AQA

A-level Maths e-library

In this section, you will find resources that will support your teaching of our A-level Maths specification, including resources for AS.

Use the menu links on the left-hand side to find resources for a particular topic.

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  • A frictional story
     (2)

    Task set on a rough inclined plane.

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  • A level maths worksheet: sigma notation
     (1)

    Worksheet to practise using sigma notation.

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    Type(s):
  • Ab-surd!
     (11)

    An activity on rationalising denominators.

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    Type(s):
  • Acceleration due to gravity
     (1)

    Strobe image showing a ball falling allowing students to see acceleration due to gravity.

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    Type(s):
  • Addition formulae
     (1)

    Worksheets for practising the addition formulae.

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    Type(s):
  • Additional integrals
     (2)

    Rich task looking at combinations of definite integrals.

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    Type(s):
  • Alternative form

    Worksheets for expressions in the form R sin(x+a) and R cos(x+a).

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  • An exercise in sampling: rolling down the river
     (1)

    Activity for understanding sampling techniques.

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    Type(s):
  • Analysing scatter plots
     (3)

    Notes and exercises (using US vocabulary) on scatter graphs, including identifying outliers.

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    Type(s):
  • Antiderivative worksheet
     (1)

    Simple worksheet for thinking about antiderivatives.

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  • Antiderivatives and indefinite integrals

    Examples and exercises.

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    Type(s):
  • AP proof sorter
     (3)

    This is a self-checking tool to learn and understand the proof of the formula for the sum of an arithmetic series. Flash required.

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  • Applying small angle approximations
     (1)

    Video explaining how to use small angle approximations.

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  • Areas of triangles

    Fluency practice for finding the area of triangles using sine.

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    Type(s):
  • Arithmetic sequences practice problems

    Worksheet for developing fluency in working with arithmetic sequences.

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  • Arithmetic series
     (1)

    Scaffolded worksheet and extension questions for arithmetic series.

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  • Arithmetic series exam questions
     (1)

    A useful bank of exam questions from the legacy specification.

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    Type(s):
  • Average speed

    Problems involving average speed.

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  • Basic exponential and logarithmic equations

    Worksheet on solving equations using log and ln.

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    Type(s):
  • Basics of vectors

    Worksheet using Cartesian components.

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  • Become friends with logarithms

    Mixed exercises using logs.

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    Type(s):
  • Binomial and hypothesis testing

    Worksheet with binomial questions including hypothesis testing.

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  • Binomial distribution

    Notes and worksheets for working with binomial graphs.

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  • Binomial distribution

    Notes and exercises for binomial distribution

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  • Binomial distribution

    Slides about when and how to use the binomial distribution.

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  • Binomial Expansion Lock Game

    Binomial expansion worksheet where answers to questions are used to obtain a 3-digit code.

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  • Binomial expansion questions
     (1)

    Fluency practice for binomial expansions.

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    Type(s):
  • Binomial expansion worksheets
     (1)

    Notes, examples and a summary activity for binomial expansions where n is negative or a non-integer.

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  • Binomial expansion worksheets

    A set of worksheets to introduce binomial expansion and develop fluency.

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  • Binomial puzzle

    A card-based puzzle for binomial distribution.

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  • Breaking Strain
     (1)

    Contextual activity for resolving forces.

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    Type(s):
  • Calculating arcs and areas of sectors of circles

    Lesson plan and resources for working with sectors in radians.

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  • Calculus in kinematics exercise

    Calculus in kinematics worksheet with answers.

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  • Calculus kinematics

    A selection of exam style questions and solutions.

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    Type(s):
  • Can we approximate the area under this sine curve?

    Review question using numerical methods to estimate the area under a sine graph.

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    Type(s):
  • Can you find... (cubic edition)
     (1)

    Rich task for exploring cubic graphs.

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  • Can you find... (trigonometry edition)

    Rich task looking at transformations of trigonometric curves.

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    Type(s):
  • Can you find... trigonometry edition

    Activity for combined transformations of sine graphs

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    Type(s):
  • Can you find… chain rule edition
     (1)

    A rich task finding functions to meet certain criteria.

