Mathematics Department – Medium Term Plan
End Game
The aims for our curriculum is to ensure that all pupils:
o
o
o
Become fluent in the fundamentals of mathematics.
Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication
1
Year 8
2
3
4
Fertile Question
Content



Concepts
Number
Number, Algebra
Knowledge
Weeks 1 to 3
Review of Y7
 Four operations
 Order of operations
 Negative numbers
 Fractions 1
 Percentages 1
 Algebra 1
Weeks 11 to 13
Number: Percentages 2
Express one quantity as a percentage of another
Compare two quantities using percentages, and
work with percentages greater than 100%
Solve problems involving percentage
change, including:
Indices
Prime numbers
Fractions
Weeks 4 to 7
Number: Indices and Primes
Use integer powers and associated real roots
(square, cube and higher), recognise powers of
2, 3, 4, 5 and distinguish between exact
representations of roots and their decimal
approximations.
Find the prime factor decomposition of a
number.
Use prime factor decomposition to find LCM,
HCF, squares, and cubes.
Enumerate sets and unions/intersections of sets
systematically using Venn diagrams.
Weeks 8 to 10
Number: Fractions 2
Find a fraction of an amount.
Multiply and divide proper and improper
fractions and mixed numbers both positive
and negative.
 Fraction x Integer
 Fraction x Fraction
 Fraction ÷ Integer


Percentages
Algebra
 Percentage increase, decrease
 Original value problems
 Simple interest in financial
mathematics
Weeks 14 to 20
Algebra 2
Substitute numerical values into formulae
and expressions, including scientific
formulae

Include all prior learning specifically
fractions, decimals and negatives
Simplify and manipulate algebraic
expressions to maintain equivalence by:

multiplying a single term over a
bracket
 taking out common factors
 expanding products of two or more
binomials
 simplifying expressions involving
sums, products and powers
Rearrange formulae to change the subject,
where the subject appears once.
Use algebraic methods to solve linear
equations in one variable (including all
forms that require rearrangement)


Include equations with brackets
Include fractional equations
Understand and use the concepts
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

2D shapes
Statistics
Ratio
Geometry
Statistics
Number
Weeks 20 to 23
Geometry: 2D Shapes
Convert between cm2 and m2
Derive and apply formulae to calculate and
solve problems involving area of circles,
composite shapes and trapeziums.
Calculate and solve problems involving
perimeters of 2-D shapes (including
circles).
Include examples using algebra, fractions,
decimals, etc.
Weeks 24 to 26
Statistics
Construct and analyse stem and leaf diagrams,
including back to back.
For non-grouped data given in the form of a
table, find the mean, median, mode and range
Weeks 27 to 29
Number: Ratio
Change freely between related standard units
[for example time, length, area,
volume/capacity, mass]
Use ratio notation, including reduction
simplest form.
Divide a given quantity into two or more
parts.
Given information about one part, find the
whole or other part(s).
Understand that a multiplicative relationship
between two quantities can be expressed as a
ratio or a fraction.
Use compound units such as speed, unit
pricing and density to solve problems.


Proportion
3D shapes
Number, Geometry
Weeks 30 to 32
Number: Proportion
Solve problems involving direct and
inverse proportion, including graphical
and algebraic representations.
Examples may include:



Recipe problems
Best buy problems
Exchange rates
Weeks 33 to 35
Geometry: 3D Shapes
Use the properties of faces, surfaces, edges
and vertices of cubes, cuboids, prisms,
cylinders, pyramids, cones and spheres to
solve problems in 3D.
Convert between cm3 and m3
Know and use the fact that 1 litre =
1000cm3
Derive and apply formulae to calculate and
solve problems involving volume and
surface area of cuboids (including cubes)
and other prisms (including cylinders).
Construct and interpret plans and elevations of
3D shapes.
Week 36
Time at the beginning or end of the term for
consolidation gap filling, seasonal activities,
end of year assessments, etc.
Mathematics Department – Medium Term Plan
 Integer ÷ Fraction
 Fraction ÷ Fraction
 All of the above proper, improper,
mixed, positive and negative.
Find the whole amount, given a fraction of
the amount.
Find a fractional increase and decrease
and vocabulary of inequalities.



Represent the solution set to an
inequality on a number line and vice
versa
Find the integer solutions of an
inequality
Solve linear inequalities in one variable
Mathematics Department – Medium Term Plan
End Game
The aims for our curriculum is to ensure that all pupils:
o
o
o
Become fluent in the fundamentals of mathematics.
Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication.
1
Year 7 Fertile Question
Content
2



