Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Edexcel GCSE Maths Higher
New two-tier specification mapped to the old three-tier Heinemann series
References to the relevant sections in the old books are given in the following form: H15.2 refers
to the Higher tier book Chapter 15 section 2.
Page numbers are not included, so this document can be used with any of the previous versions of
the textbooks.
Ma2 Number and algebra
Content
1
Section references
Using and Applying Number and Algebra
Students should be taught to:
Problem solving
a
select and use appropriate and efficient
techniques and strategies to solve problems
of increasing complexity, involving
numerical and algebraic manipulation
b
identify what further information may be
required in order to pursue a particular line
of enquiry and give reasons for following or
rejecting particular approaches
c
break down a complex calculation into
simpler steps before attempting to solve it
and justify their choice of methods
d
make mental estimates of the answers to
calculations
Questions in this section will normally be
found in the Mixed exercises at the end of
each chapter on Number and Algebra.
present answers to sensible levels of
accuracy
understand how errors are compounded
in certain calculations
Communicating
e
discuss their work and explain their
reasoning using an increasing range of
mathematical language and notation
f
use a variety of strategies and diagrams for
establishing
algebraic
or
graphical
representations of a problem and its solution
move from one form of representation to
another to get different perspectives on the
problem
g
present and interpret solutions in the context
of the original problem
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
h
use notation and symbols correctly and
consistently within a given problem
i
examine critically, improve, then justify their
choice of mathematical presentation, present
a concise, reasoned argument
Section references
Reasoning
j
explore, identify, and use pattern and
symmetry in algebraic contexts, investigating
whether particular cases can be generalised
further, and understanding the importance of
a counter-example
identify exceptional cases when solving
problems
k
understand the difference between a practical
demonstration and a proof
l
show step-by-step deduction in solving a
problem
derive proofs using short chains of deductive
reasoning
m
recognise the significance of stating
constraints and assumptions when deducing
results
recognise the limitations of any assumptions
that are made and the effect that varying the
assumptions may have on the solution to a
problem
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
2
Section references
Numbers and the Number System
Students should be taught to:
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
I1.1. I6.1
H12.1
understand and use negative integers both as
positions and translations on a number line
I1.5
order integers
I1.3
use the concepts and vocabulary of factor
(divisor), multiple, common factor, highest
common factor, least common multiple,
prime
number
and
prime
factor
decomposition
I14.1, I14.8, I14.9, I14.10
H1.1, H1.2, H1.3, H1.4
Powers and roots
b
use the terms square, positive and negative
square root, cube and cube root
I14.3, I14.7
H1.5, H1.6, H1.9
use index notation and index laws for
multiplication and division of integer powers
I14.7, H1.7, H1.8
use standard index form, expressed in
conventional notation and on a calculator
display
I14.12, H5.10
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
Section references
Fractions
c
understand equivalent fractions, simplifying
a fraction by cancelling all common factors
I11.1, I11.2, I11.3
H1.10
order fractions by rewriting them with a
common denominator
I11.4
Decimals
d
recognise that each terminating decimal is a
fraction
I11.4
H23.1
recognise that recurring decimals are exact
fractions, and that some exact fractions are
recurring decimals
I11.4
H23.1, H23.2
order decimals
I1.2
Percentages
e
e
understand that ‘percentage’ means ‘number
of parts per 100’ and use this to compare
proportions
I22.1,
H5.1
interpret percentage as the operator ‘so many
hundredths of’
I22.2
use percentage in real-life situations
I22.7, I22.8
