improvement where a more efficient method to find the solution
         is not obvious.                                                                        41ABCDEFG
    c
         Use a variety of checking procedures, including working the problem backwards,
         and considering whether a result is of the right order of magnitude.                   4E; 37D




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    d        Give solutions in the context of the problem to an appropriate degree of accuracy,
             interpreting the solution shown on a calculator display, and recognising limitations
             on the accuracy of data and measurements.                                            37E
    5        Equations, formulae and identities
             Use of symbols
    a
             Distinguish the different roles played by letter symbols in algebra, knowing that
             letter symbols represent defined quantities or variables in formulae, general,
             unspecified and independent numbers in identities and in functions they define
             new expressions or quantities by referring to know quantities.                          9AB; 15BD; 32D
    b
             Manipulate algebraic expressions by taking out single common term factors.              50CDG
             Index notation
    c        Substitute positive and negative numbers into expressions such as 3x2 + 4 and
             2x3.                                                                                    44E; 46D; 61BC
             Linear equations
    e        Solve linear equations that require prior simplification of brackets, including those
             that have negative signs occuring anywhere in the equation, and those with a
             negative solution.                                                                      66BCD
             Formulae
    f        Derive a formula.                                                                       9B; 32D; 35A; 42F; 46EF; 61E
    6        Sequences, functions and graphs
             Graphs of linear functions
    b
             Plot graphs of functions in which y is given explicitly in terms of x, or implicitly.   35BCD
    c
             Construct linear functions from real-life problems and plot their corresponding
             graphs; discuss and interpret graphs arising from real situations.                      9D; 12ABC; 18AB; 46G; 70AB
             Interpet graphical information
    e
         Interpret information presented in a range of linear and non-linear graphs.                 12ABC; 18AB; 54E; 70A
    Ma3 Shape, space and measures
    2    Geometrical reasoning
         Properties of triangles and other rectilinear shapes
    c
         Use parallel lines, alternate angles and corresponding angles; understand the
         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.                                       23CDE; 38AB
         Properties of circles
    i    Recall the meaning of the terms chord, tangent and arc as they relate to the
         circle.                                                                                     29A
         3-D shapes
    j    Explore the geometry of cuboids (including cubes) and shapes made from
         cuboids.                                                                                    25ABC
    k
         Use 2-D representations of 3-D shapes and analyse 3-D shapes through 2-D
         projections and cross-sections, including plan and elevation.                               25ABCD
    3    Transformations and coordinates
         Properties of transformations
    b    Recognise and visualise rotations, reflections and translations, including
         reflection symmetry of 3-D shapes.                                                          25E; 64F
    c    Understand from this that any two circles and any two square are mathematically
         similar, while, in general, two rectangles are not.                                         59C
    d    Use and interpret maps and scale drawings.                                                  6; 7D; 51ABD; 68D
         Coordinates
    e
         Find the coordinates of points identified by geometrical information ; find the
         coordinates of the midpoint of the line segment AB, given points A and B.                   8D; 48AB
    4    Measures and construction
         Measures



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    a        Know rough metric equivalents of pounds, feet, miles, pints and gallons.            13AB; 45BC
    c        Understand and use speed.                                                           54DEFG
             Construction
    d        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.                                                                        25CD; 55D; 68ABC
             Mensuration
    h        Find circumferences of circles and areas enclosed by circles, recalling relevant
             formulae.                                                                           29BCD; 56ACD
    i
         Convert between area measures, including square centimetres and square
         metres, and volume measures, including cubic centimetres and cubic metres.              40E; 55C
    Ma4 Handling Data
    3    Collecting data
    c    Design and use two-way tables for discrete and grouped data.                            2A; 17G; 43AB; 54BC; 62B
    4    Processing and representing data
    a    Draw and produce, using paper and ICT, line graphs for time series.                     43E
    5    Interpreting and discussing results
    k
         Interpret social statistics including index numbers; time series and survey data.       43EF




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Intermediate Tier: Stage 1
Ma2 Number and Algebra
1           Using and applying number and algebra
2           Numbers and the number system
            Integers

           Use their previous understanding of integers and place value to deal with arbitrarily large
           positive numbers and round them to a given power of 10; understand and use negative
           integers both as positions and translations on a number line; order integers; use the
           concepts and vocabulary of factor (divisor), multiple, common factor, highest common
a          factor, least common multiple, prime number and prime factor decomposition.
           Powers and roots

b          Use the terms square, positive square root, negative square root, cube and cube root
           Fractions
           Understand equivalent fractions, simplifying a fraction by cancelling all common factors;
c          order fractions by rewriting them with a common denominator.
           Decimals