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    Type(s):
  • Cartesian components of vectors
     (1)

    Notes and exercises on writing vectors in Cartesian component form

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    Type(s):
  • Cartesian components of vectors 2

    Notes and exercises on writing vectors in Cartesian component form.

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    Type(s):
  • Cartesian components of vectors powerpoint

    Slides giving an introduction of i and j components in vectors.

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    Type(s):
  • Census or sample?

    An activity looking at types of sampling and sample size.

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    Type(s):
  • Chain rule resources
     (1)

    Notes, examples and exercises for the chain rule.

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  • Chain rule worksheet
     (1)

    Fluency practice for using the chain rule.

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    Type(s):
  • Change of sign video

    Video showing what a root is and how to show that a root lies in a given interval by using the change of sign method.

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    Type(s):
  • Change one thing

    Rich task exploring arithmetic sequences.

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    Type(s):
  • Circle Geometry

    Rich tasks for teaching the equation of a circle.

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  • Circle worksheets

    Circle geometry notes and worksheets including a summary exercise.

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  • Circles exam questions
     (1)

    A collection of legacy specification exam questions on circle geometry, with answers.

    E-libraryDownload Circles exam questions  in PDF format Open link

    Type(s):
  • Classifying equations of parallel and perpendicular lines
     (1)

    Activities and discussion prompts for parallel and perpendicular lines.

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  • Coastal erosion: estimating area

    Students approximate the area of a piece of land with an irregular coastline, and the area lost to coastal erosion over time.

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  • Comparing averages and spread

    Worksheet in which students alter the original data set and analyse what happens to the averages and spreads.

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  • Compose!
     (1)

    Rich task looking at composite functions.

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    Type(s):
  • Composite and inverse functions

    Worksheets on composite and inverse functions.

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    Type(s):
  • Conditional probability puzzler

    Scaffolded tree diagram activity.

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  • Constant acceleration equations
     (1)

    Notes, examples and exercises.

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    Type(s):
  • Coordinate Geometry Group Cards
     (1)

    Tasks for solving linear graph problems.

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    Type(s):
  • Correlation and regression

    Notes and activities for correlation and regression.

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  • Correlation coefficient
     (1)

    Lesson plans and activities for correlation coefficient.

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    Type(s):
  • Cricketing MMM

    This is a Powerpoint that covers all the different situations in which calculating measures of location might be required.

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    Type(s):
  • Currency

    A geometric progression activity involving logs.

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    Type(s):
  • Curve Match

    Rich task for thinking about curve sketches.

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    Type(s):
  • Data types and sampling methods

    A gap fill on data collection and sampling

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    Type(s):
  • Defining vectors

    Activity for developing fluency in vector addition.

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    Type(s):
  • Definite integration worksheets
     (1)

    Examples, worksheets and activities on definite integration.

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  • Definite integration worksheets

    Examples, worksheets and activities on definite integration.

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    Type(s):
  • Describing motion with words

    Notes and examples on the vocabulary of kinematics.

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    Type(s):
  • Differential equations

    Worksheet on solving first order differential equations.

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  • Differential equations

    Examples of forming and solving differential equations.

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  • Differential Equations

    Worksheets for differential equations involving exponential growth.

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  • Differential equations legacy exam questions

    Legacy exam questions on forming and solving differential equations.

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    Type(s):
  • Differential equations textbook chapter

    Textbook chapter with detailed explanations.

    E-libraryDownload Differential equations textbook chapter in PDF format Open link

    Type(s):
  • Differentiating logarithmic and exponential functions

    Notes on differentiating e and ln from first principles.

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    Type(s):
  • Differentiating trig functions

    Worksheets for trig differentiation (includes chain, product and quotient rule).

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  • Differentiation dominoes - simple polynomials

    Matching activity for differentiating simple polynomials.

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  • Differentiation from first principles
     (2)

    A group activity investigating gradients of curves.

