Year11SchemeofworkAutumnTerm‐Halfterm1
Higher level Year 11 Higher TopicTitle: Algebra:furtherquadratics,rearrangingformulaeandidentities6 lessons
Pre‐requisiteknowledge:

Keywords:
Function, inverse, expression, input, output
Basic algebraic substitution and equation solving skills.
4 rules with fractions and decimals.

Studentsshouldbeableto:
Numberoflessonsrequired:
6 lessons.
Higher Content:
A4
Simplify and manipulate algebraic expressions (including those involving surds) by:
expanding products of two or more binomials
factorising quadratic expressions of the form
squares
including the difference of two
factorising quadratic expressions of the form
simplifying expressions involving sums, products and powers, including the laws of indices
A5
Understand and use standard mathematical formulae
Rearrange formulae to change the subject
A6
Know the difference between an equation and an identity
Argue mathematically to show algebraic expressions are equivalent, and use algebra to
support and construct arguments and proofs
A7
Where appropriate, interpret simple expressions as functions with inputs and outputs
Interpret the reverse process as the ‘inverse function’
Year 11 Higher Routemap: 3 Year Higher
Interpret the succession of two functions as a ‘composite function’
Topiccommentary:
Quadratics have been covered in year 10. This is an opportunity to consolidate and extend. This unit covers factorising only. Solving is covered in the next
unit although you may choose to teach them together.
Functions (A7) is covered in detail in the AQA resources. The PowerPoint slides take students through simple functions, inverse, graphing and composite
functions. The notes section suggests which activities from the resource fit in where.
The worksheet gives some basic practise with simple functions and includes solving equations, also including composite functions.
The Jigsaw activity requires students to evaluate composite functions. NB Students will need to be given the functions required.
The dominoes activity requires students to match functions with their inverse to complete a puzzle.
Each activity can be used alone or alongside the PowerPoint as a complete lesson.
LessonPlansavailable
Notes
AQA
1powerpoint,2activitiesand1worksheet available
Pearsons
2.7Expandingandfactorisingquadratics
2.4,17.1Rearrangingformulae
17.7Functions
17.8Proofs
LessonAssessment
ProblemSolvingactivity
Year 11 Higher TopicTitle: Further equations and graphs 6 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Keywords
Studentsshouldbeableto:
Numberoflessonsrequired:
6 lessons.
Higher Content:
A17
Solve linear equations in one unknown algebraically including those with
the unknown on both sides of the equation
Find approximate solutions using a graph
A18
Solve quadratic equations (including those that require
rearrangement) algebraically by factorising, by completing the square
and by using the quadratic formula
Find approximate solutions using a graph
A12
Recognise, sketch and interpret graphs of linear and quadratic functions
A11
Identify and interpret roots, intercepts and turning points of quadratic
functions graphically; deduce roots algebraically and turning points by
completing the square
including use of
brackets
including the
symmetrical
property of a
quadratic
Year 11 Higher A21
Translate simple situations or procedures into algebraic expressions or
formulae
derive an equation, solve the equation and interpret the solution
including solution
of geometrical
problems and
problems set in
context
Topiccommentary:
LessonPlansavailable
AQA
Pearsons
Notes
2.3Solvinglinearequations
9.1‐9.3Solvingquadraticsincludingcompletingthesquare
6.6,6.8Quadraticgraphs
15.3Graphsofquadraticfunctions
15.4Solvingquadraticfunctionsgraphically
LessonAssessment
ProblemSolvingactivity
Year 11 Higher TopicTitle: Sketching graphs 3 lessons
Pre‐requisiteknowledge:
Trigonometrical ratios and how to find on a calculator. Plotting points joining with a curve.
Routemap: 3 Year Higher
Keywords
Cosine,tangent,exponential,period.
Understanding of 2 < x > -2 notation for values of x
Studentsshouldbeableto:

draw, sketch, recognise and interpret graphs of the form y = kx for positive values of k