H5.1 to H5.7 inclusive
Ratio
f
use ratio notation, including reduction to its
simplest form and its various links to fraction
notation
3
Calculations
I25.1, I25.2, I25.3
H5.9, Chapter H17
Students should be taught to:
Number
operations
and
relationships between them
a
the
multiply or divide any number by powers of
10, and any positive number by a number
between 0 and 1
I1.2
H1.1
find the prime factor decomposition of
positive integers
I14.8, I14.9, I14.10
H1.2, H1.3, H1.4
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)
H1.7
multiply and divide by a negative number
I1.5
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
Section references
use index laws to simplify and calculate the
value of numerical expressions involving
multiplication and division of integer,
fractional and negative powers
I14.6, I14.7
H1.7, H1.8, H1.9
use inverse operations, understanding that
the inverse operation of raising a positive
number to power n is raising the result of
1
this operation to power
n
H1.8
b
use brackets and the hierarchy of operations
I21.4
Chapter H10
c
calculate a given fraction of a given quantity,
expressing the answer as a fraction
I11.6
express a given number as a fraction of
another
I11.7
add and subtract fractions by writing them
with a common denominator
I11.5
H1.10
perform short division to convert a simple
fraction to a decimal
I11.4
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)
H23.1
convert a recurring decimal to a fraction
H23.2
understand and use
multiplicative inverses
11.6, H1.10
d
e
unit
fractions
as
multiply and divide a given fraction by an
integer, by a unit fraction and by a general
fraction
I11.6
H1.10
convert simple fractions of a whole to
percentages of the whole and vice versa
I22.1
H5.1, H5.2
then understand the multiplicative nature of
percentages as operators
H5.1 to H5.5 inclusive
calculate an original amount when given
the transformed amount after a
percentage change
H5.6
reverse percentage problems
f
divide a quantity in a given ratio
I25.4, I25.5
H5.9
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
Section references
Mental methods
g
recall integer squares from 2  2 to 15  15
and the corresponding square roots, the
cubes of 2, 3, 4, 5 and 10, the fact that
n0 = 1 and n–1 =
the
H1.6, H1.7, H1.8
1
for positive integers n,
n
corresponding
1
2
rule
for
1
3
negative
numbers, n  n and n  n for any
positive number n
h
3
round to a given number of significant
figures
Chapter I6
Chapter H12
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 and/or
division
i
develop a range of strategies for mental
calculation
Use ideas in Chapter I6
add and subtract mentally numbers with up
to one decimal place
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
Written methods
k
division by decimal (up to 2 decimal places)
by division using an integer
I1.4
understand where to position the decimal
point by considering what happens if they
multiply equivalent fractions
i
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
I11.2, I11.5, I11.6
H1.10
j
solve percentage problems, including
percentage increase and decrease
I22.3, I22.6
H5.1 to H5.8
reverse percentages
n
solve word problems about ratio and
proportion, including using informal
strategies and the unitary method of solution
I25.2
H5.9
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
Section references
k
represent repeated proportional change
using a multiplier raised to a power
H5.7
l
calculate an unknown quantity from
quantities that vary in direct or inverse
proportion
Chapter H17
m
calculate with standard index form
H5.10
n
use surds and  in exact calculations, without
a calculator
H23.2
rationalise
1
3

3
3
a
denominator
such
as
Calculator methods
o
use calculators effectively and efficiently,
knowing how to enter complex calculations
Ideas should introduced and reinforced at
appropriate moments during the course
use an extended range of function keys,
including trigonometrical and statistical
functions relevant across this programme
of study
p
enter a range of calculations, including those
involving measures
I30.1
H29
p
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 calculation
Ideas for this section need to be emphasised
in any calculations involving more than one
step.