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    Type(s):
  • Differentiation of e and ln
     (1)

    Worksheets for e and ln differentiation (includes chain rule).

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  • Differentiation practice problems

    Exercise for developing fluency in differentiation.

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    Type(s):
  • Differentiation revision

    Mixed worksheet on differentiation.

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    Type(s):
  • Differentiation worksheets

    Worksheets to practice basic differentiation.

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    Type(s):
  • Disciminating
     (3)

    Rich task for exploring the discriminant.

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  • Discriminant exam questions

    Legacy A level exam questions involving the discriminant, with answers.

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    Type(s):
  • Discussing distance

    Rich task looking at two different motion graphs.

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  • Domain and range dominoes
     (1)

    Rich task featuring a card match for domain and range.

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  • Equation or identity?

    Trigonometric proof activity in which students classify identities and equations.

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  • Equations

    Examples and exercises on quadratic simultaneous equations.

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    Type(s):
  • Estimating gradients

    Task involving the gradient of y = sinx.

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  • Estimating the coefficient of friction

    Practical activity looking at friction.

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    Type(s):
  • Evaluating Statements about Radicals

    Always, sometimes, never activity.

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  • Ever wondered why?
     (1)

    Codebreaker activity for numerical negative and fractional indices from JustMaths. In this codebreaker resource, each row is arranged in a group of three: an answer, a letter and a question. First do the question under 'Start' and write down the corresponding letter. Find the answer and do the same again - continue until you reach 'finish'

    E-libraryDownload Ever wondered why? in PDF format Open link

    Type(s):
  • Exact Value Trigonometry

    A worksheet requiring students to use their understanding of exact values.

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  • Exercise on differential equations in mechanics
     (1)

    Worksheet with solutions.

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  • Exploring equations in parametric form

    Rich tasks looking at the gradient and intercepts of curves given in parametric form.

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  • Exploring trigonometrical graphs
     (1)

    Tasks looking at transformations of trigonometric graphs.

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  • Exponential and logarithmic regression

    Worksheet and video on regression using logs.

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    Type(s):
  • Exponential and natural logarithmic functions

    Worksheets for plotting and transforming e and ln graphs.

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  • Exponential and natural logarithmic functions

    Worksheets for plotting and transforming e and ln graphs.

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  • Exponential functions and their graphs
     (3)

    Practice questions for graphing and applying y = a^x and y = e^x.

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  • Exponential growth and decay
     (1)

    An introduction to exponential growth and decay from the perspective of calculus applications to the physical world. Includes links to video examples and an exploration of population growth.

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  • Exponential growth and decay
     (1)

    Examples and questions for applied exponential functions.

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  • Exponential growth and decay: differential equations

    Textbook chapter with explanations, examples and questions.

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  • Exponentially increasing like rabbits
     (1)

    An exponential growth problem that can be solved using natural logs.

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    Type(s):
  • Factor theorem and algebraic division worksheets

    Fluency exercise for algebraic division.

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  • Factor Theorem Teaching Resources

    Rich tasks for the factor theorem.

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  • Factorising quadratics

    Fluency exercise for factorising quadratics.

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  • False positive

    Probability tree activity.

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  • First order differential equations

    Worked examples for differential equations.

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  • First order differential equations with applications

    Notes including various contexts.

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    Type(s):
  • First steps into differentiation
     (1)

    An IT task investigating gradient.

    E-libraryDownload First steps into differentiation in On-screen activity format Open link

    Type(s):
  • Floppy Hair

    Graph matching task looking at maximum points.

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  • Force and motion

    Interactive simulation: force and motion basics.

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  • Force as a vector

    Notes and exercises.

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  • Force as a vector

    Notes and examples.

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  • Forces acting at an angle: Resolving Forces

    Worked examples and exercises for resolving forces.

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  • Forces at a point

    Worksheets for drawing diagrams and forces in equilibrium.

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  • Forming differential equations

    Short worksheet on forming differential equations.

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  • Four Functions
     (1)

    Rich task considering domain, range and inverse. For each of these functions, can you draw their graph? Can you find the inverse function? Their domain and range?