           Recognise that each terminating decimal is a fraction; recognise that recurring decimals
d          are exact fractions, and that some exact fractions are recurring decimals; order decimals.
           Percentages
           Understand that ‘percentage’ means ‘number of parts per 100’, and interpret percentage
e          as the operator ‘so many hundredths of’.
3          Calculations
           Number operations and the relationships between them
           Multiply or divide any number by powers of 10, and any positive number by a number
           between 0 and 1; find the prime factor decomposition of positive integers; multiply and
a          divide by a negative number.
b          Use brackets and the hierarchy of operations.
           Calculate a given fraction of a given quantity, 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;
           distinguish between fractions with denominators that have only prime factors of 2 and 5
           (which are represented by terminating decimals), and other fractions (which are
c          represented by recurring decimals).
           Understand and use unit fractions as multiplicative inverses; multiply and divide a given
d          fraction by an integer, by a unit fraction and by a general fraction.
e          Convert simple fractions of a whole to percentages of the whole and vice versa.
           Written methods
           Use efficient methods to calculate with fractions, including cancelling common factors
           before carrying out the calculation, recognising that in many cases only a fraction can
I          express the exact answer.
j          Solve percentage problems, including percentage increase and decrease.
           Calculator methods
           Understand the calculator display, knowing when to interpret the display, when the display
           has been rounded by the calculator, and not to round during the intermediate steps of a
p          calculation.
5          Equations, formulae and identities
           Use of symbols
           Distinguish the different roles played by letter symbols in algebra, using the correct
           notational conventions for multiplying or dividing by a given number, and knowing that
           letter symbols represent definite unknown numbers in equations, defined quantities or
           variables in formula, general, unspecified and independent numbers in identities, and in
a          functions they define new expressions or quantities by referring to known quantities.

           Understand that the transformation of algebraic entities obeys and generalises the well-
           defined rules of generalised arithmetic; manipulate algebraic expressions by collecting like
b          terms, multiplying a single term over a bracket and taking out common factors.

c          Know the meaning of and use the words ‘equation’, ‘formula’, ‘identity’ and ‘expression’.
           Equations
           Set up simple equations; solve simple equations by using inverse operations or by
e          transforming both sides in the same way.
           Linear equations

           Solve linear equations in one unknown, with integer or fractional coefficients, in 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
f          occurring anywhere in the equation, and those with a negative solution.
           Formulae

g          Use formulae from mathematics and other subjects; substitute numbers into a formula.
6          Sequences, functions and graphs
           Sequences

          Generate common integer sequences (including sequences of odd or even integers,
          squared integers, powers of 2, powers of 10, triangular numbers); 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, justifying its form by
a         reference to the activity or context from which it was generated.
          Graphs of linear functions
b         Use conventions for coordinates in the plane; plot points in all four quadrants.
Ma3 Shape, space and measures
1         Using and applying shape, space and measures
2         Geometrical reasoning
          Properties of triangles and other rectilinear shapes

           Distinguish between lines and line segments; use parallel lines, alternate angles and
           corresponding 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
a          angle of a triangle is equal to the sum of the interior angles at the other two vertices.
           Use angle properties of equilateral, isosceles and right-angled triangles; explain why the
b          angle sum of a quadrilateral is 360 degrees.
           Recall the definitions of special types of quadrilateral, including square, rectangle,
           parallelogram, trapezium and rhombus; classify quadrilaterals by their geometric
c          properties.
           Calculate and use the sums of the interior and exterior angles of quadrilaterals,
d          pentagons, hexagons; calculate and use the angles of regular polygons.
           Properties of circles
           Recall the definition of a circle and the meaning of related terms, including centre, radius,
h          chord, diameter, circumference, tangent, arc, sector and segment.
3          Transformations and coordinates
            Specifying transformations

            Understand that rotations are specified by a centre and an (anticlockwise) angle; use any
            point as the centre of rotation; measure the angle of rotation, using right angles, fractions
a           of a turn or degrees; understand that reflections are specified by a (mirror) line.
            Properties of transformations
            Recognise and visualise rotations, reflections and translations including reflection
            symmetry of 2-D and 3-D shapes, and rotation symmetry of 2-D shapes; transform
b           triangles and other 2-D shapes by translation, rotation and reflection.
            Coordinates

            Use axes and coordinates to specify points in all four quadrants; locate points with given
e           coordinates; find the coordinates of points identified by geometrical information.
4           Measures and construction
            Measures
            Use angle measure; know that measurements using real numbers depend on the choice
a           of unit; convert measurements from one unit to another.
            Construction

           Draw approximate constructions of triangles and other 2-D shapes, using a ruler and
           protractor, given information about side lengths and angles; construct specified cubes,
b          regular tetrahedra, square-based pyramids and other 3-D shapes.
Ma4 Handling data
1          Using an applying handling data
           Problem solving
a          Carry out each of the four aspects of the handling data cycle to solve problems:

            Specify the problem and plan: formulate questions in terms of the data needed, and
            consider what inferences can be drawn from the data; decide what data to collect
I           (including sample size and data format) and what statistical analysis is needed.
            Collect data from a variety of suitable sources, including experiments and surveys, and
ii          primary and secondary sources.
            Process and represent the data: turn the raw data into usable information that gives insight
iii         into the problem.
            Interpret and discuss the data: answer the initial question by drawing conclusions from the
iv          data.
            Select the problem-solving strategies to use in statistical work, and monitor their
            effectiveness (these strategies should address the scale and manageability of the tasks,
            and should consider whether the mathematics and approach used are delivering the most
b           appropriate solutions).
            Communicating
            Communicate mathematically, with emphasis on the use of an increasing range of
            diagrams and related explanatory text, on the selection of their mathematical presentation,
            explaining its purpose and approach, and on the use of symbols to convey statistical
c           meaning.
            Reasoning
            Apply mathematical reasoning, explaining and justifying inferences and deductions,
d           justifying arguments and solutions.
e           Identify exceptional or unexpected cases when solving statistical problems.
            Explore connections in mathematics and look for relationships between variables when
f           analysing data.
            Recognise the limitations of any assumptions and the effects that varying the assumptions
g           could have on the conclusions drawn from data analysis.
3           Collecting data
            Collect data using various methods, including observation, controlled experiment, data
a           logging, questionnaires and surveys.
            Gather data from secondary sources, including printed tables and lists from ICT-based
b           sources.
c           Design and use two-way tables for discrete and grouped data.
d           Deal with practical problems such as non-response or missing data.
4           Processing and representing data