Place value
Addition and
Subtraction
Multiplication
and division
3



Negative Numbers
Fractions
Percentages
4



Data Handling
Notation,
Substitution and Basic Manipulation

(Angles and
Lines)
Concepts
Number
Number
Number
Statistics
Algebra
Geometry
Knowledge
Week 1 to 3
Number: Place Value
Understand and use place value for decimals,
measures and integers of any size.
Order positive and negative integers, use the
number line as a model for ordering of the real
numbers; use the symbols =, ≠, <, >, ≤, ≥
Round numbers and measures to an appropriate
degree of accuracy [for example, to a number of
decimal places or significant figures].
Week 10 -12
Number: Multiplication and Division
Week 19 - 21
Number: Percentages 1
Define percentage as ‘number of parts per
hundred’
Interpret diagrams as percentages and vice
versa
Interpret fractions and percentages as operators,
with and without a calculator.
Interpret percentages as a fraction or as a
decimal
Week 28 - 30
Algebra 1
Number: Addition and
Subtraction
Use formal written
methods for addition and
subtraction of integers and
decimals.
Recognise and use
relationships between
addition and subtraction
including inverse
operations.
Calculate and solve
problems involving
perimeter.
(Week 7 -9)
Number: Multiplication
and Division
Calculate and solve problems involving area of
rectangles, triangles and parallelograms.
Calculate the mean average.
Use approximation through rounding to
estimate answers and calculate possible
resulting errors expressed using inequality
notation a < x ≤ b
Number: Negative Numbers
Calculate and solve problems involving area of
rectangles, triangles and parallelograms.
Calculate the mean average.
Use approximation through rounding to
estimate answers and calculate possible
resulting errors expressed using inequality
notation a < x ≤ b
Week 13 - 15
Number: Fractions 1
Represent fractions using diagrams and on a
number line.
Express one quantity as a fraction of another.
Identify and use equivalent fractions.
Simplify fractions.
Compare and order fractions; use the symbols
=, ≠, <, >, ≤, ≥
Week 22 -24
Statistics: Data Handling
Understand the data handling cycle.
Understand the different types of data.
Collect, organise and interpret data.
Draw and interpret bar charts, pictograms, line
graphs and pie charts.
Week 25 - 27
Algebra 1
Introduction to algebra
variable.
expression, equation, formula, term, function
and identity.
Substitute numerical values into formulae and
expressions including scientific formulae
(including examples with negatives)
Simplify and manipulate algebraic expressions
to maintain equivalence by:
Use algebraic methods to solve simple linear
equations in one variable where the unknown
appears on one side of the equation.
Generate terms of a sequence from either a
term-to-term or a position-to-term rule.
Week 31 -34
Geometry: Angles and Lines
Describe, sketch and draw using conventional
terms and notations: points, lines, parallel lines,
perpendicular lines, right angles, regular
polygons, and other polygons that are
reflectively and rotationally symmetric.
Derive and illustrate properties of triangles,
quadrilaterals, circles, and other plane figures
[for example, equal lengths and angles] using
appropriate language and technologies
Use a protractor to measure and draw angles.
Apply the properties of angles at a point, angles
at a point on a straight line, vertically opposite
angles.
Understand and use alternate and corresponding
angles on parallel lines.
Mathematics Department – Medium Term Plan
Multiply and divide by 10,
100 and 1000
Use formal written
methods for multiplication
and division of integers
and decimals.
Recognise and use
relationships between
operations including
inverse operations.
Understand the order of
operations.
Use the concepts and
vocabulary of factors (or
divisors), common factors,
and highest common factor
(HCF).
Week 16 -18
Convert between mixed numbers and improper
fractions.
Convert between fractions and decimals
in words.
convert any fraction to a decimal.
a2 in place of a × a; a3 in place of a × a ×
a; a2b in place of a × a × b
b/a
b÷a
Add and subtract any fraction.
that is a
multiple of the other.
Pupils should be taught to use and interpret
algebraic notation, including:
ab in place of a × b
as decimals
Derive and use the sum of angles in a triangle
and a quadrilateral.
Derive and use the sum of angles in a triangle
and use it to deduce the angle sum in any
polygon, and to derive properties of regular
polygons.
Week 35-36
Time at the beginning or end of the term for
consolidation gap filling, seasonal activities,
end of year assessments, etc.
Mathematics Department – Medium Term Plan
End Game
The aims for our curriculum is to ensure that all pupils:
o
o
o
Become fluent in the fundamentals of mathematics.
Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.
Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication.
1
Year 9 Fertile Question
Content
2





Review of Year 7
Number: Operations, BIDMAS, Factors,
Powers, FDP, Rounding
Algebra: Expressions, Solving
Equations.
Ratio and Proportion.
Linear Graphs
3


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
Direct and Inverse Proportion
Sequences
Inequalities
Geometry (Transformations)
Geometry (Angles & Constructions)
4


Geometry (Angles & Constructions)
Statistics and Probability



Geometry
(Pythagoras and
Trigonometry)
Standard Form
Concepts
Number
Algebra
Algebra
Geometry
Geometry
Algebra
Geometry
Number
Knowledge
Week 1-5
Review of content taught in Year 7 & Year 8.
Four operations (N1, N2)
Order of operations (N3)
Negative numbers (N1, N2)
Multiples, factors, primes, powers, roots and
reciprocals (N4, N6)
Fractions, decimals and percentages (N1, N2)
Rounding and estimation (N14, N15)
Algebraic expressions, substitution, solving
simple linear equations and expanding brackets
(A1, A3, A4, A5, A6, A7, A21)
Ratio and proportion (R4, R5)
Week 10-11
Direct and Inverse Proportion
Interpret mathematical relationships both
algebraically and graphically e.g. direct and
inverse proportion and real life graphs.
Find approximate solutions to contextual
problems from given graphs of a variety of
functions, including piece-wise linear,
exponential and reciprocal graphs.
Week 20-21
Geometry (Angles & Constructions)
Use scale factors, scale diagrams and maps.
Identify and construct congruent triangles, and
construct similar shapes by enlargement, with
and without coordinate grids. Derive and use
the standard ruler and compass constructions
(perpendicular bisector of a line segment,
constructing a perpendicular to a given line
from/at a given point, bisecting a given angle);
recognise and use the perpendicular distance
from a point to a line as the shortest distance to
the line.
Loci.
Week 27
Number (Standard Form)
Interpret and compare numbers in standard
form A x 10n 1 ≤ A < 10, where n is a positive
or negative integer or zero. Add and subtract
two numbers in standard form.
Week 28-30
Number (Surds)
Evaluate simple fractional and negative indices
in the form: a-n, a1/n, a-1/n where n is an
integer.
Understand what a surd is and simplify basic
surds.
Week 31-34
Geometry (Pythagoras and Trigonometry)
Apply angle facts, triangle congruence,
similarity and properties of quadrilaterals to
derive results about angles and sides, including
angles in polygons, Pythagoras’ Theorem, and
use known results to obtain simple proofs.
Use Pythagoras’ Theorem and trigonometric
ratios in similar triangles to solve problems
involving right - angled triangles.
Know the formulae for: Pythagoras’ theorem
and the trigonometric ratios:
Apply them to find angles and lengths in right angled triangles and, where possible, general
Week 6-9
Linear Graphs
Work with coordinates in all four quadrants.
Recognise, sketch and produce graphs of:
• Linear functions of one variable
• Quadratic functions of one variable
Algebraic manipulation including:
• Changing the subject of a formula
• Expansion and factorisation
• Understand and use standard mathematical
formulae
• Rearranging formulae to change the subject,
including where the subject appears more than
Week 12
Sequences
Recognise and generate geometric and
arithmetic sequences.
Week 13
Inequalities
Construct and solve equations and inequalities.
Week 14-17
Geometry (Transformations)
Identify properties of, and describe the results
of, translations, rotations, reflections and
enlargement applied to given figures.
Week 18-19
Geometry (Angles & Constructions)
Week 22-26
Statistics and Probability
Statistics
Use and interpret scatter graphs of bivariate
data and recognise correlation.
Draw and analyse frequency polygons.
For continuous data given in the form of a table
find an estimate of the mean, modal class
interval and class interval that contains the
median
Probability
Record, describe and analyse the frequency of
Mathematics Department – Medium Term Plan
once
Reduce a given linear equation in two variables
to the standard form y = mx + c
Calculate and interpret gradients and intercepts
of graphs of such linear equations numerically,
graphically and algebraically.
Use linear and quadratic graphs to estimate
values of y for given values of x and vice versa
and to find approximate solutions of
simultaneous linear equations.
Draw and measure line segments and angles in
geometric figures, including interpreting scale
drawings and use of bearings.
outcomes of simple probability experiments
involving randomness, fairness, equally and
unequally likely outcomes, using appropriate
language and the 0 - 1 probability scale.
Understand that the probabilities of all possible
outcomes sum to 1
Enumerate sets and unions/intersections of sets
systematically, using tables, grids and Venn
diagrams.
Generate theoretical sample spaces for single
and combined events with equally likely,
mutually exclusive outcomes and use these to
calculate theoretical probabilities.
triangles in two and three dimensional figures.
Week 35-36
Time at the beginning or end of the term for
consolidation gap filling, seasonal activities,
end of year assessments, etc.
Mathematics Department – Medium Term Plan
End Game
Foundation:
Higher:
]
For all students to achieve a minimum of 3 LOP in final examination, regardless of their starting point.
1
Year 10
Foundation
2
Fertile Question
Does data always
tell you the real
Story? the whole
Story? or the
Truth?
Content