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  • Friction

    Examples and worksheet for the coefficient of friction.

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  • Friction exam revision

    PowerPoint with examples.

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  • Frightening function
     (1)

    Rich task to start thinking about partial fractions.

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  • Functions stack
     (1)

    Rich task looking at symmetry and asymptotes in graphs.

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  • Further calculus in kinematics exercise

    Exercise and examples for calculus in kinematics, displacement/velocity/acceleration varying with time, in 2D and 3D.

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  • Further projectiles materials
     (1)

    Worksheet and notes.

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  • General solutions

    Rich task with interactive tools for exploring trigonometric graphs.

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  • Geometric sequences

    Contextual practice problems for geometric sequences.

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  • Geometric sequences and exponetial growth and decay

    Lesson ideas and activities for modelling with sequences

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  • Geometric series

    Scaffolded worksheet, activities and extension questions for geometric series.

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  • Geometric series exam questions

    A useful bank of exam questions from the legacy specification.

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  • Going round in circles

    Rich task for discovering the reciprocal Pythagorean identities.

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    Type(s):
  • Gradient match
     (1)

    A rich task matching graphs of functions to their gradients.

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  • Gradients of gradients

    Task looking at graphs of second derivatives.

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    Type(s):
  • Graph transforms

    Activities for developing fluency in graph transformations.

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    Type(s):
  • Graphical iteration (staircase and cobweb)

    8 Questions with graphs to iterate and find estimates for solutions.

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  • Graphing exponential functions

    Straightforward fluency practice for graphing y = a^x

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    Type(s):
  • Graphing exponential functions

    Notes and practice problems for drawing exponential graphs.

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    Type(s):
  • Graphs of exponential functions

    Lesson and worksheets for graphing y = a^x.

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  • Graphs of inverse trigonometric functions

    Activity in which students plot the inverse trigonometric graphs and consider their features.

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    Type(s):
  • Guessing correlations game

    Online game looking at correlation coefficients.

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    Type(s):
  • Haircut Costs

    A box plot comparison activity.

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    Type(s):
  • Have a sine

    Rich extension activity exploring trigonometric ratios and identities.

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  • Heave Ho!

    Activity looking at the motion of a heaving line.

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  • Hexagon puzzle

    Activity to introduce vectors

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  • Histograms

    Histograms practice.

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  • Histograms

    Slides and questions for histograms.

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    Type(s):
  • Hit the spot
     (2)

    Rich task involving magnitude, direction and Cartesian component form.

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    Type(s):
  • How Far Did the Earth Move?

    Task using logs to model magnitude and energy.

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    Type(s):
  • Hypothesis testing
     (1)

    Notes and example including testing for the sample mean.

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    Type(s):
  • Hypothesis testing

    Notes and examples on how to conduct hypothesis tests.

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    Type(s):
  • Hypothesis testing for the binomial distribution

    Video explaining how to conduct binomial hypothesis tests.

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    Type(s):
  • Hypothesis testing topic mat

    Template to complete the stages of hypothesis testing.

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    Type(s):
  • Hypothesis testing using the binomial distribution

    Geogebra tool for binomial hypothesis tests.

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    Type(s):
  • Hypothesis testing worksheets

    Worksheets including binomial testing.

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    Type(s):
  • I can see u!

    Task to develop fluency in writing expressions in terms of u in order to use the chain rule.

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    Type(s):
  • Identifying distributions

    Classification activity to identify the appropriate statistical model (also includes Binomial, Poisson, Normal, Continuous Uniform Distribution so will need to be adapted).

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    Type(s):
  • Identifying distributions

    Classification activity to identify the appropriate statistical model (also includes Binomial, Poisson, Normal, Continuous Uniform Distribution so will need to be adapted).

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    Type(s):
  • Identifying outliers

    Task involving constructing a box plot and considering outliers.

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    Type(s):
  • Implicit circles

    Task looking at various approaches for finding the gradient of a circle.

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    Type(s):
  • Implicit differentiation

    Structured worksheets on implicit differentiation.