know the shapes of the graphs of functions y = sin x, y = cos x and y = tan x

Sketch y = sin x, y = cos x and y = tan x, know that the maximum and minimum values for Sin
and Cos are 1 and -1. Know that the graphs of sin, cos and tan are periodic.
Numberoflessonsrequired:
3 lessons.
Higher Content:
Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions,
the reciprocal function, y =
1
with x ≠ 0, exponential functions y = kx for positive values of k, and the
x
trigonometrical functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any
size. (A12h)
Topiccommentary:
Triggraphsareintroducedinthisunitaswellasothergraphs.Thefollowingunitsrecaponbasictrig,followedbythesineruleandcosinerule.You
maywishtodelaytriggraphsuntilyouhaverecappedtrigonometry
Year 11 Higher AQA: The resource is designed to be used in a variety of ways.
The PowerPoint covers all the knowledge of graphs which students will need to know.
The Trigonometrical Functions worksheet leads students through an investigation looking at graphs of sin, cos and tan. The PowerPoint contains the correct
graphs and properties.
The True False activity provides a way of checking knowledge of what the graphs should look like. Answers are provided.
A set of exam paper questions are provided. Full papers can be found on AQA’s website.
The resource lends itself to a variety of lesson formats. From a short revision PowerPoint with students sketching graphs on mini whiteboards to a full 1 hour
lesson.
E.g. Starter discussion of slide 1.
Time spent doing Trigonometric Functions use PowerPoint to check and discuss.
True/ False in groups or whole class to consolidate.
Exam questions to finish off or for homework.
In order to do the activities students will need to be able to use their calculators to find trig ratios, draw accurate graphs, and sketch graphs. The resource
could be used as a way to revise all of these skills.
LessonPlansavailable
AQA
Pearsons
Notes
Powerpointsandresources.Seenotesintopiccommentary.
6.7Cubicandreciprocalgraphs
15.5Cubicgraphs
19.4Exponentialfunctions
13.2‐13.4Triggraphs
LessonAssessment
ProblemSolvingactivity
Year 11 Higher TopicTitle: Trigonometry recap and extension 3 lessons
(TrigonometrywaspreviouslycoveredinYear9)
Routemap: 3 Year Higher
Pre‐requisiteknowledge:

Convert fractions to decimals.

