Download Edexcel A-level Mathematics Year 1 and AS

Edexcel A-level Mathematics
Year 1 and AS
Scheme of Work
© HarperCollinsPublishers Ltd 2017
Scheme of Work
Edexcel A-level Mathematics Year 1 and AS
This course covers the requirements of the first year of the Edexcel AS and A-level Mathematics specification. This scheme of work is designed to
accompany the use of Collins’ Edexcel A-level Mathematics Year 1 and AS Student Book, and references to sections in that book are given for each lesson.
The scheme of work follows the order of the Student Book, which broadly corresponds to the Edexcel 2017 specification order: this is not a suggested
teaching order but is designed for flexible planning. Each chapter from the Student Book is divided into one-hour lessons. We have assumed that
approximately 120 one-hour lessons are taught during the year, however lessons can be combined as you choose depending on your timetabling and
preferred teaching order, and we have left some free time for additional linking, problem-solving or investigation work and assessments. We have
suggested at the start of each chapter which chapters it would be beneficial to have already covered, to get the most out of the materials. In addition, we
have brought out links and cross-references between different topics in column 4 to assist you with planning your own route through the course and
making synoptic connections between topics for students.



Chapters 1 – 11 cover the pure mathematics content that is tested on AS paper 1 / A-level papers 1 & 2.
Chapters 12 – 14 cover the statistics content that is tested on AS paper 2 / A-level paper 3.
Chapters 15 – 16 cover the mechanics content that is tested on AS paper 2 / A-level paper 3.
Each lesson is matched to the specification content and the corresponding Student Book section with all relevant exercises and activities listed. Learning
objectives for each lesson are given, and a brief description of the lesson’s coverage to aid with your planning. A review lesson with assessment
opportunities is plotted at the end of each chapter, with exam-style practice available from the Student Book and our Collins Connect digital platform.
At the start of each chapter, we have suggested opportunities for you to use technology in the classroom. These ideas are developed further in the Student
Book with in-context Technology boxes. In addition, you’ll find activities in the Student Book to explore the Edexcel-provided large data set using a range of
technologies. These are clearly indicated in the scheme of work, and can be flexibly adapted to be the focus of class, group or individual work.
The scheme suggested is of course flexible and editable to correspond with your timetabling and to enable you to plan your own route through the course.
We hope that you will find this a useful aid to your planning and teaching.
KEY
Ex – exercise
DS – Data set activity (Statistics chapters only)
© HarperCollinsPublishers Ltd 2017
Scheme of Work
Edexcel A-level Mathematics Year 1 and AS (120 hours)
CHAPTER 1 – Algebra and functions 1: Manipulating algebraic expressions (8 Hours)
Prior knowledge needed
CHAPTER 2 – Algebra and functions 2: Equations and inequalities (8 Hours)
GCSE Maths only
Prior
knowledge needed
Technology
Chapter
1
Use the factorial
and combinations button on a calculator.
Technology
Onetohour
lessons
objectives
Specification content
Topic links
Use a calculator
check
solutions to quadratic equationsLearning
that have
been solved by hand.
Use
a graphing software
to plot
lines when solving
simultaneous
equationsalgebraically
so that studentsAS
can
see that
wherePapers
the lines
is the
solution.
Paper
1/A-level
1 &intersect
2:
Links
back
to GCSE
1 Manipulating
polynomials
algebraically
 Manipulate
polynomials
Use graphing software to show the solutions to quadratic
inequalities.
1.1 – mathematical proof
including:
Students collect like terms with
2.6 – manipulate
polynomials
o
expanding
brackets
and
simplifying
One include
hour lessons
Learning objectives
Specification
content
Topic links
expressions that
fractional
algebraically
by collecting like terms
are expected to write
AS Paper 1/A-level Papers 1 & 2:
Make connections back to
1coefficients
Quadratic and
functions
 Work with quadratic functions and
expressions with terms written in
2.3 – work with quadratics
factorising in 1.4
their graphs
Students
draw
andofwork
outThey
key expand
aspects a
functions and their graphs
Factorisation
descending
order
index.
of
quadratic
functions,
theyand
alsoexpand
work out
single
term over
a bracket
equations
of given
graphs.
two binomials.
Theyquadratic
use the same
Make
students
aware
that
the
techniques to go on to expand notation
three
f(x)
maybinomials.
be used.
simple
Consider
the multiple
difference
between drawing
2 Expanding
binomials
and sketching.
Students are introduced to Pascal’s
2triangle
The discriminant
quadratic
and use thisoftoa expand
multiple
function
binomials. One check students can use
when expanding
multiple
binomials
is to
Students
are reminded
that
the
2 the indices in each
ensure
the
sum
of
discriminant is 𝑏 – 4𝑎𝑐 and that the value
term
the total of the
index what
of thetype of
of
theisdiscriminant
indicates
original
expansion.
Students
use
factorial
roots and number of solutions a quadratic
notation
when
solve
problems
involving
has. Link this to how students will sketch
combinations.
quadratics
in the next chapter. Students
need to make sure they have a quadratic
© HarperCollinsPublishers Ltd 2017
 Understand and use the notation 𝑛!
and 𝑛𝐶𝑟
 Calculate and use the discriminant of a
quadratic function, including the
conditions for real and repeated roots
AS Paper 1/A-level Papers 1 & 2:
2.6 – manipulate polynomials
algebraically
AS
Paper 1/A-level Papers 1 & 2:
4.1 –– work
binomial
2.3
withexpansion
the discriminant
Links to Chapter 13
Probability and statistical
distributions:
13.1 The
Links
to 3.1 Sketching
binomial
distribution
curves of quadratic
of a quadratic function, including
the conditions for real and
repeated roots
functions
Student Book
references
1.1
Ex 1.1A
Student Book
references
2.1
Ex 2.1A
1.2
Ex 1.2A
2.2
Ex 2.2A
Ex 1.2B
AS Paper 1/A-level Papers 1 & 2:
The binomial expansion is
in
3 The
the binomial
form 𝑎𝑥 2 expansion
+ 𝑏𝑥 + 𝑐 = 0 before they  Understand and use the binomial
2.6 – manipulate polynomials
used in Chapter 13
expansion of (𝑎 + 𝑏)𝑛
calculate the discriminant.
Students are
the binomial
CHAPTER
3 – introduced
Algebra andtofunctions
3: Sketching curves (9 Hours)
algebraically
Probability and statistical
expansion
formula
as a way of solving any
4.1 – binomial expansion
distributions for binomial
Prior
knowledge
needed
binomial2expansion, they should state
distributions
Chapter
formulathe
they
are using at the start
AS Paper 1/A-level Papers 1 & 2:
5.1 Equations of circles
3which
Completing
square
 Complete the square
Technology
of any answer.
1.1 – mathematical proof
uses completing the square
Graphing
software can be heavily used in this chapter; some examples are below.
Students
complete
the to
square
the
2.3 – complete the square
when solving problems
Use graphing
software
checkonanswers.
general
expression
of ato
quadratic.
They
go of inflection and see what happens to the gradient of the curve each side of the pointinvolving
circles
Use graphing
software
zoom into
a point
of inflection.
ontographing
solving quadratic
equations
byhow to graphs behave.
Links
to
3.1
Use
software
to
compare
AS Paper 1/A-level Papers 1 & 2:
Factorisationsketching
is used in
4 Factorisation
 Manipulate polynomials algebraically
completing
the
square.to look at approximate coordinates of turning points.
curves
Use
graphing
software
2.6 – manipulate polynomials
Chapterof2quadratic
Algebra and
including:
Students factorise different sorts of
functions
algebraically
functionsTopic
2: Equations
and
o factorisation
The
general formula
for
solving a They
One hour
lessons
Learning objectives
Specification content
links
expressions
including
quadratics.
inequalities
when
working
quadratic
equation
can be of
derived
by
factorise
a difference
twofunctions
squares.
AS Paper 1/A-level Papers 1 & 2:
Builds
on from equations
Chapter 2
1also
Sketching
curves
of quadratic
 Use and understand the graphs of
with quadratic
completing
the square
on the
generalto
Some questions
are given
in relation
2.3
–
work
with
quadratic
Algebra
and
functions
2:
functions
and
in
Chapter
3 Algebra
form
𝑦=
𝑎𝑥 2 +curves
𝑏𝑥
𝑐of– quadratic
this
Students
sketch
real life
problems
to+
show
howis question
functions and their graphs
Equations
and3:
inequalities
and functions
Sketching
 Sketch curves defined by simple
6factorisation
in Ex 2.4A.
used.
equations
andis find
quadratic equations
2.7 – understand and use graphs
curves
quadratic equations
from sketches knowing that a sketch
of
functions;
sketch
curves
Algebraic
division equations
Link ability
algebraic
division
to
45 Solving
quadratic
AS Paper 1/A-level Papers 1 & 2:
The
to find
solutions
Manipulate
polynomials
 Solve
quadratic
equationsalgebraically
using
shows the curve along with its key
defined
by simplepolynomials
equations
2.6 – mathematical
manipulate
numerical
division
1.1
proof
will
help you
solve
oincluding:
completing the square
features.
Theare
keythen
features
being;
All the skills
combined
write
algebraically,
including
expanding
Students
use
factorisation,
usingtothe
2.3
– solve quadratic
equations
distance, speed and time
o the
expanding
formulabrackets and simplifying
maximum
or minimum
turning
point
and
algebraiccompleting
fractions
inthe
their
simplest
brackets,
collecting
like
terms,
formula,
square
andform.
problems in Chapter 15
by collecting like terms
o factorisation
its
coordinates,
the quadratic
roots
with
x
Students
work
through
the
factor
factorisation
and
simple
algebraic
calculators
to solve
equations,
Kinematics and in Chapter
o factorisation
intercept/s
if
appropriate,
the
y
intercept.
theorem
and
the
remainder
theorem.
division;
use
of
the
factor
theorem
they consider advantages and
6 Trigonometry and
o simple algebraic division
Students then divide
disadvantages
of eachpolynomials
method. by an
Chapter 7 Exponentials
o use of the factor theorem
AS Paper 1/A-level Papers 1 & 2:
Builds on from Chapter 2
2expression
Sketching–curves
ofclear
cubictofunctions
make
students
that  Use and understand the graphs of
It’s important
not toit be
seen as
a discrete
and logarithms
2.7 - understand and use graphs
Algebra and functions 2:
functions
theyofuse
the
same
method
as they
do for
set
skills
but
providing
different
Link to graph drawing, 3.1
Students
consider
how
the
cubic
functions
of
functions;
sketch
curves
Equations and inequalities
 Sketch curves defined by simple cubic
numerical
long
division.
information
about
the
same
equation.
Sketching curves of
behaves as it tends to positive and
defined
by
simple
equations
equations
quadratic
functions
6
Laws
of
indices,
manipulating
surds
AS
Paper
1/A-level
Papers
1
&
2:
Builds on GCSE
skills