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  • Inclined plane model

    Interactive geogebra file of an object on an inclined plane.

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    Type(s):
  • Increasing and decreasing functions

    Worksheets looking at increasing and decreasing functions.

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    Type(s):
  • Increasing, decreasing and not monotonic sequences

    Video explaining the different types of sequence.

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    Type(s):
  • Indefinite integration

    Examples, worksheets and activities on indefinite integration.

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    Type(s):
  • Indefinite integration

    Examples, worksheets and activities on indefinite integration.

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    Type(s):
  • Independence, dependence, mutually exclusive or not?

    Worksheet using set notation to look at independence and related concepts.

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    Type(s):
  • Independent, dependent and mutually exclusive events

    Video summarising what we mean by dependent, independent and mutually exclusive events and related probability formulae.

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    Type(s):
  • Indices activities
     (2)

    Five rich tasks for exploring indices both numerically and algebraically.

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  • Indices matching
     (1)

    Worksheet for practising index laws and algebraic fractional and negative indices

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    Type(s):
  • Inequalities

    Examples and exercises for linear, quadratic and graphical inequalities.

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    Type(s):
  • Inequalities for some occasions

    Rich task on quadratic inequalities.

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  • Inequalities worksheets

    A set of exercises on linear and quadratic inequalities.

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  • Inequality Exam Questions
     (1)

    Legacy A level exam questions on linear and quadratic inequalities, with answers.

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    Type(s):
  • Inequations: Regions

    Fluency practice for graphical inequalities.

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    Type(s):
  • Integral chasing

    Rich task for developing fluency in definite integration.

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    Type(s):
  • Integral sorting

    Card match activity for integration by substitution.

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    Type(s):
  • Integrating algebraic fractions

    Notes and exercises for integrating with partial fractions

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    Type(s):
  • Integrating basic functions

    Worksheet for practising integration

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    Type(s):
  • Integration

    Slides and worksheet for area under curve.

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    Type(s):
  • Integration

    Slides introducing integration.

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    Type(s):
  • Integration by parts

    Integration by parts questions.

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    Type(s):
  • Integration by substitution

    Integration questions that require substitution.

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    Type(s):
  • International System of Units (SI)

    Website defining the SI base units and providing information about their historical context.

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    Type(s):
  • Interpreting frequency graph, cumulative frequency graphs and box and whisker plots

    Lesson plan and card sort.

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  • Interpreting frequency graph, cumulative frequency graphs and box and whisker plots

    Lesson plan and card sort.

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  • Interpreting the regression line constants, explanatory and response variables

    Video on interpreting regression lines.

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  • Introducing e

    Lesson plans and activities for introducing the concept of e.

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    Type(s):
  • Introduction to algebra
     (1)

    Fluency exercise for simplifying algebra.

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    Type(s):
  • Introduction to series

    Straightforward worksheet on sigma notation, to develop fluency.

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    Type(s):
  • Introduction to vectors

    Notes, examples and worksheets on component vectors.

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    Type(s):
  • Inverse functions notes and solutions

    Lecture notes and exercises for inverse functions.

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    Type(s):
  • Inverse trignometric functions

    Simple worksheet for developing fluency in inverse trigonometric functions.

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    Type(s):
  • Inverse, composite, domain and range of functions

    Gap fill activity designed for pairs or groups

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    Type(s):
  • Is the gradient function increasing or decreasing on this curve? 

    Task looking at where functions are increasing and decreasing .

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    Type(s):
  • Is the Serpentine Lake really 40m acres?

    Approximation task linked to introducing calculus.

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    Type(s):
  • Is the Serpentine Lake really 40m?

    Rich task looking at approximating areas.

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    Type(s):
  • Iteration
     (2)

    Video on how to solve an equation using iteration.

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    Type(s):
  • Iteration
     (1)

    Slides and activities for iteration.

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    Type(s):
  • Iteration
     (4)

    Slides and activities for iteration.

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    Type(s):
  • Kangaroo lovers

    A activity to explore the sum to infinity of convergent geometric progressions.