c           List all outcomes for single events, and for two successive events, in a systematic way.
            Identify different mutually exclusive outcomes and know that the sum of the probabilities of
d           all these outcomes is 1.
Intermediate Tier: Stage 2
Ma2 Number and Algebra
            Powers and roots

b           Use standard index form, expressed in conventional notation and on a calculator display.
            Ratio
            Use ratio notation, including reduction to its simplest form and its various links to fraction
f           notation.
3           Calculations
            Number operations and the relationships between them
f           Divide a quantity in a given ratio.
            Mental methods
h           Round to a given number of significant figures.
            Calculator methods
            Use calculators effectively and efficiently, knowing how to enter complex calculations; use
            an extended range of function keys, including trigonometrical and statistical functions
o           relevant across this programme of study.
4           Solving numerical problems
            Check and estimate answers to problems; select and justify appropriate degrees of
b           accuracy for answers to problems.
5           Equations, formulae and identities
            Expand the product of two linear expressions; manipulate algebraic expressions by
b           factorising quadratic expressions.
            Index notation

d           Substitute positive and negative numbers into expressions such as 3x2 + 4 and 2x3.
            Formulae
g           Change the subject of a formula; generate a formula.
            Simultaneous linear equations
            Solve simple linear inequalities in one variable, and represent the solution set on a
j           number line.
            Numerical methods
            Use systematic trial and improvement to find approximate solutions of equations where
m           there is no simple analytical method of solving them.
6           Sequences, functions and graphs
            Graphs of linear functions
            Plot graphs of functions in which y is given explicitly in terms of x (as in y = 2x + 3), or
b           implicitly (as in x + y = 7)
            Interpreting graphical information
            Construct linear functions and plot the corresponding graphs arising from real-life
d           problems; discuss and interpret graphs modelling real situations.
            Quadratic functions
          Generate points and plot graphs of simple quadratic functions, then more general
e         quadratic functions.
Ma3 Shape, space and measures
2         Geometrical reasoning
          Properties of triangles and other rectilinear shapes
f         Understand, recall and use Pythagoras’ theorem in 2-D problems.
          Understand, recall and use trigonometrical relationships in right-angled triangles, and use
g         these to solve problems, including those involving bearings.
          Properties of circles
          Understand that the tangent at any point on a circle is perpendicular to the radius at that
          point; understand and use the fact that tangents from an external point are equal in length;
          understand that inscribed regular polygons can be constructed by equal division of a
h         circle.
3         Transformations and coordinates
          Specifying transformations
          Understand that translations are specified by giving a distance and direction (or a vector),
a         and enlargements by a centre and a positive scale factor.
          Properties of transformations
          Recognise, visualise and construct enlargements of objects; understand from this that any
          two circles and any two squares are mathematically similar, while, in general, two
c         rectangles are not, then use positive fractional scale factors.
          Recognise that enlargements preserve angle but not length; identify the scale factor of an
          enlargement as the ratio of the lengths of any two corresponding line segments;
          understand the implications of enlargement for perimeter; use and interpret maps and
d         scale drawings.
4         Measures and construction
          Measures
          Recognise that measurements given to the nearest whole unit may be inaccurate by up to
          one half in either direction; understand and use compound measures, including speed and
a         density.
          Mensuration

           Find the surface area of simple shapes by using the formulae for the areas of triangles
           and rectangles; find volumes of cuboids, recalling the formula and understanding the
           connection to counting cubes and how it extends this approach; calculate volumes of right
           prisms and of shapes made from cubes and cuboids; find circumferences of circles and
d          areas enclosed by circles, recalling relevant formulae.
Ma4 Handling data
2          Specifying the problem and planning
a          See that random processes are unpredictable.
b          Identify key questions that can be addressed by statistical methods.
           Discuss how data relate to a problem; identify possible sources of bias and plan to
c          minimise it.
           Identify which primary data they need to collect and in what format, including grouped
d          data, considering appropriate equal class intervals.
e          Design an experiment or survey; decide what primary and secondary data to use.
4          Processing and representing data

            Draw and produce, using paper and ICT, pie charts for categorical data, and diagrams for
            continuous data, including line graphs (time series), scatter graphs, frequency diagrams,
a           stem-and-leaf diagrams, cumulative frequency tables and diagrams, box plots.
            Understand and use estimates or measures of probability from theoretical models, or from
b           relative frequency.
            Find the median, quartiles and interquartile range for large data sets and calculate the
e           mean for large data sets with grouped data.
I           Draw lines of best fit by eye, understanding what these represent.
5           Interpreting and discussing results
a           Relate summarised data to the initial questions.

b           Interpret a wide range of graphs and diagrams and draw conclusions.
c           Look at data to find patterns and exceptions.
e           Consider and check results, and modify their approaches if necessary.