Understand
and
use
the
laws
of
indices
negative infinity, this determines the
2.7 – interpret algebraic solutions
5
Solving
simultaneous
equations
AS
Paper
1/A-level
Papers
1
&
2:
This
is
used
when
finding
1.1
–
mathematical
proof
Laws
of
indices
is used
in

Solve
simultaneous
equations
in
two
for
all
rational
exponents
shape of the curve. The coordinates of the
of equations graphically
2.4
simultaneous
of7intersection
with
Students solve questions using the laws of  variables
2.1 – solve
understand
and use the laws points
Chapter
Exponentials
by
Use
and
manipulate
surds
axes intercepts and point of inflection are
Students
go through
solvingand
twofractional
linear
equations
in two
variables by
circles
and straight
lines 7.2
in
indices, including
negative
of indices for
all rational
and logarithms,
section
o elimination or
included on the graph. Students use this
simultaneous
by elimination
elimination
Chapter
5 Coordinate
indexes. They equations
are reminded
that surds are
exponents and by substitution,
Manipulation
of indices
o by substitution,
information
sketch
curves
cubicto
and
by to
substitution.
They
need
including
onemanipulate
linear and one
geometry
2:used
Circles
rootsthen
of rational
numbers
andofsimplify
2.2 - use and
surds,
and surds is
in
including one linear and one quadratic
functions.
think
about which
is the
best method and
quadratic
equation the
expressions
involving
surds.
including rationalising
Chapter 8 Differentiation
equation
why.
denominator
and Chapter
9 Integration
AS
Paper 1/A-level Papers 1 & 2:
Builds
on from
Chapter 2
3 Sketching curves of quartic functions
 Use and understand the graphs of
7 Rationalising the denominator
AS Paper
1/A-leveland
Papers
1 & 2:
 functions
Use and manipulate surds, including
2.7
- understand
use graphs
Algebra and function 2:
Students
turning
points and points of  Solve
6 Solving find
linear
and quadratic
AS
Paper
1/A-level
1.1functions;
– mathematical
proof
simultaneous
equations
in quartic
two
rationalising
denominator
of
sketchPapers
curves1 & 2:
Equations and inequalities
 Sketch
curvesthe
defined
by simple
simultaneous
variables
by
intersection
toequations
sketch curves of quartic
defined by simple equations
equations
© HarperCollinsPublishers Ltd 2017
1.3
Ex 1.3A
2.3
Ex 2.3A
1.4
Ex 1.4A
Student Book
references
3.1
Ex 3.1A
1.5
2.4
Ex 1.5A
2.4A
3.2
Ex 3.2A
Ex 3.2B
1.6
2.5
1.7
Ex 2.5A
1.6A
Ex 2.5B
1.7A
3.3
1.8
Ex 3.3A
2.6
Ex
Ex 1.8A
3.3B
Ex 2.6A
Recap manipulating
and complete
o elimination
or
functions.
They look surds
at maximum
and
 Interpret
the algebraic
solution of
Student
Ex 1.7A ifsolve
required
linear
and
andthen
quadratic
go
o by substitution,
equations
graphically
minimum
turning
points
andstudents
then at the
simultaneous
on to of
rationalise
equations
the denominator
considering
ofwhich
including one linear and one quadratic
roots
the equation.
A typical
example
method
algebraic
is
fractions.
the
most
appropriate
to
use.
equation
of a quartic to be sketched is 𝑦 =
2Chapter review
2
8
lesson

Identify areas of strength and
𝑥 (2𝑥 − 1) .
7 Solving linear and quadratic
development
within
the content
of the
 Solve
linear and
quadratic
inequalities
inequalities
Recap
key points
ofof
chapter.
Students
to
4
Sketching
curves
reciprocal
functions
chapter
a single
variable and
interpret
such
 inUse
and understand
the
graphs of
complete the exam-style questions,
inequalities
functions graphically, including
extensionsketch
solve
questions,
inequalities,
or of
online
useend-ofset of
Students
graphs
reciprocals
with
brackets
fractions
 inequalities
Sketch curves
defined
by and
simple
𝑎
𝑎
notation
chapter
test
to
list
integer
members
of
two
or
 Express
solutions through correct use
reciprocals
linear 𝑦 = and quadratic 𝑦 = 2
𝑥
𝑥
more
combined
inequalities
andto the
Assessment
‘and’ and
or through
set of
 of
Interpret
the‘or’,
algebraic
solution
functions.
They are
introduced
represent
inequalities
Strict
Exam-style
questions
1graphically.
in
Student
Book
notation
equations graphically
word
discontinuity
and
know
that this
is a
inequalities
are
aindotted
Exam-style
Student Book
point
whereextension
therepresented
valuequestions
of x orwith
y is1not
line,
inclusive
inequalities
are
represented
End-of-chapter
testare
1 on
Collins
Connect
defined.
They also
told
that an
with
a solidisline.
asymptote
a straight line that a curve
Link
to
solving
drawing
approaches butequations,
never meets,
thesegraphs
should
and
looking
at
inequalities
from
the They
be clearly highlighted on the graph.
sketch
of the
a graph.
also give
points of interception on the
8
Chapter
review lesson
 Identify areas of strength and
axis.
development
within
theofcontent
of the
5 Intersection points
 Use
intersection
points
graphs to
Recap key points of chapter. Students to
chapter
solve equations
complete
the exam-style
questions,
Students sketch
more than
one function
extension
or the
online
end-ofon a graphquestions,
to work out
intersection
chapter
test
points of the functions and link this to
Assessment
solve an equation which includes these
Exam-styleThey
questions
2 in
Student Book
functions.
use the
information
they
Exam-style
questions
2 in in
Student
have
learnt extension
for the previous
section
this Book
End-of-chapter
2 on
Collins Connect
exercise
to solvetest
these
problems.
6 Proportional relationships
Students express the relationship
between two variables using the
proportion symbol and then find the
equation between the two variables. They
also recognise and use graphs that show
proportion.
© HarperCollinsPublishers Ltd 2017
 Understand and use proportional
relationships and their graphs
2.4
2.2 –- use
solve
and
simultaneous
manipulate
surds,
2.7
interpret
algebraic solutions
equations
including
rationalising
in two
variables
the by
of
equations
graphically
elimination
denominator
and by substitution,
including one linear and one
quadratic equation
AS Paper 1/A-level Papers 1 & 2:
2.5Paper
- solve1/A-level
linear and
quadratic
AS
Papers
1 & 2:
inequalities
in a single
variable
2.7
- understand
and use
graphs
andfunctions;
interpretsketch
such inequalities
of
curves
graphically,
including
inequalities
defined
by simple
equations
𝑎
with
brackets
and
fractions
including polynomials 𝑦 = and
𝑥
𝑎
2.5 - express
solutions through
𝑦 = 2 (including their vertical
𝑥 use of ‘and’ and ‘or’, or
correct
and
horizontal
asymptotes)
through
set notation
This is used in Chapter 5
Coordinate
geometry
2:
Graph
sketching
skills are
Circles when
solving
further
developed
in
problems7involving
Chapter
Exponentials
equations
of circles
and
logarithms
See below
2.7
Ex 2.7A
3.4
Ex 3.4A
2.83.4B
Ex
Ex 2.8A
See below
AS Paper 1/A-level Papers 1 & 2:
2.7 interpret algebraic solution of
equations graphically; use
intersection points of graphs to
solve problems
Links back to 2.5 Solving
simultaneous equations
3.5
Ex 3.5A
AS Paper 1/A-level Papers 1 & 2:
2.7 – understand and use
proportional relationships and
their graphs
Links back to GCSE
3.6
Ex 3.6A
AS Paper 1:
Translations and stretches
3.7
 Understand the effects of simple
2.8 – effects of simple
arise in 6.5 solving
Ex 3.7A
transformations on the graphs of
CHAPTER
4 – Coordinate
5
geometry
1: Circles
2:
Equations
(6 Hours)
lines (5 𝑦
Hours)
Students transform
functions
and sketch
transformations including
trigonometric equations
𝑦of=straight
f(𝑥), including
= f(𝑥) + 𝑎 and
the
graphs
using the two
sketching associated graphs
𝑦 = f(𝑥 + 𝑎)
Priorresulting
knowledge
needed
transformations
identified in the learning
Chapter
1
2
objective.
A-level Papers 1 & 2:
Chapter
4
Technology
2.9 – effects of simple
Use graphing software to check answers.
Technology
transformations
to investigate
location
as the
varies
both
positive
and
negative
and integer
and fractional
values.
Use graphing software draw
𝑥 2 + 𝑦 2 the
= 25
and 𝑥 2of+the
𝑦 2 x-intercept
= 36 to show
howgradient
the centre
of awith
circle
is always
(0,including
0) and
the radius
is the square
root of the
number on the rightsketching
associated
graphs
Use
graphing
software
to
find
equations
of
lines
that
are
parallel.
hand side of the equation. Get students to predict what other circles will look like given an equation of a circle in this form.
8
Stretches
AS
Paper
1:not about
Translations
and stretches
 circles
Understand
the
effects
of simple
Use
graphing
software
thatatintersect
but are
not
perpendicular.
What
do the
students
notice
the products
of their
gradients?
Graphing
software
can to
beplot
usedlines
to look
other
(still
with
the
equation
written
in this
form
but
with centre
(0, 0) ) and
link the
equation
of the circle 3.8
to the
2.8
–
effects
of
simple
arise
in
6.5
solving
Ex
3.8A Book
transformations
on
the
graphs
of
coordinates of the centre and length of radius.
Student
One hour
lessonsand sketch
Learning
objectives
Specification
content
Topic links
Students
transform
functions
transformations
including
trigonometric
equations
𝑦
=
f(𝑥),
including
𝑦
=
𝑎f(𝑥)
and
Use graphing software to find midpoints of line segments.
references
the
resulting
the1 two
sketching
associated
graphs#
𝑦 = f(𝑎𝑥).
Use
graphing
software
plot
a circle and tangent.
AS Paper 1/A-level
Papers
1 & 2:
4.2 and 4.3 link to Chapter
4.1
1 Straight
linegraphs
graphsusing
–topart
 Write
the equation of a straight line in
transformations identified in the learning
Student
3.1 – understand and use the
15 Kinematics
Ex
4.1A Book
the form 𝑎𝑥 + 𝑏𝑦 + 𝑐 = 0
One hour
lessons of straight
Learning objectives
Specification
Topic links
Students
equations
objective.rearrange
A-level
Papers
1 & 2:content
references
equation
of a straight
line,
 Find the equation of a straight line
lines
to the form
𝑎𝑥 +–𝑏𝑦
+ 𝑐1 = 0
2.9Paper
– effects
simple
including
theof
forms
4.2
AS
1/A-level
Papers 1 & 2:
Links back to GCSE
5.1
1 Equations
of circles
part
through
point
withcircle
a given
 Find
the one
centre
of the
andgradient
the
transformations
including
𝑦–
𝑦
=
𝑚(𝑥–
𝑥
)
and
4.2A
3.2
–
understand
and
use
the
Ex 5.1A
using the
radius
from
formula
the equation of a circle
1
1
Students
find equations
the equation
of a line
Students link
of circles
to given
sketching
associated
graphs
𝑎𝑥
+
𝑏𝑦
+
𝑐
=
0
coordinate
geometry
of
the
circle
𝑦– 𝑦1 the
= 𝑚(𝑥–
𝑥1 ) of a circle
 Write
equation
the
gradient
and alesson
point
on learn
the line
Pythagoras’
theorem.
They
theand
9 Chapter
review
See below
 Identify areas of strength and
including using the equation of a
solve
problems
using
general
equation
of a this.
circle and solve
development within the content of the circle in the form
Recap key points
of chapter.
Students
chapter
problems.
They find
the equation
of a to
(𝑥– 𝑎)2 + (𝑦– 𝑏)2 = 𝑟 2
2
Straight
line
graphs
–
part
2
AS
1/A-level
2:
Graph sketching skills are
4.3