Review of KS3- Numeracy, algebra, sequences
Averages and Range
Graphs, tables and charts

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
3
Fractions and percentages
Ratio and proportion
Parallel lines and interior and exterior angles in
polygons.



4
Multiplicative reasoning
Graphs-linear graphs
Perimeter, area and volume



Quadratic equations and graphs
Right angles triangles: trigonometry and
Pythagoras.
Probability
Concepts
Algebra, Number and Data and Probability
Number, Geometry, Ratio and proportion
Ratio and proportion, Algebra, Geometry
Algebra, Geometry, Data and probability
Knowledge
Review of KS3:
Integer/Decimal- 4 operations
Basic indices, powers and roots
Factors, multiples and primes
Basic algebra: Simplifying, expanding and
factorising singles brackets, substitution, solving
linear equation and inequalities.
Sequences.
Fractions and percentages
Apply four operations to fractions (proper and
improper, mixed number)
Use fractions to solve problems.
Convert between percentages, fractions and
decimals.
Find a percentage of a quantity, Calculate simple
interest and percentage increases and decreases.
Calculate a percentage profit or loss and find the
original amount given the final amount after a
percentage increase or decrease
Multiplicative reasoning
Convert between metric speed measures.
Calculate average speed, distance and time.
Quadratic equations and graphs
Recognise, simplify and factorise quadratic
equations and function.
Solve quadratic equations using a graph and
algebraically.
Ratio and proportion
Use ratio notation, divide a given quantity into two
parts, expression the division of a quantity into parts
of a ratio, apply ratio to real contexts.
Solve problem involving direct proportion; scales,
recipes, currencies.
Recognise and use direct proportion on a graph.
Perimeter, area and volume.
calculate perimeters of 2D shapes, including circles
calculate areas of circles and composite shapes
know and apply formulae to calculate volume of
right prisms (including cylinders)
Averages and range
Calculating median, mode, mean and range from a
data set and from a table.
Explain and understand Sampling.
Carry out a statistical investigation and explain how
biased data would result and how to eliminate it.
Graphs, tables and charts
Construct a frequency table for a continuous data
set, deciding on appropriate intervals using
inequalities
Plan a journey using timetables.
Produce and interpret:
pictograms;
composite bar charts;
dual/comparative bar charts for categorical and
ungrouped discrete data;
bar-line charts;
vertical line charts;
line graphs;
line graphs for time–series data;
histograms with equal class intervals;
stem and leaf (including back-to-back);
Pie Charts
Given two sets of data in a table, model the
relationship and make predictions using scatter
Parallel lines and interior and exterior angles in
polygons.
Recap: apply the properties of angles at a point,
angles at a point
on a straight line, vertically opposite angles
understand and use alternate and corresponding
angles on parallel
lines
Derive and use the sum of angles in a triangle (e.g.
to deduce and
use the angle sum in any polygon, and to derive
properties of
regular polygons)
Graphs-linear graphs
Draw graphs to represent relationships.
Find the equations of straight-line graphs and from
parallel and perpendicular lines.
Draw and interpret graphs from real data.
Use and draw distance–time graphs to solve
problems and interpret a range of graphs.
Right angles triangles: trigonometry and
Pythagoras.
Understand, recall and use Pythagoras theorem in
2D shapes.
Understand, use and recall the trigonometric ratios
sine, cosine and tan and apply them to find angles
and lengths.
Know the exact values of Sin, Cos and tan 0, 30,
45, 60 and 90.
Probability
Calculate simple probabilities and Understand
mutually exclusive and exhaustive outcomes.
Use two-way tables and sample space diagrams to
record the outcomes from two events.
Find and interpret probabilities based on
experimental data.
Use Venn diagrams, frequency tables and tree
diagrams to work out probabilities.
.
Mathematics Department – Medium Term Plan
graphs and lines of best fit.
Year 11
foundation.
ADAPTED PEARSON ASSESSMENT
ADAPTED PEARSON ASSESSMENT
ADAPTED PEARSON ASSESSMENT
FULL GCSE EDEXCEL PAPER
Content




Revision Grid.
Revision Grid.
Concepts
Geometry, Number, Algebra
Geometry , Algebra
Number, Algebra, Geometry, Ratio and Proportion,
Data and Probability
Number, Algebra, Geometry, Ratio and Proportion,
Data and Probability
Knowledge
Transformations
Describe and transform a given shape by reflection,
rotation, translation and enlargement.
Describe and transform 2D shapes using combined
rotations, reflections, translations, or enlargements.
Congruence, similarity and vectors
Use the basic congruence criteria for triangles
(SSS, SAS, ASA and RHS);
Identify shapes which are similar; including all
circles or all regular polygons with equal number of
sides;
Calculate using column vectors, and represent
graphically, the sum of two vectors, the difference of
two vectors and a scalar multiple of a vector.
Personalised Revision Grid prepared by class
teachers with the intension of filling in GAPs in
Exam paper.
Personalised Revision Grid prepared by class
teachers with the intension of filling in GAPs in
Exam paper.
Fertile Question
Transformations
Indices and standard form
Indices and standard form
To know and use the laws of indices.
Convert numbers from standard form into ordinary
numbers and vice versa and calculate with standard
form.
Year 10
Higher
Fertile Question
Content
Congruence, similarity and vectors
Algebra Extension
Extension Algebra
Change the subject of a formula. Identify
expressions, equations, formulae and identities and
Prove results using algebra
Draw and interpret Draw and interpret graphs of
cubic functions and reciprocals.
Solve and write simultaneous equations
algebraically and graphically.
FULL GCSE EDEXCEL PAPER
FULL GCSE EDEXCEL PAPER
FULL GCSE EDEXCEL PAPER
FULL GCSE EDEXCEL PAPER
How do I make a reasonable
Estimation?
 Accuracy, estimating and bounds.
 Algebra Review and changing the subject.
 Standard form, indices and surds.
 Fractions