            Appreciate that correlation is a measure of the strength of the association between two
f           variables; distinguish between positive, negative and zero correlation using lines of best fit.

g           Use the vocabulary of probability to interpret results involving uncertainty and prediction.
h           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
I           probability and population parameters.
Intermediate Tier: Stage 3
Ma2 Number and Algebra
2           Numbers and the number system
            Powers and roots

b           Use index notation and index laws for multiplication and division of integer powers.
3           Calculations
            Number operations and the relationships between them

            Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number
            multiplied by its reciprocal is 1 (and that zero has no reciprocal, because division by zero
            is not defined); use index laws to simplify and calculate the value of numerical expressions
a           involving multiplication and division of integer powers; use inverse operations.
            Understand the multiplicative nature of percentages as operators; calculate an original
            amount when given the transformed amount after a percentage change; reverse
e           percentage problems.
            Mental methods
            Recall integer squares from 2 x 2 to 15 x 15 and the corresponding square roots, the
g           cubes of 2, 3, 4, 5 and 10.
            Develop a range of strategies for mental calculation; derive unknown facts from those they
            know; convert between ordinary and standard index form representations, converting to
            standard index form to make sensible estimates for calculations involving multiplication
h           and/or division.
            Written methods
j           Solve percentage problems including reverse percentages.
k           Represent repeated proportional change using a multiplier raised to a power.
l           Calculate an unknown quantity from quantities that vary in direct proportion.
m           Calculate with standard index form.
n           Use surds and π in exact calculations, without a calculator.
            Calculator methods

r           Use standard index form display and how to enter numbers in standard index form.

s           Use calculators for reverse percentage calculations by doing an appropriate division.
4           Solving numerical problems
            Draw on their knowledge of operations and inverse operations (including powers and
            roots) and of methods of simplification (including factorisation and the use of the
            commutative, associative and distributive laws of addition, multiplication and factorisation)
            in order to select and use suitable strategies and techniques to solve problems and word
            problems, including those involving ratio and proportion, repeated proportional change,
            fractions, percentages and reverse percentages, surds, measures and conversion
a           between measures, and compound measures defined within a particular situation.
b           Recognise limitations on the accuracy of data and measurement.
5           Equations, formulae and identities
            Use of symbols
            Manipulate algebraic expressions using the difference of two squares and by cancelling
b           common factors in rational expressions.
            Index notation

d         Use index notation for simple integer powers, and simple instances of index laws.
          Formulae
          Change the subject of a formula, including cases where the subject occurs twice, or where
g         a power of the subject appears.
          Simultaneous linear equations
          Find the exact solution of two simultaneous equations in two unknowns by eliminating a
          variable, and interpret the equations as lines and their common solution as the point of
I         intersection.
j         Solve several linear inequalities in two variables and find the solution set.
          Quadratic equations
k         Solve quadratic equations by factorisation.
          Sequences, functions and graphs
          Graphs of linear functions
          Recognise (when values are given for m and c) that equations of the form y = mx + c
b         correspond to the straight-line graphs in the coordinate plane.
          Find the gradient of lines given by equations of the form y = mx + c (when values are given
          for m and c); 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; explore the gradients of
c         parallel lines.
          Quadratic functions
          Find approximate solutions of a quadratic equation from the graph of the corresponding
e         quadratic function.
          Other functions
          Plot graphs of: simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, using a
          spreadsheet or graph plotter as well as pencil and paper; recognise the characteristic
f         shapes of all these functions.
          Loci
h         Construct the graphs of simple loci.
Ma3 Shape, space and measures
2         Geometrical reasoning
          Properties of triangles and other rectilinear shapes

f           Investigate the geometry of cuboids including cubes, and shapes made from cuboids.
            Understand similarity of triangles and of other plane figures, and use this to make
g           geometric inferences.
            Properties of circles
           Explain why the perpendicular from the centre to a chord bisects the chord; use the facts
           that the angle subtended by an arc at the centre of a circle is twice the angle subtended at
           any point on the circumference, the angle subtended at the circumference by a semicircle
           is a right angle, that angles in the same segment are equal, and that opposite angles of a
h          cyclic quadrilateral sum to 180 degrees.
           3-D shapes
           Use 2-D representations of 3-D shapes and analyse 3-D shapes through 2-D projections
           and cross-sections, including plan and elevation; solve problems involving surface areas
I          and volumes of prisms.
3          Transformations and coordinates
           Properties of transformations
           Transform triangles and other 2-D shapes by translation, rotation and reflection and
           combinations of these transformations; distinguish properties that are preserved under
b          particular transformations.
           Understand the difference between formulae for perimeter, area and volume by
d          considering dimensions.
           Coordinates
           Understand that one coordinate identifies a point on a number line, that 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’; find the coordinates of the midpoint of the line segment AB, given the
e          points A and B, then calculate the length AB.
           Vectors
f          Understand and use vector notation.
4          Measures and construction
           Construction
           Use straight edge and compasses to do standard constructions including an equilateral
           triangle with a given side, the midpoint and perpendicular bisector of a line segment, the
           perpendicular from a point to a line, the perpendicular from a point on a line, and the
c          bisector of an angle.
           Mensuration
d          Convert between volume measures including cm3 and m3.
           Loci
e          Find loci, both by reasoning and by using ICT to produce shapes and paths.
Ma4 Handling data
4          Processing and representing data
f          Calculate an appropriate moving average.
           Use tree diagrams to represent outcomes of compound events, recognising when events
h          are independent.
j          Use relevant statistical functions on a calculator or spreadsheet.
5          Interpreting and discussing results
b          Identify seasonality and trends in time series.
           Compare distributions and make inferences, using shapes of distributions and measures
d          of average and spread, including median and quartiles.
           Appreciate that zero correlation does not necessarily imply ‘no relationship’ but merely ‘no
f          linear relationship’.
6ADE; 7A; 9ABC; 40B