Find
the
gradient
of
the
straight
line
complete
the
exam-style
questions,
circle from its centre and a point on the
3.2Paper
– complete
the Papers
square 1to&find
3.1
–
understand
and
use
the
further
developed
in
Ex 4.3A
between two points
extension
questions,
end-ofthe centre and radius of a circle
circumference.
Givenor
anonline
equation
of a
Students
find
the
gradient
given
two
equation
of
a
straight
line,
Chapter
7
Exponentials
 Find the equation of a straight line
chapter
test find the centre and radius
circle students
𝑦–𝑦1
𝑥–𝑥1
points
on
the
line
and
solve
problems
including the forms
and logarithms
4.4
using the formula
=
Assessment
by
completing
the
square
on
𝑥
and
𝑦.
𝑦2–𝑦1
𝑥2–𝑥1
using
this.
𝑦–
𝑦
=
𝑚(𝑥–
𝑥
)
and
Ex 4.4A
1
1
Exam-style questions 3 in Student Book
𝑎𝑥
+
𝑏𝑦
+
𝑐
=
0
Exam-style extension questions 3 in Student Book
Given
two points
on3aon
students
use
AS Paper 1/A-level Papers 1 & 2:
5.1
2
Equations
of circles
–line
part
2 Connect
 Find the centre of the circle and the
End-of-chapter
test
Collins
the formula to find the equation of the
3.2 – understand and use the
Ex 5.1B
radius from the equation of a circle
Recap
straightlesson
line. one and then students find
coordinate geometry of the circle
 Write the equation of a circle
the
equation
a circle from the
including
using the Papers
equation
3 Parallel
andofperpendicular
linesends of a  Understand and use the gradient
AS Paper 1/A-level
1 &of2:a
Links back to GCSE
4.5
diameter, this involves them using the
circle
in the form
3.1 – gradient
conditions for two
Ex 4.5A
conditions for parallel lines
formula
of agradients
line
(𝑥– 𝑎)2 lines
+ (𝑦–
= 𝑟 2 or
Studentsfor
usethe
themidpoint
facts about
of
straight
to𝑏)
be2 parallel
Ex 4.5B
 Understand and use the gradient
3.2
–
complete
the
square
to
find
segment.
parallel and perpendicular straight lines to
perpendicular
conditions for perpendicular lines
the centre and radius of a circle
solve problems.
4 Straight line models
AS Paper 1/A-level Papers 1 & 2:
This is used in Chapter 5
4.6
 Be able to use straight line models in a
3.1 – be able to use straight line
Coordinate geometry 2:
Ex 4.6A
variety of contexts
Students apply what they have learnt in
models in a variety of contexts
Circles when finding a
this chapter to solve problems in a variety
gradient to solve problems
7 Translations
© HarperCollinsPublishers Ltd 2017
ofAngles
different
contexts including real-world
3
in semicircles
 Find the equation of a circle given
scenarios.
different information such as the end
A geometric proof is used to show that for
points of a diameter
three points on the circumference of a
 Use circle theorems to solve problems
circle,
if two
pointslesson
are on a diameter,
5 Chapter
review
 Identify areas of strength and
then the triangle is right-angled. Students
development within the content of the
are
alsokey
reminded
Pythagoras’
Recap
points ofthat
chapter.
Students to
chapter
theorem
that a questions,
triangle has a
completewill
theshow
exam-style
extension
or online
end-ofright
anglequestions,
and gradients
can be
used to
chapter
test
show that two lines are perpendicular.
Assessment
4
Perpendicular
from 4the
centre toBook
a
 Find the equation of a perpendicular
Exam-style
questions
in Student
bisector
chord
Exam-style extension questions 4 in Student Book

Use circle theorems to solve problems
End-of-chapter test 4 on Collins Connect
A geometric proof is used to show that
congruent triangles are identical and then
links to show that the perpendicular from
the centre of the circle to a chord bisects
the chord.
5 Radius perpendicular to the tangent
A geometric proof by contradiction is used
to show that a radius and tangent are
perpendicular at the point of contact.
Pythagoras’ theorem is used to find the
length of a tangent. Students then go on
to consider that for any circle there are
two tangents with the same gradient.
Given the gradient of the tangent and the
equation of the circle they can find both
points where the two tangents touch the
circle. The second method used it to show
that a line is tangent to a circle is that the
discriminant will be zero i.e. 𝑏 2 – 4𝑎𝑐 = 0.
6 Chapter review lesson
© HarperCollinsPublishers Ltd 2017
 Find the equation and length of a
tangent
 Use circle theorems to solve problems

Identify areas of strength and
development within the content of the
chapter
AS Paper 1/A-level Papers 1 & 2:
1.1 - mathematical proof
3.2 - use of the following
properties:
the angle in a semicircle is a right
angle
Links backtangents
involving
to GCSE and radii
of circles and points of
intersections of circles with
straight lines
AS Paper 1/A-level Papers 1 & 2:
3.2 - use of the following
properties: the perpendicular
from the centre to a chord bisects
to chord
Links back to GCSE
AS Paper 1/A-level Papers 1 & 2:
3.2 - use of the following
properties: the radius of a circle at
a given point on its circumference
is perpendicular to the tangent to
the circle at that point
5.2
Ex 5.2A
See below
5.3
Ex 5.3A
5.4
Ex 5.4A
Ex 5.4B
See below
Recap key points of chapter. Students to
complete the exam-style questions,
extension questions, or online end-ofchapter test
Assessment
Exam-style questions 5 in Student Book
Exam-style extension questions 5 in Student Book
End-of-chapter test 5 on Collins Connect
CHAPTER 6 – Trigonometry (7 Hours)
Prior knowledge needed
Chapter 2
Chapter 3
Technology
Use calculators to check values.
Use graphic software to confirm the shapes of graphs.
One hour lessons
1 Sine and cosine
Students extend their knowledge of sine
and cosine beyond 90° to between 0° and
180° by imagining a rod of length one unit
on a coordinate grid.
2 The sine rule and the cosine rule
Students work through proofs for the sine
rule, cosine rule and formula for the area
of a triangle and then use these to solve
problems.
Learning objectives
 Define sine for any angle
 Define cosine for any angle
 Use the sine rule
 Use the cosine rule
 Use the formula for the area of a
triangle
CHAPTER 7 – Exponentials and logarithms (8 Hours)
© HarperCollinsPublishers Ltd 2017
Specification content
Topic links
AS Paper 1/A-level Papers 1 & 2:
5.1 – understand and use the
definitions of sine and cosine for
all arguments
Links back to GCSE
AS Paper 1/A-level Papers 1 & 2:
5.1 - the sine and cosine rule
5.1 – the area of a triangle in the
1
form 𝑎𝑏sin𝐶
Links back to GCSE
2
Student Book
references
6.1
Ex 6.1A
Bearings will be extended
further in Chapter 10
Vectors
6.2
Ex 6.2A
AS Paper 1:
3 Trigonometric
 Understand the graph of the sine
Prior
knowledgegraphs
needed
5.2 – Understand and use the sine
function and interpret its symmetry
Chapter 1
Students start
by considering the sine and
CHAPTER
and cosine functions; their graphs,
and periodicity
Chapter 2 8 – Differentiation (8 Hours)
cosine
of3any angle
using x and y
symmetries and periodicity
Chapter
 Understand the graph of the cosine
Prior
knowledge
needed
coordinates
4 of points on the unit circle.
function and interpret its symmetry
Chapter 1
This
is then
A-level Papers 1 & 2:
and periodicity
Chapter
3 linked to the trigonometric
Technology
graphsplotting
and
symmetries
andthe graphs 𝑦 = 1.2𝑥 .
5.3 – Understand and use the sine
Chapter
4 their
Graph
software
to draw
and cosine functions; their graphs,
periodicity.
Use
the log, power of e and ln button on a calculator.
Technology
Use spreadsheet
software
to
calculate
values
of
logarithms.
graphical software to find the gradients of a quadratic curve in example 2 in section 8.2.symmetries and periodicity
4
The
tangent
function
AS Paper
1:
 Define
the tangent
foralso
any need
angleto find them
Graphical
software
can be used to look for stationary
points
– students
using differentiation.
One hour lessons
Learning objectives
Specification
5.1
–
understand
andcontent
use the
 Understand the graph of the tangent
One
hour
lessons
Learning
objectives
Specification
content
𝒙 when the tangent
Students
consider
definition
of
tangent
for
all1 & 2:
function
and interpret
its symmetry
AS Paper 1/A-level Papers
1 The function 𝒂
 Use
and manipulate
expressions
in the
𝑥
cannot
be
calculated
and
look
at
the
arguments
and
periodicity
6.1Paper
– Know
and usePapers
the function
1/A-level
1 & 2:
1 The gradient of a curve
form
𝑦 = 𝑎 the
where
the variable
x is an AS
 To
consider
relationship
between
Students
learn
the terms
exponential
similarities
between
the tangent
graph
-– understand
Understand
and use
use
the
 the
Usetangent
an important
formula
connecting
𝑎 𝑥 and
its graph, where
a the
is
7.1
and
index
to a curve
and the
gradient 5.2
Students
areexponential
introduced
to the concept
growth
decay.
The
and theand
sine
and
cosine graphs.
Theydraw
use
tangent
graph,
sin
𝑥,and
cosinterpret
𝑥 at
and
tangraphs
𝑥
positive functions;
derivative
of f(𝑥) asitsthe
gradient
the
curve
a point
 of
Draw
of the form
sinƟ
𝑥
that
of𝑦a=
curve
at any
symmetry
and
periodicity
𝑥
graphs
theto
form
𝑎 and
arepoint
madeis  Introduction
tanƟthe
=ofgradient
solve
problems.
of
the
tangent
to
a
graph
of 𝑦 =
𝑦=𝑎
of the term derivative
cosƟ
5.3
–
understand
and
use
equal
thethere
gradient
of the tangent
at
awareto
that
is a difference
in the
f(𝑥)
at
a
general
point
(𝑥,
𝑦); the
Use the graph
to find approximate
 Recognise
the derivative
function of
sinƟas a limit;
2
that
point.
shape
of the graph when a < 1 and a > 1,
gradient
of
the
tangent
solutions
𝑦
=𝑥
tanƟ =
interpretation as a cosƟ
rate of change
they should understand this.2
Students then look at 𝑦 = 𝑥 and see that
A-level Papers 1 & 2:
the gradient at any point on the curve is
5.1 – understand and use the
2𝑥. The derivative is then introduced as
AS
Paper 1/A-level
Papers
2
Logarithms

