# edexcelb colouredn by w1F535

VIEWS: 2 PAGES: 30

• pg 1
```									    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,
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
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
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.
Generate points and plot graphs of simple quadratic functions, then more general
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.
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.
Find approximate solutions of a quadratic equation from the graph of the corresponding
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’.

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

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

14ABCDEFGH

21A; 56A

25AB; 45BC

45CD

45A

45DE

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

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
e         Generate points and plot graphs of simple quadratic functions, then more general
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
k           Solve quadratic equations by factorisation, completing the square and using the          20E; 34ADFG; 41B;
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
e           Find approximate solutions of a quadratic equation from the graph of the
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
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
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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