1C; 51ABC


11AB; 15B; 17A




11FG


13ABCDEF; 18A; 44A




3ABCDEFGH; 6DE; 7A
20AB




11CDEFG; 13CF; 17A

17BCDEFG; 33ACD
13ACF; 44A




11CD; 15B; 58A
13G; 44BCDEFG




20ABC; 26AB; 32EF
2AE; 4A; 8A; 21A; 43A




2BCD; 4B; 19AB; 28ABCDE

2A; 4A; 8A; 43A


4AC; 7C; 41CD




4AD; 7C; 19C; 41ABEF


2A; 7B; 8A; 12ACD; 33E




14ABCDEFGH

21A; 56A




25AB; 45BC

45CD


45A

45DE


10D; 61AD
53ACD




30D; 45A; 53ABCD




56A




16F; 36D




30B




24ABCD; 29CDEF

24ABCD; 29CDEF

24ABCD; 29CDEF

24ABCD; 29CDEF




24ABCD; 29CDEF




24ABCD; 29CDEF


24ABCD; 29CDEF
24ABCD; 29CDEF

24ABCD; 29CDEF

24ABCD; 29CDEF
24D

22A; 29ABCDEF
5CD
24B


34CD

34B




40ABCDEF


37ABDE; 38D



37C

9DEF; 20ACD



6B; 20ABCE; 32EF; 42A;
49BE; 51D; 57E


9G; 20D; 60A


43ABCDEF; 47AB


7B; 12AB; 28AD

8AB; 28F; 50ABCDG


31ABC; 55ABCDE


57D




21A; 39A


21BD; 32B; 35ABC
21C; 57B




1BCD

42ABCD; 49ABCDEF




61D




53ABE




38ABCD; 53E




36ABCD; 38ABCD




16E; 32ABCDEFG; 35B; 60B




10ABCDEF; 16ABC



24ABCD
24D; 29DEF

24BCD

24D
24D; 29F




5BCD; 18DEF; 22A; 27ABCE;
59A

34AB; 58B
5E; 27D
22B; 39E

24CD

5ABCD; 18BC; 22C; 27E; 59A
22ABC; 24CD; 29ABDEF
24CD


22ABC

34AB
34A


34A




6BC; 23ABCDEFGHIJ; 51E




23CEGHIJ; 33B; 51E


44CD; 48ABD


1C; 51AB




40ABCEF

48DE
48C
15ABCDE
40H
62ABC


40DGI

48D
15ACDE; 16E; 26AB;
32ABCDEFG; 44G; 48E
60ABCDE




47BFG


23CDEFGHIJ


50EFGH




46ABCDEFGHI
52ABCDE

47CDEG




21A; 39A




39ABCD


21C; 57B




57ACEF




16A; 30ABC

38CDE
61ABCDE




16ABCD; 30ABC




53F

63




1D; 56BCD

53B; 56A




54CDEF

16F

54ABCDEFG



59B

58CD
29F

59B

27E

22AC
Higher Tier: Stage 1
Ma2 Number and Algebra
1            Using and applying number and algebra
2            Numbers and the number system
             Integers
a            Use the concepts and vocabulary of highest common factor, least common multiple,
             prime number and prime factor decomposition.                                            4B
             Powers and roots
b
             Use index laws for multiplication and division of integer powers; use standard index
             form, expressed in conventional notation and on a calculator display.                   4ACD; 12ABCDEF
             Decimals
d            Recognise that recurring decimals are exact fractions, and that some exact fractions
             are recurring decimals.                                                                 45AB
             Ratio
f            Use ratio notation, including reduction to its simplest form and its various links to
             fraction notation.                                                                      22A
3            Calculations
             Number operations and the relationship between them
a
             Multiply or divide any number by a number between 0 and 1; find the prime factor
             decomposition of positive integers; multiply and divide by a negative number.           4B
c
             Distinguish between fractions with denominators that have only prime factors of 2 and
             5 (which are represented by terminating decimals), and other fractions (which are
             represented by recurring decimals); convert a recurring decimal to a fraction.          45AB
d            Multiply and divide a given fraction by a unit fraction and by a general fraction.      3BDE
e            Understand the multiplicative nature of percentages as operators; calculate an
             original amount when given the transformed amount after a percentage change;
             reverse percentage problems.                                                            9ABDE
f            Divide a quantity in a given ratio                                                      22A
             Mental methods
g            Recall integer squares from 2 x 2 to 15 x 15 and the corresponding square roots, the
             cubes of 2, 3, 4, 5 and 10.
h            Round to a given number of significant figures; convert between ordinary and
             standard index form representations.                                                    12CE
             Written methods
j            Solve percentage problems; reverse percentages.                                         9BDE
k
             Represent repeated proportional change using a multiplier raised to a power.            9C
             Calculator methods
r
             Use standard index form display and how to enter numbers in standard index form.        12DF
s
             Use calculators for reverse percentage calculations by doing an appropriate division.   9D
4            Solving numerical problems
a
            Draw on their knowledge of operations and inverse operations and of methods of
            simplification (including factorisation and the use of the commutative, associative and
            distributive laws of addition, multiplication and factorisation) in order to select and use
            suitable strategies and techniques to solve problems and word problems, including
            those involving ratio and proportion, repeated proportional change, fractions,
            percentages and reverse percentages, inverse proportion, measures and conversion 3E; 6ACDE; 9BCDE;
            between measures, and compound measures defined within a particular situation.              10DFG; 22CDF
b           Check and estimate answers to problems.
5           Equations, formulae and identities
            Use of symbols
a           Distinguish the different roles played by letter symbols in algebra, using the correct
            notational conventions for multiplying or dividing by a given number, and knowing that
            letter symbols represent definite unknown numbers in equations, defined quantities
            or variables in formula, general, unspecified and independent numbers in identities,
            and in functions they define new expressions or quantities by referring to known
            quantities.                                                                              4C; 5A; 8A; 41E
b           Understand that the transformation of algebraic entities obeys and generalises the
            well-defined rules of generalised arithmetic; manipulate algebraic expressions by
            collecting like terms, multiplying a single term over a bracket, taking out common
            factors.                                                                                 20AB; 27C
c           Know the meaning of and use the words ‘equation’, ‘formula’, ‘identity’ and
            ‘expression’.                                                                            4CD; 5A; 8A
            Index notation
d           Use index notation for simple instances of index laws.                                   4CD; 27AB; 38A
            Equations
e           Set up simple equations; solve simple equations by using inverse operations or by
            transforming both sides in the same way.                                                 5ABCDE
            Linear equations
f
            Solve linear equations in one unknown, with integer or fractional coefficients, in which
            the unknown appears on either side or on both sides of the equation.                     5ABCE
            Formulae
g           Use formulae from mathematics and other subjects; substitute numbers info a
            formula; generate a formula.                                                             8A; 10B; 27A; 30D