Understand
and
use
logarithms
and
definition
of tangent
for all1 & 2:
the connection between the x coordinate
6.3
– know and use the definition
their
connection
with
indices
arguments
of
a pointstart
and the
curve at
Students
withgradient
the lawsofofthe
logarithms
𝑥
of
as the inverse
of 𝑎
 Understand the proof of the laws of
5.3log𝑎𝑥
- Understand
and use
the,
that
point.
in
base
10 and the laws of logarithms are
where
is positiveits
and
𝑥≥0
logarithms
tangent𝑎functions;
graph,
linked to laws of indices with a proof for
6.4
–
understand
and
use
symmetry
and periodicity
AS
Paper 1/A-level
Papersthe
1 &laws
2:
2 The gradient of a quadratic curve
 Extend the result for the derivative of
each law. They work out basic logarithms
of
logarithms
2
2
5.5 – sketching
understand
and
use
7.1
the
gradient
𝑦 = 𝑥 to the general case 𝑦 = 𝑎𝑥
From
exercise
8.2Aastudents
areThey
lead then
to
in base
10 without
calculator.
sinƟ
function for
a given
 Be able to differentiate any quadratic
2
tanƟ
= curve
the
general
resultthe
thatlaws
if 𝑦for
= 𝑎𝑥
then
𝑛
move
onto using
logarithms
7.2 – differentiate 𝑥cosƟ
, for rational
equation
𝑑𝑦
5 Solving
trigonometric
equations
AS Paper
1:
= 2𝑎𝑥.
After
some the
examples
students
of
any
base
and
using
log𝑎𝑏
button
on

Solve
simple
trigonometric
equations
values
of
𝑛,
and
related
constant
𝑑𝑥
5.4 – solvesums
simple
trigonometric
a calculator.
multiples,
and
differences
are
given the general result when
Students thing aabout
the multiple
equations in a given interval,
differentiating
quadratic.
It is also made
𝒙
AS
Paper 1/A-level
1 & in
2:
3
Thethat
equation
𝒂should
= 𝒃 be equations
 Solve equations in the form 𝑎 𝑥 = 𝑏
solutions
of
trigonometric
and
including
quadraticPapers
equations
clear
terms
differentiated
6.5
–
solve
equations
in
the
form
 Understand a proof of the formula to
link
this to in
the graphs
of the
function.
sin, cos and tan and equations
separately
quadratic
equation.
They
Students
solvea equations
of the form
𝑥
𝑎
= 𝑏 multiples of the
change
the
base
of
a
logarithm
involving
start
to
sketch
curves
of
the
derivative.
𝒙
𝒂 = 𝒃 by taking the logarithms of both
unknown angle
sides. The work through a proof of the
A-level Papers 1 & 2:
© HarperCollinsPublishers Ltd 2017
Link back to GCSE
6.3
Ex 6.3A
Link to Chapter 4
Topic
links 1:
Coordinate
geometry
Topic
links
Equations
Links back of
to straight
GCSE lines
6.4
Student Book
Ex
6.4A Book
references
Student
7.1references
Ex 7.1A
8.1
Ex 8.1A
The skills learnt in this
chapter are essential when
students learn Chapter 9
Integration
8.2
Ex 8.2A
The skills learnt in 1.6 Laws
of indices are used here
7.2
Ex 7.2A
Ex 7.2B
8.2
Ex 8.2B
Link this back to
transformation of graphs in
Chapter 3 Algebra and
functions 3
6.5
Ex 6.5A
7.3
Ex 7.3A
formula
to changeofthe
3
Differentiation
𝒙𝟐 base
and 𝒙of𝟑 a
 Understand a proof that if 𝑓(𝑥) = 𝑥 2
then 𝑓’(𝑥) = 2𝑥
logarithm.
Students work through a proof that the
derivative of 𝑥 2 is 2𝑥, they are told that
using the formula is called differentiation
from
first principles.
4 Logarithmic
graphs
 Use and manipulate expressions in the
6 A useful formula
forman𝑦 important
= 𝑘𝑎 𝑥 where
the variable
x is
 Use
formula
connecting
Students
look at two
types of
4
Differentiation
of adifferent
polynomial
an
sinindex
𝑥, cos 𝑥 and
tan 𝑥 containing
 Differentiate
expressions
𝑥
curve
𝑦 =diagrammatically
𝑎𝑥 𝑛 and 𝑦 = 𝑘𝑏 see
. To
find the
Students
that
powers graphs to estimate
 integer
Use logarithmic
2
2
parameters
the
logarithms
of
sin Ɵ
The
general
+ costhey
result
Ɵ =take
1for
and
differentiation
then
use thisis
parameters in relationships of the form
both
sides
then
rearrange
this are
identity
introduced
to and
go
to on
students
to solve
and
trigonometric
examples
𝑦 = 𝑎𝑥 𝑛 and 𝑦 = 𝑘𝑏 𝑥 , given data for 𝑥
equation
into theThey
formthen
𝑦 = go
𝑚𝑥on
+ to
𝑐. In the
equations.
worked
through.
and 𝑦
first caseatthey
plot log 𝑦 against
looking
differentiating
the sumlog
or𝑥 and
obtain
straight
linetheorem.
where the intercept
difference
of terms.
Link to aPythagoras’
is
log
𝑎
and
the
gradient
5
Differentiation
𝒙𝒏 is 𝑛 and in the
7 Chapter
reviewof
lesson
 Differentiate
Identify areasexpressions
of strengthcontaining
and
second case they plot log 𝑦 against 𝑥 and
powers
development
of variables
within the content of the
obtain
a straight
where
the
intercept
Recap key
Students
move
points
online
oftochapter.
work with
Students
powers
to
chapter
is
logare
𝑘 and
the
gradient
isquestions,
log
complete
that
not
the
integer
exam-style
values
and𝑏.variables
5
The than
number
e y. Differentiation
other
x and
is again  Know that the gradient of 𝑒 𝑘𝑥 is equal
extension
questions,
or online end-ofchaptertotest
linked
being the gradient of the graph
to 𝑘𝑒 𝑘𝑥 and hence understand why the
Students
lookofatchange.
graphs of the form
and
the rate
exponential model is suitable in many
Assessment
𝑦Stationary
= 𝑎 𝑥 . and
see the
is always
Exam-style
6
questions
points
and
6gradient
inthe
Student
second
Book a
 applications
Determine geometrical properties of a
multiplier
𝑦. When the
multiplier
one Book
Exam-stylex extension
derivative
questions
6 inisStudent
curve
then
the function
is 6ofon
theCollins
form 𝑦
= 𝑒𝑥
End-of-chapter
test
Connect
and
go on to generalise
𝑦 = 𝑒 𝑎𝑥
Differentiation
is used tothat
findfor
stationary
𝑎𝑥
𝑑𝑦 for any
then
thei.e.
gradient
= 𝑎𝑒
= 𝑎𝑦
points,
the point
where
= 0.
value of 𝑎. Students should 𝑑𝑥
realise that
Students are shown that the second
when the rate of change is proportional to
derivative will show if a turning point is a
the 𝑦 value, an exponential model should
maximum or minimum point so there is
be used. Insure that students include the
no need to draw𝑎𝑥the graph to ascertain
graphs of 𝑦 = 𝑒 + 𝑏 + 𝑐.
this information.
6 Natural logarithms
 Know and use the function ln𝑥 and its
graphs
7 Tangents and normal
 Find
equations of tangents and normal
Students are introduced to the fact that
 using
Know differentiation
and use ln𝑥 as the inverse
ln𝑦 means
to the
𝑒 and
function of 𝑒 𝑥
The
normallogarithm
at any point
on abase
curve
is
that if 𝑒 𝑥 = 𝑦 then
= 𝑥. The
graphs
of
perpendicular
to theln𝑦
tangent
at that
point.
𝑥
𝑦 =the
ln𝑥product
and 𝑦 =
show
students
As
of 𝑒their
gradients
is that
they are a reflection of each other in the
line 𝑦 = 𝑥 due to the fact they are inverse
© HarperCollinsPublishers Ltd 2017
AS Paper
5.7
– solve1/A-level
simple trigonometric
Papers 1 & 2:
equations
7.1
– differentiation
in a given from
interval,
first
including quadratic
principals
for small positive
equations in
sin, cos powers
integer
and tan of
and
𝑥 equations
𝑛
involving
7.2
- differentiate
multiples𝑥of
, the
for rational
unknown
values
of 1/A-level
𝑛,
angle
and related
constant
AS
Paper
Papers
1 & 2:
multiples,
differences
6.3
– know
and and
use the
definition
AS Paper
1:sums
of
as
inverse
of sin
𝑎1𝑥&
,2 Ɵ2:+
5.3log𝑎𝑥
AS
Paper
– understand
1: the
A-level
and
Papers
use
2
𝑛
where
𝑎
≥0
cos - Ɵ
7.2
differentiate
= is1 positive𝑥and
, for𝑥 rational
6.6 – use
graphs
to
values
of logarithmic
𝑛 , and related
constant
A-level Papers
& 2:differences
estimate
parameters
in
multiples,
sums1 and
5.5 – understand
and
use sin
relationships
of the
form
𝑦 =2 Ɵ𝑎𝑥+𝑛
2
𝑥
cos 𝑦Ɵ =
and
= 𝑘𝑏
1 , given data for 𝑥 and
𝑦
AS Paper 1/ A-level Papers 1 & 2:
7.2 - differentiate 𝑥 𝑛 , for rational
values of 𝑛, and related constant
multiples, sums and differences
AS Paper 1/A-level Papers 1 & 2:
6.1 – Know and use the function
𝑒 𝑥 and its graph
6.2Paper
– Know
thePapers
gradient
AS
1: that
A-level
1 &of2:
𝑒 𝑘𝑥 –issecond
equal to
𝑘𝑒 𝑘𝑥 and hence
7.1
derivatives
understand
why the
7.1
– understand
andexponential
use the
model
is
suitable
in
many
second derivative as the rate of
applications
change of gradient
7.3 – apply differentiation to find
gradients, tangents and normal,
maxima and minima and
stationary points
7.3 – identify where functions are
AS Paper 1/A-level
Papers 1 & 2:
increasing
and decreasing
6.3Paper
– know
use Papers
the function
AS
1:and
A-level
1 & 2:
ln𝑥 –and
its graph
7.3
apply
differentiation to find
6.3 – knowtangents
and use and
ln𝑥 as
the
gradients,
normal,
inverse function
of 𝑒 𝑥and
maxima
and minima
stationary points
8.3
Ex 8.3A
Link to Pythagoras’
theorem.
7.4
Ex
6.67.4A
Ex 6.6A
8.4
Ex 8.4A
8.5
See below
Ex 8.5A
Ex 8.5B
7.5
Ex 7.5A
8.6
Ex 8.6A
7.6
Ex 7.6A
8.7
Ex 8.7A
-1 differentiation
function.
Solutionscan
of be
equations
used to of
find
thethe
equations
tangent
and
the=normal.
form 𝑒 𝑎𝑥+𝑏of=the
𝑝 and
ln(𝑎𝑥
+ 𝑏)
𝑞 is
expected.
7 Chapter
8
Exponential
review
growth
lesson
and decay
7.3 – identify where functions are
increasing and decreasing
 Recognise
Identify areas
and of
interpret
strength
exponential
and
growth
development
and decay
within
in modelling
the content
change
of the
chapter
Recap key of
Equations
points
exponential
of chapter.
growth
Students
and to
decay are the
complete
often
exam-style
written inquestions,
terms of
powers of questions,
extension
e as it makes
or online
it easy end-ofto find the
rate of change
chapter
test at any time. Exponential
growth and decay are often described by
Assessment
a relationship
of the form
𝑦 = 𝑎𝑒 𝑘𝑥Book
Exam-style
questions
8 in Student
where 𝑎 and
𝑘 are parameters.
Exam-style
extension
questions For
8 in Student Book
growth 𝑎 > 0 and
decay
𝑎 <Connect
0.
End-of-chapter
testfor
8 on
Collins
8 Chapter review lesson