q
use calculators, or written methods, to
calculate the upper and lower bounds of
calculations, particularly when working
with measurements
H23.5, H23.6, H23.7
r
use standard index form display and know
how to enter numbers in standard index
form
H5.10
s
use calculators for reverse percentage
calculations by doing an appropriate
division
H5.7
t
use calculators to explore exponential
growth and decay, using a multiplier and
the power key
H28.1
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
4
Section references
Solving Numerical Problems
Students should be taught to:
a
b
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,
inverse proportion, surds, measures and
conversion
between
measures,
and
compound measures defined within a
particular situation
I1.1, I1.2, I1.4, I6.4,
Chapter I11
Chapter I14
Chapter I22
Chapter I25
check and estimate answers to problems
H23.4
select and justify appropriate degrees of
accuracy for answers to problems
H16.1, H16.2
H23.6, H23.7
Chapter H1
Chapter H5
Chapter H12
Chapter H23
recognise limitations on the accuracy of data
and measurements
5
Equations, Formulae and Identities
Students should be taught to:
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 formulae, general,
unspecified and independent numbers in
identities, and in functions they define new
expressions or quantities by referring to
known quantities
Chapter H2
Chapter H10
b
understand that the transformation of
algebraic entities obeys and generalises the
well-defined rules of generalised arithmetic
Chapter H2
Chapter H10
expand the product of two linear expressions
I21.5, H10.2
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
c
Section references
manipulate algebraic expressions by
collecting like terms, multiplying a single
term over a bracket, taking out common
factors, factorising quadratic expressions
including the difference of two squares
and cancelling common factors in rational
expressions
I21.3, I21.4, I21.5
H10.1, H10.2, H10.3
H20.1, H20.2, H20.3
know the meaning of and use the words
‘equation’,
‘formula’,
‘identity’
and
‘expression’
H20.1
Index notation
d
use index notation for simple integer powers
I21.3, H20.2, H20.3
use simple instances of index laws
I21.3, H20.4
substitute positive and negative numbers into
expressions such as 3x2 + 4 and 2x3
I21.1, I21.2
Equations
e
set up simple equations
H10.6, H10.7
solve simple equations by using inverse
operations or by transforming both sides in
the same way
I28.3
H2.1, H2.2, H10.5
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
I28.1, I28.2, I28.3
H2.1, H2.2
solve linear equations that require prior
simplification of brackets, including those
that have negative signs occurring anywhere
in the equation, and those with a negative
solution
I28.3
H10.5
Formulae
g
use formulae from mathematics and other
subjects
I21.1, I21.2
substitute numbers into a formula
I21.2, I21.2
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
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Section references
change the subject of a formula including
cases where the subject occurs twice, or
where a power of the subject appears
I21.7
H2.3, H14.5, H10.8
generate a formula
H10.6
Direct and inverse proportion
h
H17.5, H17.6, H17.7
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
Simultaneous linear equations
i
I28.5, I28.6
H7.4, H7.5, H7.6
find exact solutions 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
Inequalities
j
solve linear inequalities in one variable, and
represent the solution set on a number line
I28.7
H2.4, H2.5
solve several linear inequalities in two
variables and find the solution set
H7.7
Quadratic equations
k
Simultaneous
equations
l
I28.8
H21.1 to H21.5
solve simple quadratic equations by
factorisation, completing the square and
using the quadratic formula
linear
and
quadratic
H21.6
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
Numerical methods
m
use systematic trial and improvement to find
approximate solutions of equations where
there is no simple analytical method of
solving them
I18.8, I30.4
H18.6
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
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6
Section references
Sequences, Functions and Graphs
Students should be taught to:
Sequences
a
generate terms of a sequence using term-toterm and position-to-term definitions of the
sequence
Ideas in Chapter I2
H14.1, H14.2,
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
I2.9
H14.2, H14.3
generate
common integer
sequences
(including sequences of odd or even integers,
squared integers, powers of 2, powers of 10,
triangular numbers)
I2.5
Chapter H11A
Graphs of linear functions
b
use the conventions for coordinates in the
plane
plot points in all four quadrants
c
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
I7.1, I7.3
H7.1, H7.2
plot graphs of functions in which y is given
explicitly in terms of x, or implicitly
I7.3
H7.2
find the gradient of lines given by equations
of the form y = mx + c (when values are
given for m and c)
I7.3, I7.4
H7.1, H7.2
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
H7.2
explore the gradients of parallel lines and
lines perpendicular to each other
H7.2, H7.3
Interpreting graphical information
d
construct linear functions and plot the
corresponding graphs arising from real-life
problems
H18.7
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
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Section references
discuss and interpret graphs modelling real
situations
I18.9, H18.7
Quadratic functions
e
generate points and plot graphs of simple
quadratic functions, then more general
quadratic functions
I18.1 to I18.4
H18.1
find approximate solutions of a quadratic
equation from the graph of the corresponding
quadratic function
I18.5
H18.1
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
H21.6
Other functions
f
I18.6, I18.7
H18.2, H18.3, H18.4
plot graphs of simple cubic functions, the
1
reciprocal function y =
with x  0,
x
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 as pencil and paper
recognise the characteristic shapes of all
these functions
Transformation of functions
g
All Chapter H24
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)
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
H21.6
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
H21.6
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Ma3 Shape, space and measures
Content
1
Section references
Using and Applying Shape, Space and
Measures
Students should be taught to:
Problem solving
a
select the problem-solving strategies to use
in geometrical work, and consider and
explain the extent to which the selections
they made were appropriate
b
select and combine known facts and
problem-solving strategies to solve more
complex geometrical problems
c
develop and follow alternative lines of
enquiry, justifying their decisions to follow
or reject particular approaches
Questions in this section will normally be
found in the Mixed exercises at the end of
each chapter on Shape, Space and Measures
Communicating
d
communicate mathematically, with emphasis
on a critical examination of the presentation
and organisation of results, and on effective
use of symbols and geometrical diagrams
e
use precise formal language and exact
methods for analysing geometrical
configurations
g
review and justify their
mathematics presentation
choices
of
Reasoning
h
distinguish between practical demonstrations
and proofs
f
apply mathematical reasoning, progressing
from brief mathematical explanations
towards full justifications in more
complex contexts
g
explore connections in geometry
pose conditional constraints of the type
‘If… then…’
ask questions ‘What if…?’ or ‘Why?’