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

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

Geometry, Algebra, Data and probability
Data and probability, Algebra
Area, perimeter and volume.
Know and apply formulae to calculate area of
shapes and composite shapes surface area and
volume of spheres, pyramids, cones, hemispheres,
frustum and composite solids.
Averages and graphs
Understand limitations of sampling.
Interpret and construct table, charts and diagrams,
including frequency tables, bar charts, pie charts,
tables interpret histograms with equal and unequal
Concepts
Number, Algebra,
Sequences
Ratio and proportion
Multiplicative reasoning.
Linear graphs , coordinate geometry and real
life graphs
Algebra, Ratio and proportion
Knowledge
Accuracy, estimating and bounds
Round numbers and measures to and appropriate
degree of accuracy (d.p or s.f). Use inequality
notation to specify error intervals due to truncation
or rounding. Check answers using approximation
Sequences
Generate terms of a sequence from either term-to –
term or a position-to-term rule
Recognise and use sequences of arithmetic
progressions, Fibonacci, quadratic and geometric
Area, perimeter and volume.
Similarity/ congruence
Further Trigonometry:
Probability
Averages and graphs
Complex quadratic equations.
Graphs of cubic and quadratic.
Mathematics Department – Medium Term Plan
and estimation.
Apply and interpret limits of accuracy, including
upper and lower bounds and calculate the bounds
of an expressions involving the four operations.
Basic Algebra
Review basics, solving equations, rearranging and
solving equations. Linear simultaneous equations,
factoring and expanding quadratic equationssimple. Simplifying and expanding quadratic
brackets.
More complex changing the subject
Standard form, indices and surds
Calculate with roots and with integers and fractional
indices.
Calculate with and interpret standard form A × 10n
simplify surd expressions involving squares
including expanding brackets and rationalise
denominators
Fractions.
Apply four operations to fractions (proper and
improper, mixed number)
Change recurring decimals into fractions and vice
versa.
simplify and manipulate algebraic expressions
involving algebraic fractions
sequences.
Ratio and proportion.
Use ratio notation, divide a given quantity into two
parts, expression the division of a quantity into parts
of a ratio, apply ratio to real contexts.
Solve problem involving direct proportion; scales,
recipes, currencies.
Multiplicative reasoning:
Solve problems involving direct and inverse
proportion including graphical and algebraic
representations
Use and convert compound units such as speed,
rates of pay, unit pricing, density and pressure. Use
kinematics formulae to calculate speed and
acceleration.
Linear graphs ,coordinate geometry and real life
graphs
Find the gradient and y-intercept from a linear
equation and calculate the equation of a line
through 2 points, parallel and perpendicular to a
given line.
Draw and interpret distance–time graphs and real
life linear graphs and understand velocity–time
graphs.
Calculate the area of circles, areas of sectors of
circles and arc lengths and sectors of circles.
Similarity/ congruent Shapes.
Use the basic congruence criteria for triangles.
(SSS, SAS, RHS, ASA)
Apply the concepts of congruence and similarity,
including the relationships between lengths, area
and volumes in similar figure.
class interval and line graphs for time series data
and know their appropriate use.
Calculate the mean, mode, median and range from
a frequency table and from appropriate diagrams.
Interpret and produce box plots to find quartiles,
interquartile ranges and identify any outliers.
Given two sets of data in a table, model the
relationship and make predictions using scatter
graphs and lines of best fit.
Trigonometry
Understand, recall and use Pythagoras theorem in
2D and 3D shapes.
Understand, use and recall the trigonometric ratios
sine, cosine and tan and apply them to find angles
and lengths.
Know the exact values of Sin, Cos and tan 0, 30,
45, 60 and 90.
Know and apply the sine rule and cosine rule to find
unknown lengths and angles and trigonometric area
to calculate the area, sides and angles of any
triangle.
Complex quadratic equations.
simplify and manipulate algebraic expressions
(including those involving surds and algebraic
fractions) by expanding products of two or more
binomials
solve quadratic equations by completing the
square and by using the quadratic formula
solve quadratic inequalities in one variable
solve two simultaneous equations in two variables
where one is quadratic algebraically
find approximate solutions to equations numerically
using iteration
Probability
Review of frequency trees, theoretical probability,
scales, expected frequency and independent and
dependent events.
Calculate and interpret conditional probabilities
through representation using expected frequencies
with two-way tables, tree diagrams and Venn
diagrams.
Graphs of cubic, quadratic- identify turning
points.
Sketch quadratic and cubic functions. Know where
a graph will cross the x-axis
Understand maximum and minimum points.
Find roots of an equation by completing the square
and using the quadratic formula.
ADAPTED PEARSON ASSESSMENT
FULL GCSE EDEXCEL PAPER
ADAPTED PEARSON ASSESSMENT
ADAPTED PEARSON ASSESSMENT
Fertile Question
Year 11
Higher
Content



Concepts
Geometry, Algebra
Knowledge
Functions and transformation of functions.
Use function notation and find composite function
and inverses.
Interpret and analyse transformations of graphs of
cubic, quadratic and trigonometric functions and
write the functions algebraically
Transformations
Functions
Circle theorem
Transformations.
Describe and transform a given shape by reflection,
rotation, translation and enlargement (fractional and
negative scale)
Draw and use scales on maps and scale drawings.
Solve problems involving bearings.
Construct triangles, bisect angles and construct the
perpendicular bisector of a line.