            Numerical methods
m           Use systematic trial and improvement to find approximate solutions of equations
            where there is no simple analytical method of solving them.                              28AD
6           Sequences, function and graphs
            Sequences
a
          Generate common integer sequences (including sequences of odd or even integers,
          squared integers, powers of 2, powers of 10, triangular numbers); use linear
          expressions to describe the nth term of an arithmetic sequence, justifying its form by
          reference to the activity or context from which it was generated.                          36ABCE
          Graphs of linear functions
b         Recognise (when values are given for m and c) that equations of the form y = mx + c
          correspond to straight-line graphs in the coordinate plane.                                13CD
          Interpreting graphical information
d         Construct linear functions and plot the corresponding graphs arising from real-life
          problems; discuss and interpret graphs modelling real situations.                          6B; 13B; 22B
          Quadratic functions
e         Generate points and plot graphs of simple quadratic functions, then more general
          quadratic functions.                                                                       26AB; 28A
Ma3 Shape, space and measures
1         Using and applying shape, space and measures
2         Geometrical reasoning
          Properties of triangles and other rectilinear shapes
a         Distinguish between lines and line segments.                                               14A
f         Understand recall and use Pythagoras’ theorem in 2-D problems.                             46A
g         Understand, recall and use trigonometrical relationships in right angled triangles, and    2ABCD; 11ABCDEF;
          use these to solve problems, including those using bearings.                               46A
            Properties of circles
h           Recall the definition of a circle and the meaning of related terms, including sector and
            segment; understand that the tangent at any point on a circle is perpendicular to the
            radius at that point; understand and use the fact that tangents from an external point
            are equal in length.                                                                     25AB; 29D
3           Transformations and coordinates
            Specifying transformations
a
           Use any point as the centre of rotation; measure the angle of rotation, using fractions
           of a turn or degrees; understand that translations are specified by a vector.             16A
           Properties of transformations
c          Recognise, visualise and construct enlargements of objects using positive fractional
           and negative scale factors.                                                               16B; 33A
           Coordinates
e          Given the coordinates of the points A and B, calculate the length AB.                     11F
4          Measures and construction
           Measures
a          Know that measurements using real numbers depend on the choice of unit.                   31A
           Mensuration
d          Find the surface area of simple shapes by using the formulae for the areas of
           triangles and rectangles; find volumes of cuboids, recalling the formula and
           understanding the connection to counting cubes and how it extends this approach;
           calculate volumes of right prisms.                                                        10ACE
Ma4 Handling data
1          Using and applying handling data
           Problem solving
a
           Carry out each of the four aspects of the handling data cycle to solve problems:
I
           Specify the problem and plan: formulate questions in terms of the data needed, and
           consider what inferences can be drawn from the data; decide what data to collect
           (including sample size and data format) and what statistical analysis is needed.          1ABCD; 24ABCDEF
ii         Collect data from a variety of suitable sources, including experiments and surveys,
           and primary and secondary sources.                                                        1ABCD; 24ABCDEF
iii        Process and represent the data: turn the raw data into usable information that gives
           insight into the problem.                                                                 1ABCD; 24ABCDEF
iv         Interpret and discuss the data: answer the initial question by drawing conclusions
           from the data.                                                                            1ABCD; 24ABCDEF
b          Select the problem-solving strategies to use in statistical work, and monitor their
           effectiveness (these strategies should address the scale and manageability of the
           tasks, and should consider whether the mathematics and approach used are
           delivering the most appropriate solutions).                                               1ABCD; 24ABCDEF
           Communicating
c          Communicate mathematically, with emphasis on the use of an increasing range of
           diagrams and related explanatory text, on the selection of their mathematical
           presentation, explaining its purpose and approach, and on the use of symbols to
           convey statistical meaning.                                                               1ABCD; 24ABCDEF
           Reasoning
d          Apply mathematical reasoning, explaining and justifying inferences and deductions,
           justifying arguments and solutions.                                                       1ABCD; 24ABCDEF
e          Identify exceptional or unexpected cases when solving statistical problems.               1ABCD; 24ABCDEF
f          Explore connections in mathematics and look for relationships between variables
           when analysing data.                                                                      1ABCD; 24ABCDEF
g            Recognise the limitations of any assumptions and the effects that varying the
             assumptions could have on the conclusions drawn from data analysis.                          1ABCD; 24ABCDEF
2            Specifying the problem and planning
c            Identify possible sources of bias and plan to minimise it.                                   1BCD
e            Decide what primary and secondary data to use.                                               1D; 24F
3            Collecting data
d            Deal with practical problems such as non-response or missing data.                           1D; 24F
4            Processing and representing data
a            Draw and produce, using paper and ICT, cumulative frequency tables and diagrams,
             box plots and histograms for grouped continuous data.                                        15ABCE; 37C
e            Find the median, quartiles and interquartile range for large data sets and calculate
             the mean for large data sets with grouped data.                                              7ABC; 15DE
f            Calculate an appropriate moving average.                                                     7D
I            Draw lines of best fit by eye, understanding what these represent.                           13H