Identify areas of strength and
development within the content of the
chapter
AS Paper 1/A-level Papers 1 & 2:
6.7 – understand and use
exponential growth and decay;
use in modelling (examples may
include the use of e in continuous
compound interest, radioactive
decay, drug concentration decay,
exponential growth as a model for
population growth); consideration
of limitations and refinements of
exponential models
See below
7.7
Ex 7.7A
See below
Recap key points of chapter. Students to
complete the exam-style questions,
extension questions, or online end-ofchapter test
Assessment
Exam-style questions 7 in Student Book
Exam-style extension questions 7 in Student Book
End-of-chapter test 7 on Collins Connect
CHAPTER 9 – Integration (5 Hours)
Prior
knowledge
needed
CHAPTER
10 – Vectors
(5 Hours)
Chapter 1
Prior
knowledge
needed
Chapter
3
Chapter
Chapter 6
8
Technology
Technology
Use
a graphics
package to plot can
vectors
and to
investigate
how under
the angle
changes
depending
on the orientation.
Graphics
calculators/software
be used
look at areas
a curve
and model
changes.
Plotting diagrams using graphics software enables you to visualise the situation and see how the vectors will still satisfy the rules even if the orientation of the vectors
not
Studentis Book
Learning objectives
Specification content
Topic links
identical. One hour lessons
references
© HarperCollinsPublishers Ltd 2017
1 Indefinite integrals
One hour lessons
Students look at integration being the
1 Definition of a vector
reverse process of differentiation.
Because the
the finaland use
Students
lookderivative
at vectorof
notation
constant is zero
the result
of integration
Pythagoras’
theorem
to calculate
the is
sometimes of
magnitude
called
vectors.
the indefinite
They use integral
because the value
trigonometry
to find
of the
𝑐 is direct
not fixed.
of a vector
Students
integrate
thecalculate
sum or difference
or
use bearings.
They
the unit
of terms
vector
and
byuse
integrating
this to find
them
a velocity
separately.
vector.
2 Indefinite integrals continued
Students move the learning from the first
lesson forward by finding the equations of
the curve given the derivative and a point
on the curve
2
3 Adding
The areavectors
under a curve
Students
and
vectors
in both
Students add
move
onsubtract
to calculate
definitive
iintegrals
j and column
notation.
They
are
and are introduced to the
introduced to the three types of vectors
notation. This enables them to calculate
(equal, opposite and parallel) and learn
the area under curves. Students complete
that parallel vectors contain a common
the
first 6 questions of exercise 9.2A
factor.
4 The area under a curve continued
Recap knowledge from this and the
previous chapter (differentiation)
ensuring students clearly understand the
link
between
differentiation and
3
Vector
geometry
integration. Students finish exercise 9.2A.
Students add vectors using the triangle
5 Chapter
lessonto the
law
and arereview
introduced
parallelogram law which shows that that
Recap
keyinpoints
chapter.
the order
whichofvectors
areStudents
added isto
complete
the
exam-style
questions,
not important. Students go on to be
extension
or theorem
online end-ofintroducedquestions,
to the ratio
and the
chapter test
© HarperCollinsPublishers Ltd 2017
 Make use of the connections between
Learning objectives
differentiation and integration
 Write a vector in i j or as a column
vector
 Calculate the magnitude and direction
of a vector as a bearing in two
dimensions
 Identify a unit vector and scale it up as
appropriate
 Find a velocity vector
 Find the equation of a curve when you
know the gradient and point on a curve



Add
Use avectors
technique called integration to
Multiply
a vector
byaacurve
scalar
find the area
under
Use a technique called integration to
find the area under a curve
 Apply the triangle law to add vectors
 Apply the ratio and midpoint theorems

Identify areas of strength and
development within the content of the
chapter
AS Paper 1/A-level Papers 1 & 2:
Specification content
8.1 – Know and use the
Fundamental
AS
Paper 1: Theorem of Calculus
8.2 – use
Integrate
𝑥 𝑛in(excluding
𝑛=
9.1
vectors
two
−1), and related sums, differences
dimensions
and–constant
9.2
calculatemultiples
the magnitude and
direction of a vector and convert
between component form and
magnitude/direction form
A-level Papers 1 & 2:
AS
Paper
Papers
10.1
– use1/A-level
vectors in
two 1 & 2:
8.1
–
Know
and
use
the
dimensions
Fundamental
Theorem
of Calculus
10.2 – calculate
the magnitude
𝑛
8.2
–
Integrate
𝑥
(excluding
and direction of a vector and 𝑛 =
−1),
andbetween
related sums,
differences
convert
component
form
and
constant
multiples
and magnitude/direction form
AS
AS Paper
Paper 1:
1/A-level Papers 1 & 2:
9.3
vectors
8.2 –– add
Integrate
𝑥 𝑛 (excluding 𝑛 =
diagrammatically
and perform
the
−1), and related sums,
differences
algebraic
operations
of
vector
and constant multiples
addition
and multiplication
by
8.3 – Evaluate
definite integrals;
scalars
use a definite integral to find the
area under a curve
A-level Papers 1 & 2:
10.3
– add1/A-level
vectors Papers 1 & 2:
AS Paper
diagrammatically
perform 𝑛the
8.2 – Integrate 𝑥 𝑛and
(excluding
=
algebraic
operations
of differences
vector
−1), and related
sums,
addition
and multiplication
by
and constant
multiples
scalars
8.3 – Evaluate definite integrals;
usePaper
a definite
AS
1: integral to find the
area– under
a curve
9.3
add vectors
diagrammatically and perform the
algebraic operations of vector
addition and multiplication by
scalars and understand their
geometric interpretations
The fundamental theorem
Topic links
of calculus is used in 15.4
Displacement-time
and
Trigonometric
bearings
velocity-time
graphs
were
introduced
in 6.2 The
sine rule and the cosine
rule
9.1
Student Book
Exreferences
9.1A
10.1
Ex 10.1A
9.1
Ex 9.1B
Adding vectors is used to
find resultant forces in
Chapter 16 Forces
10.2
9.2
Ex
Ex 10.2A
9.2A
9.2
Ex 9.2A
10.3
Ex 10.3A
Ex 10.3B
See below
midpoint
rule (a special case of the
Assessment
Exam-styletheorem)
midpoint
questions 9 in Student Book
Exam-style extension questions 9 in Student Book
End-of-chapter test 9 on Collins Connect
4 Position vectors
Students learn that the position vector of
a point is its position relative to the origin.
They use this to calculate the relative
displacement between two position
vectors by subtracting the position
vectors. Students calculate the distance
between the two points by finding the
magnitude of the relative displacement
using Pythagoras’ theorem.
5 Chapter review lesson
 Find the position vector of a point
 Find the relative displacement between
two position vectors
A-level Papers 1 & 2:
10.3 – add vectors
diagrammatically and perform the
algebraic operations of vector
addition and multiplication by
scalars and understand their
geometric interpretations
AS Paper 1:
9.4 – understand and use position
vectors; calculate the distance
between two points represented
by position vectors
10.4
Ex 10.4A
A-level Papers 1 & 2:
10.4 – understand and use
position vectors; calculate the
distance between two points
represented by position vectors