h
show step-by-step deduction in solving a
geometrical problem
i
state constraints and give starting points
when making deductions
j
understand the necessary and sufficient
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
conditions under which generalisations,
inferences and solutions to geometrical
problems remain valid
Section references
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
2
Section references
Geometrical Reasoning
Students should be taught to:
Properties of triangles
rectilinear shapes
a
and
other
distinguish between lines and line segments
use parallel lines, alternate angles and
corresponding angles
I10.3, H3.1
understand the consequent properties of
parallelograms and a proof that the angle
sum of a triangle is 180 degrees
I4.1, I10.3
H3.2, H3.3, H3.4
understand a proof that the exterior angle of
a triangle is equal to the sum of the interior
angles at the other two vertices
I 10.3
use angle properties of equilateral, isosceles
and right-angled triangles
I10.1
H3.3
explain why the angle sum of a quadrilateral
is 360 degrees
I10.1, H3.5
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
I20.1
H16.3
c
recall the definitions of special types of
quadrilateral, including square, rectangle,
parallelogram, trapezium and rhombus
I4.1
H3.2
classify quadrilaterals by their geometric
properties
I4.1, H4.2
calculate and use the sums of the interior and
exterior angles of quadrilaterals, pentagons
and hexagons
I10.1, I10.2
calculate and use the angles of regular
polygons
I10.2
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
H3.8
f
understand, recall and use Pythagoras’
theorem in 2-D, then 3-D problems
Chapter I5
Chapter H8
investigate the geometry of cuboids
including cubes, and shapes made from
cuboids, including the use of Pythagoras’
theorem to calculate lengths in three
H22.4
b
d
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
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Section references
dimensions
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
g
Section references
understand similarity of triangles and of
other plane figures, and use this to make
geometric inferences
I26.4
H3.9
understand, recall and use trigonometrical
relationships in right-angled triangles, and
use these to solve problems, including
those involving bearings, then use these
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)
Chapter I17 and I27
Chapter H13 and H22
calculate the area of a triangle using
H22.1
1
2
ab sin C
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
H24.7
use the sine and cosine rules to solve 2-D
and 3-D problems
H22.2, H22.3, H22.4
Properties of circles
h
recall the definition of a circle and the
meaning of related terms, including centre,
radius, chord, diameter, circumference,
tangent, arc, sector and segment
Ideas in this subsection are covered in I10.4,
I10.5, H3.6 and Chapter H26
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
explain why the perpendicular from the
centre to a chord bisects the chord
understand that inscribed regular polygons
can be constructed by equal division of a
circle
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
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Section references
prove and use the alternate segment
theorem
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
Section references
3-D shapes
i
3
use 2-D representations of 3-D shapes and
analyse 3-D shapes through 2-D projections
and cross-sections, including plan and
elevation
I4.6
H16.3
solve problems involving surface areas and
volumes of prisms, pyramids, cylinders,
cones and spheres
I20.4
H16.3
solve problems involving more complex
shapes and solids, including segments of
circles and frustums of cones
Chapter H19
Transformations and Coordinates
Students should be taught to:
Specifying transformations
a
understand that rotations are specified by a
centre and an (anticlockwise) angle
I23.3
H6.3
use any point as the centre of rotation
I23.3, H6.3
measure the angle of rotation, using right
angles, fractions of a turn or degrees
I23.3, H6.3
understand that reflections are specified by a
(mirror) line
I23.2, H6.3
understand that translations are specified by
a distance and direction (or a vector), and
enlargements by a centre and a positive scale
factor
I23.1, I23.4
H6.3, H6.4
Properties of transformations
b
recognise and visualise rotations, reflections
and
translations
including reflection
symmetry of 2-D and 3-D shapes, and
rotation symmetry of 2-D shapes
I4.3, I 4.4
H6.2
transform triangles and other 2-D shapes by
translation, rotation and reflection and
combinations of these transformations
H6.4
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
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Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
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c