j            Use relevant statistical functions on a calculator or spreadsheet.                           24F
5            Interpreting and discussing results
b            Identify seasonality and trends in time series.                                              7D
d            Compare distributions and make inferences, using shapes of distributions and
             measures of average and spread, including median and quartiles.                              15DE
f            Appreciate that correlation is a measure of the strength of the association between
             two variables; distinguish between positive, negative and zero correlation using lines
             of best fit; appreciate that zero correlation does not necessarily imply ‘no relationship’
             but merely ‘no linear relationship’.                                                         13H; 24D
Higher Tier: Stage 2
Ma2 Number and algebra
3            Calculations
             Number operations and the relationship between them
a            Understand ‘reciprocal’ as multiplicative inverse, knowing that any non-zero number
             multiplied by its reciprocal is 1 (and that zero has no reciprocal, because division by
             zero is not defined); use index laws to simplify and calculate the value of numerical
             expressions involving multiplication and division of integer, fractional and negative
             powers.                                                                                      3C; 4CEF; 39ABC
             Mental methods
g
             Recall the fact that no = 1 and n-1 = ? For positive integers n and the corresponding
             rule for negative numbers; n? = ?n and n? = ?n for any positive number n.                    4E; 39AB
h            Converting to standard index form to make sensible estimates for calculations
             involving multiplication and/or division.                                                    12DEG
l            Calculate an unknown quantity from quantities that vary in direct or inverse
             proportion.                                                                                  22DEF
m            Calculate with standard index form.                                                          12G
n            Use surds and π in exact calculations, without a calculator.                                 44ABC; 45CDEGH
             Calculator methods
q            Use calculators, or written methods, to calculate the upper and lower bounds of
             calculations, particularly when working with measurements.                                   31BCDE
t            Use calculators to explore exponential growth and decay, using a multiplier and the
             power key.                                                                                   39EFG
4            Solving numerical problems
a            Draw on their knowledge of operations and inverse operations (including powers and
             roots), and of methods of simplification including surds, defined within a particular
             situation.                                                                                   45DEH
b            Select and justify appropriate degrees of accuracy for answers to problems;
             recognise limitations on the accuracy of data and measurements.                              31AB
5            Equation, formulae and identities
            Use of symbols
b           Expand the product of two linear expressions; manipulate algebraic expressions by
            factorising quadratic expressions including the difference of two squares and            20CD; 27CD; 34BCE;
            cancelling common factors irrational expressions.                                        38ABCDF
            Formulae
g           Change the subject of a formula, including cases where the subject occurs twice, or
            where a power of the subject appears.                                                    8BCD; 30ABCDE; 38E
            Simultaneous linear equations
i           Find the exact solution of two simultaneous equations in two unknowns by eliminating
            a variable, and interpret the equations as lines and their common solution as the
            point of intersection.                                                                   18ABCDEF
j           Solve simple linear inequalities in one variable, and represent the solution set on a
            number line; solve several linear inequalities in two variables and find the solution
            set.                                                                                     19ABCD; 23ABCD
            Quadratic equations
k           Solve quadratic equations by factorisation, completing the square and using the          20E; 34ADFG; 41B;
            quadratic formula.                                                                       43A; 45G
6           Sequences, functions and graphs
            Graphs of linear functions
c
            Find the gradient of lines given by equations of the form y = mx + c (when values are
            given for m and c); 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.             13CDFG
            Quadratic functions
e           Find approximate solutions of a quadratic equation from the graph of the
            corresponding quadratic function.                                                      26BCD; 28AD
            Other functions
f
          Plot graphs of: simple cubic functions, the reciprocal function y = 1/x with x ≠ 0, the
          exponential function y = kx for integer values of x and simple positive values of k, the
          circular functions y = sin x and y = cos x, using a spreadsheet or graph plotter as well   28ABC; 35AB; 39EF;
          as pencil and paper; recognise the characteristic shapes of all these functions.           41A
Ma3 Shape, space and measures
2         Geometrical reasoning
          Properties of triangles and other rectilinear shapes
e         Understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of
          triangles using formal arguments, and to verify standard ruler and compass
          constructions.                                                                             42ABCD
g         Calculate the area of a triangle using ?ab sin C.                                          46E
          Properties of circles
h         Explain why the perpendicular from the centre to a chord bisects the chord.                25B
          3-D shapes
i         Solve problems involving surface areas and volumes of prisms, pyramids, cylinders,
          cones and spheres.                                                                         10E; 25CDE
3         Pupils should be taught to:
          Properties of transformations
b
          Transform triangles and other 2-D shapes by combinations of transformations; use
          congruence to show that translations, rotations and reflections preserve length and
          angle, so that any figure is congruent to its image under any of these transformations;
          distinguish properties that are preserved under particular transformations.                16AC
          Vectors
f            Understand and use vector notation; calculate, and represent graphically the sum of
             two vectors, the difference of two vectors and a scalar multiple of a vector; calculate
             the resultant of two vectors; understand and use the commutative and associative