Identify areas of strength and
development within the content of the
chapter
See below
Recap key points of chapter. Students to
complete the exam-style questions,
extension questions, or online end-ofchapter test
Assessment
Exam-style questions 10 in Student Book
Exam-style extension questions 10 in Student Book
End-of-chapter test 10 on Collins Connect
CHAPTER 11 – Proof (4 Hours)
Prior
knowledge
needed
CHAPTER
12 – Data
presentation and interpretation (11 Hours)
Proofs in context are flagged with boxes in every chapter. It is recommended to teach this chapter as a summation of proof and to ensure tested skills have been mastered.
Prior
knowledge
Students
will needneeded
well developed algebra skills to write and understand proofs.
Chapter
1
Technology
Chapter
4
A spreadsheet
package can be used to generate values.
Technology
© HarperCollinsPublishers Ltd 2017
Calculators can be used to calculate many useful statistics – put the calculator into statistics mode.
One hour lessons
Learning objectives
Specification content
Use frequency tables on calculators.
Use
a calculator
to calculate the mean and standard
using the frequency table option.
AS Paper 1/A-level Papers 1 & 2:
1 Proof
by deduction
 Use deviation
proof by deduction
Use graph-drawing software to plot cumulative frequencies.
1.1 – understand and use the
Students
are reminded
that
proofhistograms.
by
Use graphing
software to
create
structure of mathematical proof,
deduction
was used
when proving
the set activities.
Use spreadsheet
packages
for the data
proceeding from given
sine and cosine rules in Chapter 6
assumptions through a series of
One hour lessons
Learning objectives
Specification content
Trigonometry. They work through
logical steps to a conclusion
examples
where
conclusions
are drawn by  Use discrete or continuous data
1.1
– use methods
proof;
AS Paper
2/A-level of
Paper
3:
1 Measures
of central
tendency
including
proof
by
deduction
2.3 – interpret measure of central
using general rules in mathematics and
 Use measures of central tendency:
Students review types of data, the
tendency and variation
working through logical steps.
mean, median, mode
median, the mode and the mean.
should bewhich
madeisaware
that this
Students consider
the best
is the most
used method
of
measure
of commonly
central tendency
to use and
proof throughout this specification
why.
They
usebyData
set activity one to calculate
2 Proof
exhaustion
the median and mean and comment
Students learn that when they complete a
critically on findings.
proof by exhaustion they need to divide
the
statement
a finite
number
of
2 Measures
of into
central
tendency
and
cases, prove that the list of cases
spread
identified is exhaustive and then prove
Students review measures of spread; the
that the statement is true for all the cases.
range and interquartile range
I.e. they need to try all the options
They use frequency table to calculate
3 Disproof by counter example
measure of central tendency and spread
and
estimate
fromafrequency
Students
needthe
to mean
show that
statement is
false by finding one exception, a counter
tables.
example
3 Variance and standard deviation
Students are introduced to variance and
standard deviation and the fact that these
measures use all the data items. Students
4 Chapter
review lesson
go
onto calculating
variance and standard
deviation using frequency tables.
Recap key points of chapter. Students to
complete the exam-style questions,
© HarperCollinsPublishers Ltd 2017
 Use proof by exhaustion
 Work systematically and list all
possibilities in a structured and ordered
way
 Use discrete, continuous, grouped or
ungrouped data
 Use measures of variation: range and
interpercentile ranges
AS Paper 1/A-level Papers 1 & 2:
1.1 - understand and use the
structure of mathematical proof,
proceeding from given
AS
Paper 2/A-level
Paper
3: of
assumptions
through
a series
2.3
– interpret
of central
logical
steps to measure
a conclusion
tendency
and variation
1.1 – use methods
of proof;
including proof by exhaustion
 Use proof by counter example
AS Paper 1/A-level Papers 1 & 2:
1.1 - understand and use the
structure of mathematical proof,
proceeding from given
assumptions through a series of
AS Paper 2/A-level Paper 3:
logical steps to a conclusion
2.3 – interpret measures of
1.1 – use methods of proof;
variation, extending to standard
including proof by counter
deviation
example
2.3 – be able to calculate standard
deviation, including from
summary statistics
 Use measure of variation: variance and
standard deviation
 Use the statistic
𝑠𝑥𝑥 = ∑(𝑥 − 𝑥̅ )2 = ∑ 𝑥 2
(∑ 𝑥)2
𝑛
 Use
Identify
areasdeviation
of strength
and𝑆
standard
𝜎 = √ 𝑥𝑥
𝑛
development within the content
of the
chapter
Topic links
Note: Proofs in context are
flagged with boxes in every
chapter. It is recommended
to teach this chapter as a
summation of proof and to
Topic links
ensure tested skills have
been
mastered
Links back
to GCSE
Student Book
references
11.1
Ex 11.1A
Student Book
references
12.1
DS 1
11.2
Ex 11.2A
Links back to GCSE
12.1
Ex 12.1A
11.3
Ex 11.3A
This is covered further in
Book 2, Chapter 13
Statistical distributions
12.2
Ex 12.2A
See below
extension questions, or online end-ofchapter test
Assessment
Exam-style questions 11 in Student Book
Exam-style extension questions 11 in Student Book
4
Data cleaningtest 11 on Collins Connect
End-of-chapter
 Use measure of variation: variance and
standard deviation
Recap calculating variance and standard
 Use the statistic
deviation from frequency tables and then
(∑ 𝑥)2
∑(𝑥 − 𝑥̅ )2 = ∑ 𝑥 2
𝑠
=
𝑥𝑥
introduce data cleaning as involving the
𝑛
𝑆
identification and removal of any invalid
 Use standard deviation 𝜎 = √ 𝑛𝑥𝑥
data points from the data set. Students
use Data set activity 2 to clean the data
and give reasons for their omissions.
5 Standard deviation and outliers
Student look at data sets that contain
extreme values, if a value is more than
three standard deviations away from the
mean it should be treated as an outlier.
 Use measure of variation: variance and
standard deviation
 Use the statistic
𝑠𝑥𝑥 = ∑(𝑥 − 𝑥̅ )2 = ∑ 𝑥 2
(∑ 𝑥)2
𝑛
𝑆
 Use standard deviation 𝜎 = √ 𝑛𝑥𝑥
Students use Data set activity 3 to apply
what they have learnt so far, calculating
the mean and standard deviation, and
cleaning a section of the large data set.
6 Linear coding
Students then use linear coding to make
certain calculations easier. They apply a
linear code to a section of large data in
Data set activity 4.
Learning from this and the previous three
lessons is consolidated in exercise 12.2B
© HarperCollinsPublishers Ltd 2017
 Understand and use linear coding
2.4 – select or critique data
presentation techniques in the
context of a statistical problem
AS Paper 2/A-level Paper 3:
2.4 – select or critique data
presentation techniques in the
context of a statistical problem
AS Paper 2/A-level Paper 3:
2.3 – interpret measures of
variation, extending to standard
deviation
2.3 – be able to calculate standard
deviation, including from
summary statistics
2.4 – select or critique data
presentation techniques in the
context of a statistical problem
AS Paper 2/A-level Paper 3:
2.3 – interpret measures of
variation, extending to standard
deviation
2.3 – be able to calculate standard
deviation, including from
summary statistics
2.4 – select or critique data
presentation techniques in the
context of a statistical problem
12.2
DS 2
Normal distributions are
covered in more depth in
Book 2, Chapter 13
Statistical distributions
12.2
DS 3
12.2
DS 4
Ex 12.2B
7 Displaying and interpreting data – box
and whisker plots and cumulative
frequency diagrams
Box and whiskers plots are used to
compare sets of data. The way of showing
outliers on a box and whisker plot and
identifying outliers using quartiles is
explained. Cumulative frequency diagrams
are used to plot grouped data. (0, 0)
should be plotted and the cumulative
frequencies should be plotted at the
upper bound of the interval. Percentiles
are estimated from grouped data.
Interpolation is used to find values
between two points.
8 Displaying and interpreting data –
histograms
 Interpret and draw frequency polygons,
box and whisker plots (including
outliers) and cumulative frequency
diagrams
 Use linear interpolation to calculate
percentiles from grouped data
AS Paper 2/A-level Paper 3:
2.1 – Interpret diagrams for singlevariable data, including
understanding that area in a
histogram represent frequency
2.1 – connect probability to
distributions
12.3
Ex 12.3A
 Interpret and draw histograms
2.1 – Interpret diagrams for singlevariable data, including
understanding that area in a
histogram represent frequency
12.3
DS 5
Ex 12.3B
 Describe correlation using terms such
as positive, negative, zero, strong and
weak
2.2 – understand informal
interpretation of correlation
2.2 – interpret scatter diagrams
and regression lines for bivariate
data, including recognition of
scatter diagrams which include
distinct sections of the population
(calculations involving regression
lines are excluded)
2.2 – understand that correlation
does not imply causation
12.3
DS 6
Ex 12.3C
Students plot histograms and look at the
distribution of the data. They apply what
they have learnt to Data set activity 5,
creating a histogram and performing
linear interpolation.
9 Displaying and interpreting data –
scatter graphs
Students plot scatter diagrams with
bivariate data and look for a correlation in
the data.
In Data set activity 6 students use data
interpretation skills to investigate the
evidence for global warming in the large
data set.
© HarperCollinsPublishers Ltd 2017
10 Displaying and interpreting data –
 Use and interpret the equation of a
regression line using statistical
regression lines, lines of best fit,
CHAPTER 13 – Probability and statistical distributions
(5 Hours)
functions
on your calculator and make
interpolation and extrapolation
predictions within the range of values
Prior knowledge needed
Having
scatter diagrams in the
of the explanatory variable and
Chapterplotted
1
previous
lesson
students go on to look at
understand the dangers of
Chapter 12
the link between the line of best fit and
extrapolation
Technology
regression
line, 𝑦to=perform
𝑎 + 𝑏𝑥 exact
wherebinomial
b is the distribution calculations.
Use
a calculator
Use
a calculator
perform
cumulative binomial distribution calculations.
gradient
and a isto
the
y-intercept.
Equations ofOne
regression
lines are then
hour lessons
explored. This is then used for
1
Calculating and
representing to make
interpolation
and extrapolation
probability
predictions. Finally, students look at the
correlation
between
two variables
in Data
Basic probability
is recapped
and sample
set
activity
7. are used to determine the
space
diagrams
Learning objectives
 Use both Venn diagrams and tree
diagrams to calculate probabilities
probability
equally
likely events
11 Chapter of
review
lesson
 Identify areas of strength and
happening. Students go on to calculate
development within the content of the
probabilities
of mutually
exclusive
andto
Recap
key points
of chapter.
Students
chapter
independent
usingquestions,
Venn diagrams
complete theevents
exam-style
extension
questions, or online end-ofand
tree diagrams.
chapter test
2
Discrete and continuous distributions –  Identify a discrete uniform distribution
Assessment
part
1
Exam-style
questions 12 in Student Book
Exam-style
extension
12data
in Student
Book
The term discrete
andquestions
continuous
is
End-of-chapter test 12 on Collins Connect
recapped. A discrete random variable is
then defined. Probability distribution
tables are used to show all the possible
values a discrete random variable can take
along with the probability of each value
occurring. When all events are equally
likely they form a uniform distribution.
Students go on to probability distributions
of a random variable.
© HarperCollinsPublishers Ltd 2017
2.2 – interpret scatter diagrams
and regression lines for bivariate
data, including recognition of
scatter diagrams which include
distinct sections of the population
(calculations involving regression
lines are excluded)
2.2 – understand that correlation
does not imply causation
Gradients and intercepts
were covered in Chapter 4
Coordinate geometry 1:
Equations of straight lines
Specification content
Topic links
AS Paper 2/A-level Paper 3:
3.1 – understand and use mutually
exclusive and independent events
when calculating probability
Links back to GCSE
12.3
DS 7
Ex 12.3D
Student Book
references
13.1
Ex 13.1A
This will help you in Book
2, Chapter 12 Probability
See below
AS Paper 2/A-level Paper 3:
3.1 – link to discrete and
continuous distributions
You will use knowledge
from Chapter 12 Data
presentation and
interpretation
13.2
Ex 13.2A
3 Discrete and continuous distributions –
part 2
 Identify a discrete uniform distribution
AS Paper 2/A-level Paper 3:
3.1 – link to discrete and
continuous distributions
You will use knowledge
from Chapter 12 Data
presentation and
interpretation
13.2
Ex 13.2B
 Use a calculator to find individual or
cumulative binomial probabilities
 Calculate binomial probabilities using
the notation 𝑋~B(𝑛, 𝑝)
AS Paper 2/A-level Paper 3:
4.1 – understand and use simple,
discrete probability distributions
(calculation of mean and variance
of discrete random variables
excluded), including the binomial
distribution, as a model; calculate
probabilities using the binomial
distribution
You will need the skills and
techniques learnt in
Chapter 1 Algebra and
functions 1: Manipulating
algebraic expressions
13.3
Ex 13.3A
Continuous random variables are
considered and when graphed a
continuous line is used. The graph is called
a probability density function (PDF), the
area under a pdf shows the probability
and sums to 1. Students then go on to find
cumulative probabilities.
4 The binomial distribution
Binomial distribution is about ‘success’
and ‘failure’ as there are only two possible
outcomes to each trail. Students identify
situations which can be modelled using
the binomial distribution. They then
calculate probabilities using the binomial
distribution. Several examples are worked
through.
5 Chapter review lesson