Revision Grid
Revision Grid
Geometry, Algebra, Ratio and Proportion
Number, Algebra, Geometry, Ratio and Proportion,
Data and Probability
Number, Algebra, Geometry, Ratio and Proportion,
Data and Probability
Vectors and geometric proof
Add and subtract vectors algebraically and use
column vectors.
Solve geometric problems and produce proofs.
Personalised Revision Grid prepared by class
teachers with the intension of filling in GAPs in
Exam paper.
Personalised Revision Grid prepared by class
teachers with the intension of filling in GAPs in
Exam paper.
Vectors and geometric proof
Proportion and graphs
Proportion and graphs
plot and interpret graphs (including
exponential graphs and trigonometric function) and
graphs of nonstandard functions in real contexts, to
find approximate solutions to problems such as
simple kinematic problems involving distance,
speed and acceleration
interpret the gradient at a point on a curve as
theo0zs instantaneous rate of change
calculate or estimate gradients of graphs
Mathematics Department – Medium Term Plan
Use loci to solve problems.
Circle theorem
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
identify and apply circle definitions and properties,
including: centre, radius, chord, diameter,
circumference, tangent, arc, sector and segment
apply and prove the standard circle theorems
concerning angles, radii, tangents and chords, and
use them to prove related results
FULL GCSE EDEXCEL PAPER
and areas under graphs (including quadratic
and other non-linear graphs), and interpret
results in cases such as distance-time
graphs, velocity-time graphs and graphs in
financial contexts
FULL GCSE EDEXCEL PAPER
FULL GCSE EDEXCEL PAPER
FULL GCSE EDEXCEL PAPER
Mathematics Department – Medium Term Plan
End Game
Year
13
1
2
3
4
Content
GCSE A Level Transition
Core Maths
Core Maths
Statistics
Core Maths
Statistics
Core Maths
Statistics
Concepts
•
•
•
•
Core Maths
•
Trigonometry
•
Exponentials and Logarithms
Core Maths
•
Differentiation
•
Integration
Core Maths
•
Numerical Methods
•
Vectors
Statistics
•
Statistical Modelling
•
Data Presentation and Interpretation
Statistics
•
Probability
•
Statistical Distributions
Statistics
•
Statistical Hypothesis testing
GCSE A Level Transition
Pure Mathematics
Pure Mathematics
Pure Mathematics
Pure Mathematics
1 Proof
5 Trigonometry
5.1 Understand and use the
definitions of sine, cosine
and tangent for all
arguments;
Use of x and y coordinates of points
on the unit circle to give cosine and
sine respectively,
Work with radian measure,
including use for arc length
and area of sector.
5.2 Understand and use the
standard small angle
approximations of sine, cosine
and tangent
5.3 Understand and use the
sine, cosine and tangent
functions; their graphs,
symmetries and
periodicity.
Knowledge of graphs of curves with
equations such as y = sinx,
y = cos(x + 30°), y = tan2x is
expected.
Know and use exact values of
5.4 Understand and use the
definitions of secant, cosecant
and cotangent and of arcsin,
arccos and arctan; their
relationships to sine, cosine
and tangent; understanding of
their graphs; their ranges and
7 Differentiation
7.1 Understand and use the
derivative of f ( x) as the
gradient of the tangent to
the graph of y = f ( x) at a
general point (x, y); the
gradient of the tangent as
a limit; interpretation as a
rate of change
Understand and use the
second derivative as the
rate of change of gradient
7.2 Differentiate xn
, for rational values of n, and
related constant multiples,
sums and differences.
Understand and use the
derivative of ln x
7.3 Apply differentiation to
find gradients, tangents
and normal. Use of differentiation to
find equations of tangents and
normals at specific points on a
curve. maxima and minima and
stationary points. points on inflection
To include applications to curve
sketching.
Identify where functions are
increasing or decreasing. To include
applications to curve sketching.
7.4 Differentiate using the
product rule, the quotient rule
9 Numerical methods
Fertile Question
Knowledge
Proof
Algebra and Functions
Coordinate Geometry in the (x,y) Plane
Sequences and Series
1.1 Understand and use the
structure of mathematical
proof, proceeding from
given assumptions
through a series of logical
steps to a conclusion; use
methods of proof,
including: Examples of proofs:
Proof by deduction
Proof by exhaustion
Disproof by Counter Example
2 Algebra and functions
2.1 Understand and use the
laws of indices for all
rational exponents.
2.2 Use and manipulate surds,
including rationalising the
denominator.
Students should be able to simplify
algebraic
2.3 Work with quadratic
functions and their graphs.
The notation f(x) may be used
The discriminant of a
quadratic function,
including the conditions
for real and repeated
roots.
9.1 Locate roots of f ( x) = 0 by
considering changes of sign of
f ( x) in an interval of x on
which f (x) is sufficiently well
behaved. Students should know that
sign change is appropriate for
continuous functions in a small
interval. Understand how change of
sign methods can fail. When the
interval is too large sign may not
change as there may be an even
number of roots. If the function is not
continuous, sign may change but
there may be an asymptote
(not a root).
9.2 Solve equations approximately
using simple iterative
methods; be able to draw
associated cobweb and staircase
diagrams.
Understand that many mathematical
problems cannot be solved
analytically, but numerical methods
permit solution to a required level of
accuracy.
Use an iteration of the form xn + 1 =
f (xn) to find a root of the equation x
= f (x) and show understanding of
the convergence in geometrical
terms by drawing cobweb and
Mathematics Department – Medium Term Plan
2.4 Solve simultaneous
equations in two variables
by elimination and by
substitution, including one
linear and one quadratic
equation.
2.5 Solve linear and quadratic
inequalities in a single
variable and interpret such
inequalities graphically,.
2.6 Manipulate polynomials
algebraically, including
expanding brackets and
collecting like terms,
factorisation and simple
algebraic division; use of
the factor theorem.
2.7 Understand and use
graphs of functions; sketch
curves defined by simple
equations including
polynomials
Graph to include simple cubic and
quartic functions,
The modulus of a linear
function.
Interpret algebraic
solution of equations
graphically; use
intersection points of