             properties of vector addition; solve simple geometrical problems in 2-D using vector
             methods.                                                                                    40ABCDEF
4            Measures and construction
             Measures
a            Recognise that measurements given to the nearest whole unit may be inaccurate by
             up to one half in either direction; understand and use compound measures, including
             speed and density.                                                                          6ABCDE; 10DF; 31AB
             Construction
c            Use straight edge and compasses to do standard constructions including an
             equilateral triangle with a given side, the midpoint and perpendicular bisector of a line
             segment, the perpendicular from a point to a line, the perpendicular from a point on a
             line, and the bisector of an angle.                                                         14A
             Mensuration
d            Calculate the lengths of arcs and the areas of sectors of circles.                          25A
             Loci
e            Find loci, both by reasoning and by using ICT to produce shapes and paths.                  14AB
Ma4 Handling data
4            Processing and representing data
b            Understand and use estimates or measures of probability from theoretical models, or
             from relative frequency.                                                                    17B
g
             Know when to add or multiply two probabilities: if A and B are mutually exclusive,
             then the probability of A or B occurring is P(A) + P(B), whereas if A and B are
             independent events, the probability of A and B occurring is P(A) x P(B).                    17CD
h            Use tree diagrams to represent outcomes of compound events, recognising when
             events are independent.                                                                     17EFG
5            Interpreting and discussing results
d            Understand frequency density.                                                               37ABC
Higher Tier: Stage 3
Ma2 Number and algebra
3            Calculations
             Number operations and the relationships between them
a            Use inverse operations, understanding that the inverse operation of raising a positive
             number to power n is raising the result of this operation to power ?.                       39ABCG
             Written methods
a            Rationalise a denominator such as ???                                                       45F
             Calculator methods
o
             Use calculators effectively and efficiently, knowing how to enter complex calculations;
             use an extended range of function keys, including trigonometrical and statistical
             functions relevant across this programme of study.                                          2A; 11BE; 24F; 39D
5            Equations, formulae and identities
             Direct and inverse proportion
h            Set up and use equations to solve word and other problems involving direct
             proportion or inverse proportion and relate algebraic solutions to graphical
             representation of the equations.                                                            22CDEFG
             Simultaneous linear and quadratic equations
l
             Solve exactly, by elimination of an unknown, two simultaneous equations in two
             unknowns, one of which is linear in each unknown, and the other is linear in one
             unknown and quadratic in the other, or where the second is of the form x2 + y2 + r2.        34H; 43C
6           Sequences, functions and graphs
            Graphs of linear functions
c           Explore the gradients of parallel lines and lines perpendicular to these lines.              13CEF
            Quadratic functions
e           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.                                   26E; 34H
            Transformation of functions
g           Apply to the graph of y = f(x) the transformations y = f(x) + a,y + f(ax); y = f(x + a), y =
            af(x) for linear, quadratic, sine and cosine functions f(x).                                 35D; 41ACDEF
            Loci
h
           Construct the graphs of simple loci, including the circle x2 + y2 = r2 for a circle of
           radius r centred at the origin of coordinates; find graphically the intersection points of
           a given straight line with this circle and know that this corresponds to solving the two
           simultaneous equations representing the line and the circle.                                 43BCD
Ma3 Shape, space and measures
2          Geometrical reasoning
f
           Understand, recall and use Pythagoras’ theorem in 3-D problems; investigate the
           geometry of cuboids including cubes, and shapes made from cuboids, including the
           use of Pythagoras’ theorem to calculate lengths in three dimensions.                         47ABC
g          Understand similarity of triangles and of other plane figures, and use this to make
           geometric inferences; use trigonometrical relationships in 3-D contexts, including
           finding the angles between a line and a plane (but not the angle between two planes
           or between two skew lines); draw, sketch and describe the graphs of trigonometric
           functions for angles of any size, including transformations involving scalings in either
           or both the x and y directions; use the sine and cosine rules to solve 2-D and 3-D           33AB; 35ABCD;
           problems.                                                                                    46BCDF; 47ABC
           Properties of circles
h
           Prove and use the facts that the angle subtended by an arc at the centre of a circle is
           twice the angle subtended at any point on the circumference, the angle subtended at
           the circumference by a semicircle is a right angle, that angles in the same segment
           are equal, and that opposite angles of a cyclic quadrilateral sum to 180 degrees;
           prove and use the alternate segment theorem.                                                 29BCDEF
           3-D shapes
i          Solve problems involving more complex shapes and solids, including segments of
           circles and frustums of cones.                                                               25BD
3          Transformations and coordinates
d          Understand the difference between formulae for perimeter, area and volume by
           considering dimensions; understand and use the effect of enlargement on areas and
           volumes of shapes and solids.                                                                32; 33CDE
4          Measures and construction
           Mensuration
d          Convert between volume measures including cm3 and m3                                         10G; 33E
Ma4 Handling data
2          Specifying the problem and planning
d          Select and justify a sampling scheme and a method to investigate a population,
           including random and stratified sampling.                                                    21ABCD

								
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