Identify areas of strength and
development within the content of the
chapter
Recap key points of chapter. Students to
complete the exam-style questions,
extension questions, or online end-ofchapter test
Assessment
Exam-style questions 13 in Student Book
Exam-style extension questions 13 in Student Book
End-of-chapter test 13 on Collins Connect
CHAPTER 14 – Statistical sampling and hypothesis testing (6 Hours)
Prior
knowledge
needed (10 Hours)
CHAPTER
15 – Kinematics
Chapter 12
© HarperCollinsPublishers Ltd 2017
Knowing how to calculate
binomial probabilities will
help you in Chapter 14
Statistical sampling and
hypothesis testing
See below
Prior
knowledge
needed
Chapter
13
Chapter 2
Technology
Chapter 3
Use a calculator to calculate binomial cumulative probabilities.
Chapter 4
Use spreadsheet packages for the data set activities.
Chapter 8
Chapter 9 One hour lessons
Learning objectives
Chapter 10
1 Populations and samples
 Use sampling techniques, including
Technology
simple random, stratified sampling,
Graphics
packages
can
be used
Discuss the
different
terms
and to visualise problems.
systemic sampling, quota sampling and
terminology One
within
populations
opportunity
(or convenience)
hour
lessons including;
Learning
objectives sampling
finite and infinite population, census,
 Select or critique sampling techniques
1
The language
of kinematics
 Find
SI units
displacement,
sample
survey, sampling
unit, sampling
in thethe
context
ofof
solving
a statistical
velocity
and
acceleration
frame
and
target
population.
Move
onto
problem,
including
understanding
that
Students are introduced to motion in a
looking
at
the
different
types
of
sampling;
different
sample
can
lead
to
different
straight line and the vocabulary
conclusions about population
random sampling,
stratified
sampling,
displacement,
velocity
and acceleration
opportunity
sampling,
quota sampling
and
(vectors quantities)
as opposed
to
systematic
sampling.
In
Data
set
activity
distance, time and speed (scalar
1,
students compare
random
quantities).
They use athe
SI unitsample
for
with
a
systematic
sample
from
the
large
distance (metres) and time (seconds)
to
data
set
and
draw
conclusions.
derive other units. Time permitting
introduce
the testing
five SUAT
equations.
2 Hypothesis
– part
1
2
Equations
of constant
acceleration
The
two different
types of
hypothesis –are
part
1
explained, the null and alternative
hypotheses. 1-tail and 2-tail hypothesis
(𝑣−𝑢)
The definition of acceleration (𝑎 =
)
are explained in relation to a six-sided𝑡 die.
is
used to
derive
the
SUVAT the null
Having
carried
out
anfive
experiment
equations.
Students
have
to workorout
hypothesis can only be accepted
which
of
the
equations
to
use to itsolve
rejected based on the evidence,
cannot
problems.
categorically be concluded from the
findings.
3 Equations of constant acceleration –
part
2 apply what they have learnt in
Students
this
lesson
in Data
set equations
activity 2.from the
Recap
the five
SUVAT
previous lesson. Questions become more
complicated in ex 15.2B and students are
© HarperCollinsPublishers Ltd 2017
 Apply the language of statistical
hypothesis testing, developed through
 Derive and use the equations of
a binomial model: null hypothesis,
constant acceleration
alternative hypothesis, significance
level, test statistic, 1-tail test, 2-tail
test, critical value, critical region,
acceptance region, p-value
 Have an informal appreciation that the
expected value of a binomial
distribution as given by np may be
required for a 2-tail test
 Derive and use the equations of
 Conduct a statistical hypothesis test for
constant acceleration
the proportion in the binomial
distribution and interpret that results in
context
Specification content
Topic links
AS Paper 2/A-level Paper 3:
1.1 – mathematical proof
2.4 – recognise and interpret
possible
outliers in data
sets and
Specification
content
statistical diagrams
AS
2/A-level
Paper
3:
2.4Paper
– select
or critique
data
6.1
–
understand
and
use
presentation techniques in the
fundamental
quantitiesproblem
and units
context of a statistical
in
the
S.I.
system:
length,
time,
2.4 – be able to clean data,
mass
including dealing with missing
6.1
– understand
and use derived
data,
errors and outliers
quantities and units; velocity and
acceleration
7.1 – understand and use the
language of kinematics; position;
displacement; distance travelled;
AS
Paperspeed;
2/A-level
Paper 3:
velocity;
acceleration
5.1 – understand and apply
AS Paper 2/A-level Paper 3:
statistical hypothesis testing,
7.3 – understand, use and derive
develop through a binomial
the formulae for constant
model: null hypothesis, alternative
acceleration for motion in a
hypotheses, significance level, test
straight line
statistic, 1-tail test, 2-tail test,
critical value, critical region,
acceptance region, p-value
5.2 – conduct a statistical
hypothesis test for the proportion
AS
Paper
2/A-level
Paper 3: and
in the
binomial
distribution
7.3
–
understand,
use
derive
interpret the results inand
context
the formulae for constant
acceleration for motion in a
straight line
You will need to know how
to clean data for Chapter
12 Data presentation and
interpretation
Topic links
Student Book
references
14.1
DS 1
Ex 14.1A
Student Book
references
15.1
Ex 15.1A
You will need to know
Chapter 13 Probability and
The SUVAT equations are
statistical distributions
used in Chapter 16 Forces
14.2
DS 2
15.2
Ex 15.2A
15.2
Ex 15.2B
encouraged
draw a–diagram
3 Hypothesistotesting
part 2 to assist
them in understanding the situation
Recap previous lesson and students go on
to complete exercise 14.2A
4 Vertical motion – part 1
Students continue to solve problems using
the equations of constant acceleration but
this time the acceleration is equal to
gravity. They need to decide if gravity is
influencing the situation in a positive or
negative way.
5 Vertical motion – part 2
Recap the previous lesson and move on to
look at when two objects are launched in
4
Significance
– part
different
ways,levels
students
are1advised to
look for what the journeys have in
Students look at significance levels being
common.
the probability of mistakenly rejecting the
6 Displacement-time and velocity-time
null hypothesis. The terms test statistic
graphs – part 1
and critical region are explained and
students
move onto isfinding
the critical
Where
acceleration
constant,
students
region andgraphs
criticalusing
value.
They work
construct
straight
lines and
through
the examples
up to theofend
the
concepts
that the gradient
a of
example 5.
displacement-time
graphs is velocity and
the gradient of a velocity-time graph is
5
SignificanceThe
levels
– part
2 a velocityacceleration.
area
under
time
is used
to calculate
Recapgraph
previous
lesson,
with a focus on
displacement. Students focus on
how to calculate values using calculators
displacement-time graphs.
instead of statistical tables. After working
7 Displacement-time graphs and velocitythrough the rest of the chapter from
time graphs – part 2
example 6 onwards, students go on to
complete
14.2B.
Recap theexercise
facts from
last lesson and
students go on to answer questions
focusing on velocity-time graphs.
© HarperCollinsPublishers Ltd 2017
 Apply the language of statistical
hypothesis testing, developed through
a binomial model: null hypothesis,
alternative hypothesis, significance
level, test statistic, 1-tail test, 2-tail
test, critical
value,
region,
 Derive
and use
thecritical
equations
of
acceptance
region, p-value
constant
acceleration,
including for
 situation
Have an informal
appreciation that the
with gravity
expected value of a binomial
distribution as given by 𝑛𝑝 may be
required for a 2-tail test
 Conduct a statistical hypothesis test for
the proportion in the binomial
 Derive
and use
equations
distribution
andthe
interpret
thatofresults in
constant
acceleration,
including
for
context
situation with gravity
 Appreciate that the significance level is
the probability of incorrectly rejecting
the null hypothesis
 Draw and interpret displacement-time
graphs and velocity-time graphs
 Appreciate that the significance level is
the probability of incorrectly rejecting
the null hypothesis
 Draw and interpret displacement-time
graphs and velocity-time graphs
AS Paper 2/A-level Paper 3:
5.1 – understand and apply
statistical hypothesis testing,
develop through a binomial
model: null hypothesis, alternative
hypotheses,
significance
AS
Paper 2/A-level
Paperlevel,
3: test
statistic,
1-tail test,use
2-tail
7.3
– understand,
andtest,
derive
critical
value, for
critical
region,
the
formulae
constant
acceptance region,
p-value
acceleration
for motion
in a
5.2 – conduct
straight
line a statistical
hypothesis test for the proportion
in the binomial distribution and
interpret the results in context
AS Paper 2/A-level Paper 3:
7.3 – understand, use and derive
the formulae for constant
acceleration for motion in a
5.2
– understand
that a sample is
straight
line
being used to make an inference
about the population and
appreciate
that they
significance
AS Paper 2/A-level
Paper
3:
level– is
the probability
of
7.2
understand,
use and
incorrectlygraphs
rejecting
the null for
interpret
in kinematics
hypothesis
motion in a straight line;
displacement against time and
interpretation of gradient; velocity
against time and interpretation of
gradient and area under the graph
5.2 – understand that a sample is
being used to make an inference
about the population and
appreciate that they significance
level
is the2/A-level
probability
of 3:
AS Paper
Paper
incorrectly
rejecting
the
null
7.2 – understand, use and
hypothesis
interpret graphs in kinematics for
motion in a straight line;
displacement against time and
interpretation of gradient; velocity
14.2
Ex 14.2A
15.3
Ex 15.3A
15.3
Ex 15.3B
14.2
15.4
Ex 15.4A
14.2
Ex 14.2B
15.4
Ex 15.4B
6 Chapter review lesson