graphs to solve equations.
Understand and use
proportional relationships
and their graphs.
2.8 Understand and use
composite functions; inverse
functions and their graphs.
2.9 Understand the effect of
simple transformations on
the graph of y = f(x),
including sketching
associated graphs:
quartics, reciprocal, 2
2.10 Decompose rational functions
into partial fractions
(denominators not more
complicated than squared
linear terms and with no
more than 3 terms,
numerators constant or
linear).
2.11 Use of functions in modelling,
including consideration of
domains.
Angles measured in both degrees
and
radians.
5.5 Understand and use sin, tan.
cos=θ
Understand and use
sin2θ + cos2θ = 1
sec2θ = 1 + tan2 θ and
cosec2θ = 1+ cot2θ
These identities may be used to
solve trigonometric equations and
angles may be in degrees or
radians. They may also be used to
prove further identities.
5.6 Understand and use double
angle formulae; use of
formulae for sin (A ± B),
cos (A ± B), and tan (A ± B),
understand geometrical
proofs of these formulae.
To include application to half angles.
Understand and use
expressions for
a cos θ + b sinθ in the
equivalent forms of
r cos (θ ±α ) or r sin (θ ±α )
Students should be able to solve
equations such as a cos θ + b sin θ
= c in a given interval.
5.7 Solve simple trigonometric
equations in a given
interval, including
quadratic equations in sin,
cos and tan and equations
involving multiples of the
unknown angle.
These may be in degrees or radians
5.8 Construct proofs involving
trigonometric functions and
identities.
5.9 Use trigonometric functions to
solve problems in context,
including problems involving
vectors, kinematics and
forces.
6 Exponentials and logarithms
6.1 Know and use the function
ax and its graph, where a
is positive.
Understand the difference in shape
between a < 1 and a > 1
Know and use the function
and the chain rule, including
problems involving connected
rates of change and inverse
functions.
Differentiation of cosec x, cot x and
sec x
and differentiation of arcsin x, arcos
x, and
arctan x are required. Skill will be
expected
in the differentiation of functions
generated
from standard forms using products,
quotients and composition
7.5 Differentiate simple functions
and relations defined implicitly
or parametrically, for first
derivative only.
The finding of equations of tangents
and normals to curves given
parametrically or implicitly is
required.
7.6 Construct simple differential
equations in pure
mathematics and in context,
(contexts may include
kinematics, population growth
and modelling the relationship
between price and demand).
8 Integration
8.1 Know and use the
Fundamental Theorem of
Calculus Integration as the reverse
process of differentiation. Students
should know
that for indefinite integrals a
constant of integration is required.
8.2 Integrate xn (excluding
n = −1) and related sums,
differences and constant
multiples.
Given f ′(x) and a point on the curve,
Students should be able to find an
equation of the curve in the form
y = f (x)..
8.3 Evaluate definite integrals;
use a definite integral to
find the area under a curve
and the area between two
curves Students will be expected to
be able to evaluate the area of a
region bounded by a curve and
given straight lines, or
staircase diagrams.
9.3 Solve equations using the
Newton-Raphson method and
other recurrence relations of
the form xn+1= g(xn) Understand
how such methods can fail.
For the Newton-Raphson method,
students should understand its
working in geometrical terms, so that
they understand its failure near to
points where the gradient is small.
9.4 Understand and use
numerical integration of
functions, including the use of
the trapezium rule and
estimating the approximate
area under a curve and limits
that it must lie between.
9.5 Use numerical methods to
solve problems in context.
10 Vectors
10.1 Use vectors in two
dimensions and in three
dimensions
Students should be familiar with
column vectors and with the use of i
and j unit vectors in two dimensions
and i, j and k unit vectors in three
dimensions.
10.2 Calculate the magnitude
and direction of a vector
and convert between
component form and
magnitude/direction form.
Students should be able to find a
unit vector in the direction of a,
10.3 Add vectors
diagrammatically and
perform the algebraic
operations of vector
addition and multiplication
by scalars, and understand
their geometrical
interpretations. The triangle and
parallelogram laws
of addition. Parallel vectors.
10.4 Understand and use
position vectors; calculate
the distance between two
points represented by
position vectors.
10.5 Use vectors to solve
problems in pure
Mathematics Department – Medium Term Plan
limitations and refinements of
the models.
3
3 Coordinate geometry in the (x,y) plane
3.1 Understand and use the
equation of a straight line,
including the forms
y – y1 = m(x – x1) and
ax + by + c = 0;
To include the equation of a line
through two given points, and the
equation of a line parallel (or
perpendicular) to a given line
through
a given point.
Gradient conditions for
two straight lines to be
parallel or perpendicular.
m′ = m for parallel lines and m′ =
m
−1
for perpendicular lines
Be able to use straight line
models in a variety of
contexts..
3.2 Understand and use the
coordinate geometry of the
circle including using the
equation of a circle in the
form (x – a)2 + (y – b)2 = r2
Students should be able to find the
radius and the coordinates of the
centre of the circle given the
equation
of the circle, and vice versa.
point.
3.3 Understand and use the
parametric equations of
curves and conversion
between Cartesian and
parametric forms.
4 Sequences and series
4.1 Understand and use the
binomial expansion of
(a + bx)n for positive
integer n.
4.2 Work with sequences
including those given by a
formula for the n th term and
those generated by a simple
relation of the form
xn + 1 = f(xn);
increasing sequences;
e x and its graph.
6.2 Know that the gradient of
ekx is equal to kekx and
hence understand why the
exponential model is
suitable in many
applications.
Realise that when the rate of change
is proportional to the y value, an
exponential model should be used.
6.3 Know and use the
definition of loga x as the
inverse of a x, where a is
positive and x > 0.
Know and use the function
ln x and its graph.
a≠1
Know and use ln x as the
inverse function of ex
6.4 Understand and use the