Identify the hypotenuse.
Keywords:
Studentsshouldbeableto:
Numberoflessonsrequired:
3 lessons.
Higher Content:
G20
Know the formula for Pythagoras' Theorem
Apply it to find length in right angled triangles and, where possible, general triangles in
two and three dimensional figures
Know and use the trigonometric ratios
Apply them to find angles and lengths in right-angled triangles and, where possible,
general triangles in two and three dimensional figures
G21
Know the exact values of
0°, 30° 45°, 60° and 90°
Know the exact value of
0°, 30°, 45° and 60°
G6
Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to
conjecture and derive results about angles and sides including Pythagoras’ Theorem, use
Year 11 Higher known results to obtain simple proofs
R12
Compare lengths using ratio notation; Make links to trigonometric ratios
Topiccommentary:
Students may not rearrange the equation correctly when the unknown is the denominator of the fraction. Review solving simple equations such as 3 = LessonPlansavailable
AQA
Pearsons
LessonAssessment
ProblemSolvingactivity
Notes
2lessonsavailable(5.4,5.5)
Year 11 Higher .
Year11SchemeofworkAutumnTerm‐Halfterm2
Higher level TopicTitle: Sine and cosine rules 6 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Keywords
Studentsshouldbeableto:
Numberoflessonsrequired:
6 lessons.
Higher Content:
G22
Know and apply the Sine rule
and Cosine rule
to find unknown lengths and angles
G23
Know and apply
to calculate the area, sides or angles of any triangle
Year 11 Higher Students are expected to know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°,
and the exact values of tan θ for θ = 0°, 30°, 45° and 60°. This is new to the Higher tier GCSE 2015.
Students need to know the formula for the cosine rule and be able to apply it to work out
unknown lengths and angles. This is new to the Higher tier GCSE 2015.
Students need to know the formula for area of a triangle and be able to apply it to work out sides,
angles and areas of given triangles. This is new to the Higher tier GCSE 2015.
Topiccommentary:
The only complication is the ambiguous case, where there are two possible angles. One is found using sin–1 , and the other is found by subtracting the first
value found from 180°. Refer back to the graph of the sine function to help you.
Students may not understand that practice is needed to quickly decide whether to use the sine rule or the cosine rule to solve a problem.
LessonPlansavailable
AQA
Pearsons
Notes
13.5,13.6
13.73Dtrig
LessonAssessment
ProblemSolvingactivity
Year 11 Higher TopicTitle: Transforming functions 3 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Keywords
asymptote
Applying simple transformations to coordinates
Studentsshouldbeableto:
Numberoflessonsrequired:
3 lessons.
Higher Content:
A13
Sketch translations and reflections of a given function
Topiccommentary:
LessonPlansavailable
AQA
Pearsons
Notes
13.8,13.9Transformingtriggraphs
19.6,19.7Transforminggraphs
LessonAssessment
ProblemSolvingactivity
Year 11 Higher Year 11 Higher TopicTitle: AlgebraicFractions 3 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Students should be confident with basic algebra although there will be revision, and should know how to
solve linear and quadratic equations, both by factorising and using the formula.
Keywords:
They should be able to apply Pythagoras’ theorem and be confident with a range of angle, perimeter and
area facts.
Studentsshouldbeableto:
Numberoflessonsrequired:
3 lessons.
Higher Content:
Simplify and manipulate algebraic expressions involving algebraic fractions (A4)
Topiccommentary:
The topic is introduced by revising the four operations with fractions, and simple algebra. This leads through to manipulating algebraic fractions and solving
problems. Solving quadratics is also covered as a revision topic.
Some of the plenaries are word problems which can be read out, encouraging higher level students to make notes and process information.
Some extension ideas take students into work above GCSE level – these are clearly indicated and are a good way to support students in the transition to
advanced level study.
LessonPlansavailable
Notes
AQA
4lessons
Pearsons
4lessons(17.2‐17.4,17.6)
LessonAssessment
ProblemSolvingactivity
Year 11 Higher Year 11 Higher TopicTitle: Numerical Methods 1 lesson
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Keywords
Studentsshouldbeableto:
Numberoflessonsrequired:
1 lesson
Solve quadratic equations using an iterative process.
Higher Content:
A20
Find approximate solutions to equations
numerically using iteration
including the use of suffix notation in
recursive formulae
Topiccommentary:
The iterative process (and the notation used in it) is new to the Higher tier GCSE 2015, although the process is not dissimilar to the trial and improvement
process.
LessonPlansavailable
AQA
Pearsons
LessonAssessment
ProblemSolvingactivity
Notes
15.4Q12,13
Year 11 Higher Year 11 Higher MOCK EXAMS AND REVISION Year11SchemeofworkSpringTerm‐Halfterm1
Higher level TopicTitle: Vectors 6 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Students need to know how to add and subtract negative numbers and work with co-ordinates in four
quadrants. They should also know properties of plane shapes such as parallelograms. Students may
already be familiar with column vectors for using a vector to represent a translation.
Keywords
vector, column, horizontal, vertical, scalar,
negative, sum, difference, resultant, commutative,
associative, collinear, parallel, midpoint
Numberoflessonsrequired:
6 lessons.
Higher Content:
Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and
column representations of vectors (G25).
Use vectors to construct geometrical arguments and proof (G25).
Topiccommentary:
This topic builds on students’ possible prior knowledge of column vectors from their use to represent translations in the transformations topic.
Students may confuse column vectors with co-ordinate pairs. They may also initially find the construction of a geometrical proof difficult so a lot of
opportunities to consolidate this skill are provided.
Throughout the topic, the correct use of notation should be emphasized, such as vectors being expressed in bold font in printed documents and with an arrow
.
of the form
Extension materials are provided which offer additional demand for more able students.
LessonPlansavailable
Notes
Year 11 Higher AQA
Pearsons
LessonAssessment
ProblemSolvingactivity
8lessonsavailable
18.1‐18.5
Year 11 Higher TopicTitle: Circle theorems 6 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
 Recall the sum of angles of a quadrilateral.
 Use correct mathematical vocabulary for parts of a circle
Studentsshouldbeableto:
Higher Content:
Apply and prove the standard circle theorems concerning angles, radii, tangents and chords and
use them to prove related results (G10)
Topiccommentary:
LessonPlansavailable
AQA
Pearsons
LessonAssessment
ProblemSolvingactivity
Notes
4lessonsavailable(16.1‐16.4)
Year 11 Higher Numberoflessonsrequired:
6 lessons.
Year 11 Higher TopicTitle: Equation of a circle 2 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Students should know how to calculate the area and perimeter of a circle and be able to use
Pythagoras’ theorem to solve problems. They should also be able to use coordinate geometry to find
gradients and equations of straight lines and know that the product of perpendicular lines are -1.
Students need to be able to solve both quadratic equations and simultaneous equations where one
equation is linear and one is quadratic. It is beneficial if students have some knowledge of circle
theorems and rules. Studentsshouldbeableto:
• recognise the equation of a circle, centre (0, 0), radius r
• write down the equation of a circle, centre (0, 0) and radius r
• work out coordinates of points of intersection of a given circle and a given straight line
• use the fact that the angle between the tangent and radius is 90° to work out the gradient of a
Numberoflessonsrequired:
2 lessons.
tangent and hence the equation of a tangent at a given point.
Higher Content:
Recognise and use the equation of a circle with centre at the origin
Find the equation of a tangent to a circle at a given point. (A16)
Topiccommentary:
The PowerPoint for this topic demonstrates how the equation of a circle can be derived. There are some simple questions to find the radius from the equation
of a circle and vice versa. There is also a revision / introductory activity for relevant circle theorems, leading on to using the fact that gradients of perpendicular
lines multiply to -1 to find the equation of a tangent to a circle.
The worksheet and homework provide reinforcement of these ideas.
The topic requires the candidates to be able to use Pythagoras’ theorem, circle theorems, and finding equations of lines, but could also be could be used as a
revision opportunity for these topics.
Year 11 Higher LessonPlansavailable
AQA
Pearsons
LessonAssessment
ProblemSolvingactivity
Notes
Powerpointandresourcesavailable.Seecommentaryabove.
16.5
Year 11 Higher TopicTitle: Direct and Inverse Proportion 3 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Keywords
Constant of proportionality
Recognise direct proportion
Studentsshouldbeableto:
Numberoflessonsrequired:
3 lessons.
Higher Content:
R10
Solve problems involving direct and inverse proportion, including graphical and algebraic
representations
R13
Understand that
is inversely proportional to
is equivalent to
is proportional to
Construct and interpret equations that describe direct and inverse proportion
R14
Recognise and interpret graphs that illustrate direct and inverse proportion
Year 11 Higher Topiccommentary:
Ratio and proportion was covered in Year 10
● Students may write a formula with the two variables the wrong way round (finding the inverse of the constant). Encourage students to check their formula by
substitution.
● Students may substitute into the formula, or process incorrectly. Encourage students to write down each step in their working and check their answers.
● Students may fail to identify the correct type of relationship. Encourage them to read the question carefully, writing down each piece of information as they
go.
● Some students may carry out operations in the wrong order (such as multiplying before squaring). Remind students of BIDMAS.
LessonPlansavailable
AQA
Pearsons
LessonAssessment
ProblemSolvingactivity
Notes
19.1‐19.3
Year 11 Higher TopicTitle: GradientsandRateofChange 4 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Students need to be familiar with finding the gradient of a line by using a right-angled triangle and
calculating the change in y divided by the change in x. They should also have good basic algebra and
geometry skills, including plotting coordinates and selecting axis units.
Studentsshouldbeableto:
Keywords
Parallel, perpendicular, gradient, positive, negative,
rate of change, instantaneous rate of change,
average rate of change, chord, tangent,
Numberoflessonsrequired:
4 lessons
Higher Content:
Interpret the gradient of a straight-line graph as a rate of change (R14)
Interpret the gradient at a point on a curve as the instantaneous rate of change (R15)
Apply the concepts of average and instantaneous rates of change (gradients of chords and tangents) in
numerical, algebraic and graphical contexts (R15)
Topiccommentary:
AQA:
There are 6 lessons in this topic. The topic has been approached in a systematic way working from revision of gradients of straight lines to finding and using
the gradient of a curve. There are opportunities to bring in some basic pre-calculus ideas with students if desired; indeed, there are overlaps with this topic
and the later pre-calculus and area under a curve topic, however it is suggested that this topic is completed first.
Not all lessons may be needed and several could stand alone if preferred.
LessonPlansavailable
AQA
Pearsons
Notes
6 lessonsavailable
6.3Graphingratesofchange
11.2,11.3??
Year 11 Higher LessonAssessment
ProblemSolvingactivity
Year 11 Higher Year11SchemeofworkSpringtermTerm‐Halfterm2
Higher level TopicTitle: Pre–Calculusandareaunderacurve 6 lessons
Routemap: 3 Year Higher
Pre‐requisiteknowledge:
Students should already be able to plot straight line and curved graphs. They should be able to read and
interpret distance-time and velocity-time graphs. Students are expected to be able to find the gradient of
straight line graphs.
Studentsshouldbeableto:
Numberoflessonsrequired:
6 Lessons
Higher Content:


Keywords
curve, gradient, tangent, trapezium, distance-time
graph, velocity-time graph, velocity, speed,
trapezia, vertical axis, horizontal axis, estimate,
rate of change, positive / negative gradient
Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other
non-linear graphs) (A15)
Interpret the results in cases such as distance-time graphs, velocity-time graphs and graphs in
financial contexts (A15)
Topiccommentary:
AQA: This topic overlaps with gradients and rate of change. The idea of finding a gradient of a curve is revisited in lesson 1.
Although in the examination any method of finding the area is allowed, in this topic we are introducing using the trapezium rule as the best method
LessonPlansavailable
AQA
Pearsons
LessonAssessment
Notes
6lessonsavailable
Year 11 Higher ProblemSolvingactivity
Year 11 Higher Year 11 Higher Year 11 Higher Year 11 Higher Year 9 and 10 Overview Year 11 Higher Year 11 Overview Year 11 Higher