Identify areas of strength and
development within the content of the
chapter
CHAPTER
– Forces
(8 Hours)
Recap key16
points
of chapter.
Students to
complete
the exam-style
Prior
knowledge
needed questions,
8
Variable
acceleration
– part 1end-ofextension
or online
 Use calculus to find displacement,
Chapter
10questions,
chapter test
velocity and acceleration when they are
Chapter
15
Start
the lesson with a quiz on
functions of time
Assessment
Technology
differentiation
and can
integrations.
Exam-style
questions
14beinused
Student
Book problems.
Graphics
packages
to visualise
Students
use
differentiation
and14 in Student Book
Exam-style
extension
questions
One
hour
lessons
Learning objectives
integration
to
solve
problems
where
End-of-chapter
test
14
on Collins
Connect
acceleration is not constant. This lesson
1 Forces
 Find a resultant force by adding vectors
focuses on the use of differentiation.
 Find the resultant force in a given
Students
told the SI unit
of 2force is the  Use calculus to find displacement,
9 Variableare
acceleration
– part
direction
velocity and acceleration when they are
newton and mass is the kilogram. They
Students
use
differentiation
and
functions of time
use vectors, Pythagoras’ theorem and
integration
to
solve
problems
where
trigonometry to find resultant forces.
acceleration
notface
constant.
lesson
They also useisthe
that if This
the resultant
focuses
on thetouse
of then
integration.
force is equal
zero
an object is in
10
Chapter
review
lesson
 Identify areas of strength and
equilibrium.
development within the content of the
Recap key points of chapter. Students to
chapter
complete the exam-style questions,
extension questions, or online end-ofchapter test
Assessment
Exam-style questions 15 in Student Book
Exam-style
questions
in StudentBook
2 Newton’sextension
laws of motion
part15
one
Apply Newton’s laws and the equations
End-of-chapter test 15 on Collins Connect
of constant acceleration to problems
Students are told Newton’s laws of
involving forces
motion. They apply these to problems.
 Distinguish between the forces of
Students are then introduced to the five
reaction, tension, thrust, resistance and
different types of force. These are
weight
represented diagrammatically so that they  Represent problems involving forces in
are clearly distinguishable. Students then
a diagram
go on to use simplified models to
represent real-life situation and solve
problems
© HarperCollinsPublishers Ltd 2017
against time and interpretation of
gradient and area under the graph
AS Paper 2/A-level Paper 3:
7.4 – use calculus in kinematics for
motion in a straight line: …
Specification content
AS Paper 1:
9.5 – use vectors to solve
AS
Paper 2/A-level
Paper 3:
problems
in pure mathematics
7.4
–
use
calculus
in
kinematics
and in context, including
forces for
motion in a straight line: …
A-level Papers 1 & 2:
10.5 – use vectors to solve
problems in pure mathematics
and in context, including forces
AS Paper 2/A-level Paper 3:
6.1 – understand and use derived
quantities and units; force and
weight
8.1 – understand the concept of a
force
AS Paper 2/A-level Paper 3:
8.1 – understand the concept of a
force; understand and use
Newton’s first law
8.2 – understand and use
Newton’s second law for motion
in a straight line (restricted to
forces in two perpendicular
directions or simple cases of
forces given as 2-D vectors)
See below
Links back to Chapter 8
Differentiation and
Chapter 9 Integration
Topic links
Builds on Chapter 10
Vectors
15.5
Ex 15.5A
Student Book
references
16.1
EX 16.1A
15.5
Ex 15.5B
See below
16.2
Ex 16.2A
3 Newton’s laws of motion part two
Students are told Newton’s laws of
motion. They apply these to problems.
Students are then introduced to the five
different types of force. These are
represented diagrammatically so that they
are clearly distinguishable. Students then
go on to use simplified models to
represent real-life situation and solve
problems
4 Vertical motion
Students move from particles travelling
horizontally to particles travelling in
vertically. When particles travel vertically
they have to consider the effects of
gravity and weight.
5 Connected particles – part 1
More complex problems are solved using
Newton’s laws and simultaneous
equations due to the consideration of
resistive forces. Modelling assumptions
are made and shown with diagrams when
answering questions. The connected
particles considered are particles
suspended on ropes, vehicles towing
caravans and lifts.
6 Connected particles – part 2
© HarperCollinsPublishers Ltd 2017
 Apply Newton’s laws and the equations
of constant acceleration to problems
involving forces
 Distinguish between the forces of
reaction, tension, thrust, resistance and
weight
 Represent problems involving forces in
a diagram
 Distinguish between the forces of
reaction, tension, thrust, resistance and
weight
 Model situations such as lifts,
connected particles and pulleys
 Model situations such as lifts,
connected particles and pulleys
 Represent problems involving forces in
a diagram
 Model situations such as lifts,
connected particles and pulleys
8.3 – understand and use weight
and motion in a straight line under
gravity
AS Paper 2/A-level Paper 3:
8.1 – understand the concept of a
force; understand and use
Newton’s first law
8.2 – understand and use
Newton’s second law for motion
in a straight line (restricted to
forces in two perpendicular
directions or simple cases of
forces given as 2-D vectors)
8.3 – understand and use weight
and motion in a straight line under
gravity
AS Paper 2/A-level Paper 3:
8.3 – understand and use weight
and motion in a straight line under
gravity; gravitational acceleration ,
g, and its value in S>I> units to
varying degrees of accuracy
8.4 – understand and use
Newton’s third law
AS Paper 2/A-level Paper 3:
8.4 - understand and use
Newton’s third law; equilibrium of
forces on a particle and motion in
a straight line; application to
problems involving smooth pulleys
and connected particles
AS Paper 2/A-level Paper 3:
8.4 - understand and use
Newton’s third law; equilibrium of
16.2
Ex 16.2B
16.3
Ex 16.3A
16.4
Ex 16.4A
16.4
Ex 16.4B
Recap on the chapter so far. Students
complete exercise 16.4B.
 Represent problems involving forces in
a diagram
7 Pulleys
 Model situations such as lifts,
connected particles and pulleys
 Represent problems involving forces in
a diagram
Connected particles are now considered
in the form of pulleys. The main difference
being that when an object is connected
via a pulley it will be travelling in a
different direction. Students should again
draw diagrams representing the situation
in the question. They solve problems
using Newton’s laws of motion, the
SUVAT equations and simultaneous
equations.
8 Chapter review lesson

Identify areas of strength and
development within the content of the
chapter
Recap key points of chapter. Students to
complete the exam-style questions,
extension questions, or online end-ofchapter test
Assessment
Exam-style questions 16 in Student Book
Exam-style extension questions 16 in Student Book
End-of-chapter test 16 on Collins Connect
© HarperCollinsPublishers Ltd 2017
forces on a particle and motion in
a straight line; application to
problems involving smooth pulleys
and connected particles
AS Paper 2/A-level Paper 3:
8.4 - understand and use
Newton’s third law; equilibrium of
forces on a particle and motion in
a straight line; application to
problems involving smooth pulleys
and connected particles
16.5
Ex 16.5A
See below