laws of logarithms:
6.5 Solve equations of the
form a x =b
Students may use the change of
base
formula. Questions may be of the
form, e.g. 23x – 1 = 3
6.6 Use logarithmic graphs to
estimate parameters in
relationships of the form
y = axn and y = kbx, given
data for x and y
6.7 Understand and use
exponential growth and
decay; use in modelling
; consideration of
limitations and
refinements of exponential
models.
between two curves.
8.4 Understand and use
integration as the limit of a sum.
8.5 Carry out simple cases of
integration by substitution
and integration by parts;
understand these methods as
the inverse processes of the
chain and product rules
respectively
(Integration by substitution
includes finding a suitable
substitution and is limited to
cases where one substitution
will lead to a function which
can be integrated; integration
by parts includes more than
one application of the method
but excludes reduction
formulae.)
8.6 Integrate using partial
fractions that are linear in the
denominator. Integration of rational
expressions such as those arising
from partial fractions,
8.7 Evaluate the analytical
solution of simple first order
differential equations with
separable variables, including
finding particular solutions
(Separation of variables may
require factorisation involving
a common factor.)
8.8 Interpret the solution of a
differential equation in the
context of solving a problem,
including identifying
limitations of the solution;
includes links to kinematics.
Statistics
Statistics
1 Statistical sampling
3 Probability
3.1 Understand and use
mutually exclusive and
independent events when
calculating probabilities.
3.2 Understand and use
conditional probability,
including the use of tree
diagrams, Venn diagrams,
two-way tables.
3.3 Modelling with probability,
1.1 Understand and use the
terms ‘population’ and
‘sample’.
Use samples to make
informal inferences about
the population.
Students will be expected to
comment
on the advantages and
disadvantages
mathematics and in
context, (including
forces).
Statistics
5 Statistical hypothesis testing
5.1 Understand and 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, critical region,
acceptance region,
p-value;
5.2 Conduct a statistical
hypothesis test for the
proportion in the
binomial distribution and
interpret the results in
context.
5.3 Conduct a statistical
hypothesis test for the mean
of a Normal distribution with
known, given or assumed
variance and interpret the
results in context.
Mathematics Department – Medium Term Plan
decreasing sequences;
periodic sequences.
4.3 Understand and use sigma
notation for sums of series.
4.4 Understand and work with
arithmetic sequences and
series, including the formulae
for nth term and the sum to n
terms
4.5 Understand and work with
geometric sequences and
series, including the formulae
for the nth term and the sum
of a finite geometric series;
the sum to infinity of a
convergent geometric series,
including the use of |r| < 1;
modulus notation
The proof of the sum formula should
be
known.
4.6 Use sequences and series in
modelling.
associated with a census and a
sample.
Understand and use
sampling techniques,
including simple random
sampling and opportunity
sampling.
Students will be expected to be
familiar with: simple random
sampling, stratified sampling,
systematic sampling, quota
sampling
and opportunity (or convenience)
sampling.
Select or critique
sampling techniques in
the context of solving a
statistical problem,
including understanding
that different samples
can lead to different
conclusions about the
population.
2 Data presentation and
interpretation
including critiquing
assumptions made and the
likely effect of more realistic
assumptions
4 Statistical distributions
4.1
Understand and use
simple, discrete
probability distributions
including the
binomial distribution, as
a model; calculate
probabilities using the
binomial distribution.
4.2
Understand and use the
Normal distribution as a
model; find probabilities
using the Normal
distribution
4.3
Select an appropriate
probability distribution for a
context, with appropriate
reasoning, including
recognising when the
binomial or Normal model
may not be appropriate.
2.1 Interpret diagrams for
single-variable data,
including understanding
5 Statistical hypothesis testing
that area in a histogram
represents frequency.
5.1 Understand and apply the
Students should be familiar with
language of statistical
histograms, frequency polygons, box
hypothesis testing,
and whisker plots (including outliers)
developed through a
and cumulative frequency diagrams.
binomial model: null
Connect to probability distributions
hypothesis, alternative
2.2 Interpret scatter
hypothesis, significance
diagrams and regression
level, test statistic, 1-tail
lines for bivariate data,
test, 2-tail test, critical
including recognition of
value, critical region,
scatter diagrams which
acceptance region,
include distinct sections
p-value;
of the population
5.2 Conduct a statistical
Use to make predictions within the
hypothesis test for the
range of values of the explanatory
proportion in the
variable and the dangers of
binomial distribution and
extrapolation. Derivations will not be
interpret the results in
required. Variables other than x
context.
and y may be used.
5.3 Conduct a statistical
2.3 Interpret measures of
hypothesis test for the mean
central tendency and
of a Normal distribution with
variation, extending to
known, given or assumed
standard deviation.
variance and interpret the
Mathematics Department – Medium Term Plan
Data may be discrete, continuous,
grouped or ungrouped.
Understanding and use of coding.
Measures of central tendency:
mean, median, mode. Measures of
variation: variance, standard
deviation, range and interpercentile
ranges. Use of linear interpolation to
calculate percentiles from grouped
data is expected.
2.4 Recognise and interpret
possible outliers in data
sets and statistical
diagrams.
results in context.
Mathematics Department – Medium Term Plan
End Game
Year
13
1
2
3
Content
AS-A2 Transition
Core 3
Mechanics 1
Core 3
Mechanics 1
Core 4
Mechanics 1
Core 4
Concepts
Core 3
 Algebraic fractions
 Functions
 Numerical methods
 The exponential and log functions
 Transforming graphs of functions
Mechanics 1
 Kinematics
 Moments
Core 3
Core 4
 The binomial expansion
 Coordinate geometry
 Differentiation
 Integration
Mechanics 1
 Statics
 Vectors
4
Fertile Question