recognise,
visualise
enlargements of objects
Section references
and
construct
H6.6
understand from this that any two circles and
any two squares are mathematically similar,
while, in general, two rectangles are not,
then use positive fractional and negative
scale factors
d
recognise that enlargements preserve angle
but not length
I23.4, H6.3
identify the scale factor of an enlargement as
the ratio of the lengths of any two
corresponding line segments
I26.4
H6.3
understand the implications of enlargement
for perimeter
H19.3
use and interpret maps and scale drawings
H6.6
understand the difference between formulae
for perimeter, area and volume by
considering dimensions
I20.5, H16.4
understand and use the effect of enlargement
on areas and volumes of shapes and solids
H19.3
Coordinates
e
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’
I26.5
H6.1
use axes and coordinates to specify points in
all four quadrants
I26.5, H6.1
locate points with given coordinates
H6.1
find the coordinates of points identified by
geometrical information
find the coordinates of the midpoint of the
line segment AB, given the points A and B,
calculate the length AB
I26.5, H8.3
Vectors
f
understand and use vector notation
All ideas are contained within Chapter H25
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
20
Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
associative properties of vector addition
Section references
solve simple geometrical problems in 2-D
using vector methods
21
Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
4
Section references
Measures and Construction
Students should be taught to:
Measures
a
use angle measure
I10.6, H6.2
know that measurements using real numbers
depend on the choice of unit
I12.5, H16.2
recognise that measurements given to the
nearest whole unit may be inaccurate by up
to one half in either direction
I12.5, H16.2
I12.8
convert measurements from one unit to
another
understand and use compound measures,
including speed and density
I12.7, H5.8
Construction
d
draw approximate constructions of
triangles and other 2-D shapes, using a ruler
and protractor, given information about their
side lengths and angles
I5.8, I26.1
H3.1
b
understand, from their experience of
constructing them, that triangles satisfying
SSS, SAS, ASA and RHS are unique, but
SSA triangles are not
I26.1
H3.1
construct specified cubes, regular tetrahedra,
square-based pyramids and other 3-D shapes
I4.5
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
I26.1
H6.8
c
Mensuration
f
calculate perimeters and areas of shapes
made from triangles and rectangles
I20.1
H16.3
d
find the surface area of simple shapes using
the formulae for the areas of triangles and
rectangles
I20.1
H16.3
find volumes of cuboids, recalling the
formula and understanding the connection to
counting cubes and how it extends this
approach
I20.4
H16.3
calculate volumes of right prisms and of
I20.4
22
Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
shapes made from cubes and cuboids
Section references
H16.3
23
Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
Section references
convert between area measures, including
square centimetres and square metres, and
volume
measures,
including
cubic
centimetres and cubic metres
I12.4
find circumferences of circles and areas
enclosed by circles, recalling relevant
formulae
I20.2, I20.3
H19.1
calculate the lengths of arcs and the areas
of sectors of circles
H19.1
Loci
e
find loci, both by reasoning and by using
ICT to produce shapes and paths
I26.3
H6.7
24
Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Ma4 Handling data
Content
1
Section references
Using and Applying Handling Data
Students should be taught to:
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
Questions in this section will normally be
found in the Mixed exercises at the end of
each chapter on Handling Data
Chapters H11B and I9B contain ideas on
how to set about a handling data piece of
coursework
decide what data to collect (including
sample size and data format) and what
statistical analysis is needed
(ii) collect data from a variety of suitable
sources, including experiments and
surveys, and primary and secondary
sources
(iii) process and represent the data: turn the
raw data into usable information that
gives insight into the problem
(iv) interpret and discuss the data: answer the
initial question by drawing conclusions
from the data
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)
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
Reasoning
d
apply mathematical reasoning, explaining
and justifying inferences and deductions,
justifying arguments and solutions
e
identify exceptional or unexpected cases
when solving statistical problems
Section H15.7 and Chapter I29 contain help
on how to interpret the graphs students may
wish to use in coursework.
Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
f
explore connections in mathematics and look
for relationships between variables when
analysing data
g
recognise the limitations of any assumptions
and the effects that varying the assumptions
could have on the conclusions drawn from
data analysis
2
Specifying the Problem and Planning
Section references
Students should be taught to:
a
see that random processes are unpredictable
b
identify key questions that can be addressed
by statistical methods
c
discuss how data relate to a problem, identify
possible sources of bias and plan to minimise
it
d
identify which primary data they need to
collect and in what format, including
grouped data, considering appropriate equal
class intervals
I8.5, I8.6, I8.7, I8.8
H4.1, H4.2, H4.3, H4.4
select and justify a sampling scheme and a
method to investigate a population,
including random and stratified sampling
H4.6
design an experiment or survey
I9B, 11B
decide what primary and secondary data to
use
I8.10
e
3
I8.9
H4.5
Collecting Data
Students should be taught to:
a
collect data using various methods, including
observation, controlled experiment, data
logging, questionnaires and surveys
Chapter I8
Chapter H4
b
gather data from secondary sources,
including printed tables and lists from ICTbased sources
Chapter I8
Chapter H4
c
design and use two-way tables for discrete
and grouped data
I8.1
d
deal with practical problems such as nonresponse or missing data
H4.4, H4.5
Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
4
Section references
Processing and Representing Data
Students should be taught to:
a
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,
stem-and-leaf
diagrams,
cumulative
frequency tables and diagrams, box plots
and histograms for grouped continuous
data
All of chapter I8 and I24
All of chapter H4 and H15.5
Also the ideas contained within H11B
b
understand and use estimates or measures of
probability from theoretical models, or from
relative frequency
I19.2
H9.3, H9.4
c
list all outcomes for single events, and for
two successive events, in a systematic way
I19.1
H9.1, H9.2
d
identify different mutually exclusive
outcomes and know that the sum of the
probabilities of all these outcomes is 1
H9.1, H9.2
e
find the median, quartiles and interquartile
range for large data sets and calculate the
mean for large data sets with grouped data
Chapter I16
Chapter H15
f
calculate an appropriate moving average
II24.9, H15.3
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)  P(B)
H9.5, H9.6
h
use tree diagrams to represent outcomes
of compound events, recognising when
events are independent
I19.1
H9.6
i
draw lines of best fit by eye, understanding
what these represent
I24.8
H4.9, H4.10
j
use relevant statistical functions on a
calculator or spreadsheet
5
Interpreting and Discussing Results
Students should be taught to:
a
relate summarised
questions
b
interpret a wide range of graphs and
diagrams and draw conclusions
Chapter I 29
H15.7
Chapter 11B
Chapter I29
Chapter 11B, H15.7
identify seasonality and trends in time
series
I24.3
H15.2
look at data to find patterns and exceptions
I29, H15.7
c
data
to
the
initial
Edexcel GCSE Maths (Linear) – Higher specification mapped to the old Heinemann series
Content
d
Section references
compare distributions and make inferences,
using shapes of distributions and measures of
average and spread, including median and
quartiles
H15.7
understand frequency density
Chapter 27
e
consider and check results, and modify their
approach if necessary
f
appreciate that correlation is a measure of the
strength of the association between two
variables
I24.8
H4.9
distinguish between positive, negative and
zero correlation using lines of best fit
I24.8
H4.9
appreciate that zero correlation does not
necessarily imply ‘no relationship’ but
merely ‘no linear relationship’
I24.8
H4.9
g
use the vocabulary of probability to interpret
results involving uncertainty and prediction
I3.1
H9
h
compare experimental data and theoretical
probabilities
I3.3, I19.2, H9.1, H9.2
i
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 parameters
I19.2
H9.3, H9.4
k
interpret social statistics including index
numbers
time series
and survey data