Core 4


Further Trigonometry
Trigonometry
Differentiation
Partial fractions
Vectors
Mechanics 1
 Dynamics
Knowledge
C3
C3
M1
Chapter 1: Algebraic Fractions
(completed at the end of Yr 12)
Chapter 6/7: Trigonometry Further trigonometric identities
and their applications.
Chapter 4: Statics of a particle
Add, subtract, multiply and divide
algebraic fractions, simplifying the
answer
Use algebraic long division to
simplify improper algebraic
fractions
Work with identities containing
algebraic fractions - evaluate
coefficients
Chapter 2: Functions (completed
at the end of Yr12
Know the definitions and graphs of
sec x, cosec x and cot x
Know and prove the identities
tan2x + 1 = sec2x and 1 + cot2x =
cosec2x
C3
Resolve forces into horizontal and
vertical components and use with F
= ma
Resolve forces into perpendicular
and parallel components on a
slope and use with F = ma
C4
Use friction = µR in problems
Solve trig equations containing one involving F = ma in any of the
or more of sec, cosec and cot
above contexts
Know the definitions and graphs of
arcsin x, arccos x and arctan x
Understand tension and thrust and
how to represent them on a force
diagram
Use compound angle formulae
Solve connected particle problems
Understand function notation and [e.g. sin (A + B)] to solve trig
equations or to prove trig identities involving pulleys, including
substitution into f(x)
particles on slopes
Identify the domain and range for a Prove and use the double angle
M1
Mathematics Department – Medium Term Plan
given function, possibly by using a
graph sketch
formulae - learn them (inc 3
versions for cos 2x)
Substitute into or find an
Prove and use the half angle
expression for fg(x) or gf(x) - known formulae
as composite functions
Know how to write given trig
Find an expression for the inverse expressions in the form R sin (x +/function f-1(x) of a given function
a) or R cos (x +/- a)
f(x)
Solve trig equations by using any of
Know and use the domain/range
the above formulae/expressions
match ups between f(x) and f-1(x)
Chapter 8: Differentiation.
Solve equations involving f(x), g(x),
Know and use dy/dx = 1/ (dx/dy)
fg(x), f-1(x) etc.
and dx/dy = 1/(dy/dx)
Chapter 3: The exponential and
Know the differentials of sin [f(x)],
log function (completed at end of
cos [f(x)] and tan [f(x)]
Yr 12)
Know the differentials of sec [f(x)],
Know that ex differentiated is ex
cosec [f(x)] and cot [f(x)]
(main definition of ex)
Know and use the differentials of
Know and use that if y = ex then x
ef(x) and ln [f(x)]
= ln y or if f(x) = ex then f-1(x) = ln x
Know and use the chain rule (or
Know the graphs of ex, e-x and ln x
quick methods) to differentiate a
and be able to transform them e.g.
function of a function
y = e3x+2
Know and use the product rule
Solve problems containing
exponential or ln equations
Know and use the quotient rule
Solve connected particle problems
involving a car and trailer including
on a slope
Chapter 6: Vectors.
Understand that vectors can
represent any quantity with
magnitude and direction
Calculate the magnitude and
direction of a given vector and
interpret the magnitude
Understand how to calculate and
use unit vectors
Use F = ma and v = u + at as vector
equations for 2-D acceleration
problems
Use r = r0 + tv to find the position
of a particle moving in 2-D at time t
Use ArB = rA - rB to find the
position vector of A relative to B
Calculate the closest distance
between two moving objects using
modulus of ArB
Calculate the time for which two
objects are within a certain
distance of each other
Chapter 4: Numerical methods
M1
Know how to show that the
equation f(x) = 0 has a root in a
given interval by sign change
Chapter 3: Dynamics of a particle
moving in a straight line.
C4
Use conservation of momentum
with colliding particles
Chapter 2: Coordinate geometry in
the (x,y) plane.
Use conservation of momentum
with exploding shells and
Eliminate the parameter to find an
Use graph sketching to
demonstrate the number and
location of roots of an equation
Mathematics Department – Medium Term Plan
Rearrange f(x) = 0 into the form x = bullets/guns
g(x) to obtain an iterative equation
Use conservation of momentum
xn+1 = g(xn)
with exploding shells and
Substitute x1, x2, x3 etc. into an
bullets/guns
iterative equation to obtain
Use conservation of momentum
successive approximations
with jerk in a string on connected
Justify a root of f(x) = 0 to a given
particles
degree of accuracy by substituting
Use IMPULSE = CHANGE IN
upper and lower bounds for a sign
MOMENTUM
change
Chapter 5: Transforming graphs of
functions
C4
Sketch the graph of y = |f(x)| for a
given f(x)
Chapter 5: Vectors
Find the vector for a line segment
Sketch the graph of y = |f(x)| or y = between two points and find its
f(|x|) from the graph of y = f(x)
modulus
Know and apply the graph
transformations covered in C2 to
functions covered in C3
Find the vector equation for a
straight line through two given
points
Sketch two graphs of the form y =
|mx + c| and determine the points
of intersection
Find the vector equation for a
straight line through a given point
and parallel to a given line
M1
Determine whether two lines
intersect and find the point if they
do intersect
Chapter 1: Mathematical models
in mechanics.
equation between x and y
Use the chain rule to find dy/dx
and then find a tangent, normal or
stationary point
Use ∫ y dx = ∫ y (dx/dt) dt to find
the area between a parametric
curve and the x axis
Use π∫ y2 dx = π∫ y2 (dx/dt) dt to
find the volume of revolution for a
parametric curve
Chapter 3: The binomial
expansion.
Understand how to use the
expansion (1 + x)n for negative and
rational values of n
Use |x| < 1 to identify range of
validity for a given expansion e.g.
(1 + 3/2x)-2 then |3/2x| < 1
Expand expressions such as (32x)1/2 using (1 + x)n appropriately
Use given information to find p and
n for (1 + px)n or (a + px)n
Expand expressions such as (1 2x)(1 + 3x)-1/3
Use partial fractions and then
Use scalar product to find the angle
expand appropriately
between the directions of two
Chapter 2: Kinematics of a particle vectors
Identify and substitute a small
value of x into an expansion to
moving in a straight line.
Use scalar product to find the angle
approximate a value
Know the significance of modelling between two lines given in vector
assumptions, and how they affect form
Chapter 4:Differentiation
the calculations in a problem
Calculate the angles, lengths and
Review differentiation rules and
Mathematics Department – Medium Term Plan
Know and use v = u + at
Know and use v2 = u2 + 2as
Know and use s = ut + 1/2 at2
Know and use s = vt - 1/2 at2
Know and use s = (u + v)t/2
Apply the above equations to
vertical motion under gravity using
g = 9.8ms-2
Sketch velocity/time graphs from
given information
Use the gradient of a section of a
velocity/time graph to calculate
acceleration
Use the area under a velocity/time
graph to calculate/equate to total
distance
Chapter 5: Moments
Use Fd and Fd sin θ to calculate the
moment of a force about a point
Understand that clockwise =
anticlockwise in equilibrium
situations
Calculate with moments when
forces are given as vectors and
points as co-ordinates
Solve balance problems for
uniform rods
Solve balance problems for nonuniform rods
Solve balance problems when on
area for a triangle made with three techniques from C1, C2 and C3
given points
Differentiate a pair of parametric
Find the perpendicular distance
equations in order to find dy/dx
from a point to a line
Obtain dy/dx for an implicit
equation e.g. y3 - 3xy2 + 5xy - 2x2 =
Chapter 1: Partial Fractions
50
Know how to split into partial
fractions involving up to three
Differentiate functions involving ax
linear denominators
Chapter 6: Integration
Know how to split into partial
Review integration rules and
fractions when one denominator
techniques from C1 and C2
has a repeated factor
Use integrals for the 6 trig
Use algebraic long division with
functions of the type ∫ sin (ax + b)
improper algebraic fractions and
dx
then find partial fractions
Use the integrals ∫ eax + b dx and ∫
(ax + b)n dx
Find integrals of the form ∫ f/(x)
[f(x)]n dx
Find integrals of the form ∫
f/(x)/f(x) dx
Use partial fractions to set up
integrals of the form ∫ f/(x)/f(x) dx
Use the six integrals of the squares
of trig functions e.g. ∫ cos2x dx
Use integration by parts NOT
involving ln
Integrate by parts involving ln
Use integration by
substitution/change of variable
Find integrals of the form ∫sin 5x
Mathematics Department – Medium Term Plan
the point of tilting about one pivot
cos 3x dx
Evaluate definite integrals for any
of the above types
Use A = ∫ y dx to find the area
between a curve and the x axis
Use V = π ∫ y2 dx to find the
volume of revolution around the x
axis