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    Type(s):
  • Kinematics workbook

    Comprehensive workbook containing a wide range of questions on topics in kinematics.

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    Type(s):
  • Kinematics: describing motion

    Notes and examples on the vocabulary of kinematics.

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    Type(s):
  • Laws of Logarithms

    Matching activity for log laws.

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    Type(s):
  • Least squares regression simulation

    Online interactive tool for exploring least squares regression.

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    Type(s):
  • Linear equations and Mr Venn
     (1)

    Rich task for classifying equations of straight lines.

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    Type(s):
  • Linear Functions

    Rich tasks for linear graphs.

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    Type(s):
  • Linearising Data

    Textbook chapter with investigations and exercises.

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    Type(s):
  • Linking the properties and forms of quadratic functions

    Card sort for quadratic functions.

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    Type(s):
  • Logarithm dominoes - simplifying logs

    Matching activity involving log laws.

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    Type(s):
  • Logarithm lattice
     (1)

    Rich task sorting log expressions by size

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    Type(s):
  • Logarithm worksheets

    Log law worksheets to develop fluency.

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    Type(s):
  • Logarithmic equations maze activity

    Fun worksheets for solving equations using logs and ln.

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    Type(s):
  • Magnitude and angle of the resultant force

    Overview video.

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    Type(s):
  • Make it equal

    In each situation, students are given two of the forces and the fact the particle is in equilibrium, and have to find the third force.

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    Type(s):
  • Make it stop!

    Rich task involving applying forces to particles.

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    Type(s):
  • Make it stop!

    Rich task involving applying forces to particles.

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    Type(s):
  • Making predictions and reliability of predicted values

    Video on using regression lines.

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    Type(s):
  • Making sense of differentiation

    Notes and exercises for introducing calculus.

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    Type(s):
  • Making statistics vital

    When is a reading from a Binomial distribution significant? It all depends on the level of the test. Here is a chance to test student understanding of the issue, with the help of Excel.

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    Type(s):
  • Manipulating Surds

    Card sort, dominoes and exercises for simplifying surds.

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    Type(s):
  • Matching differential equations to descriptions

    Card match activity in which students match descriptions to equations.

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    Type(s):
  • Mathematical Modelling

    Teacher package of articles and lesson ideas.

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    Type(s):
  • Maxmimums and minimums in alternative form

    Worksheet looking at graphs of R sin(x+a) and R cos(x+a) to determine maximums and minimums

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    Type(s):
  • Meaningful areas

    Task looking at the area between two curves.

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    Type(s):
  • Mechanics 1 PowerPoints

    A set of PowerPoints including one on vectors for mechanics which includes magnitude/direction form.

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    Type(s):
  • Mechanics 1 Videos

    A set of videos including vectors.

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    Type(s):
  • Mechanics PowerPoint
     (1)

    PowerPoint and workbook for mechanics topics.

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    Type(s):
  • Methods of sampling
     (1)

    A series of activities on sampling methods.

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    Type(s):
  • Modulus always, sometimes, never
     (1)

    Activity in which students classify statements about modulus graphs and transformations.

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    Type(s):
  • Modulus function worksheets
     (1)

    Worksheets for Modulus equations, inequalities, graphs and transformations.

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    Type(s):
  • Moments
     (1)

    Moments puzzle challenge.

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    Type(s):
  • Moments revision sheet and problems
     (1)

    A set of problems on moments.

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    Type(s):
  • Moments worksheets
     (1)

    Worksheets and examples for moments.

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    Type(s):
  • Money matters
     (1)

    Contextual worksheet to practise calculating terms and sums from an arithmetic series.

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    Type(s):
  • Muddled trig
     (1)

    A matching activity involve trigonometric graphs.

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    Type(s):
  • Nested Surds
     (1)

    A rich task to explore surds.

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    Type(s):
  • Newton's first law conceptual worksheet
     (1)

    Questions on Newton's first law.

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    Type(s):
  • Newton's first law conceptual worksheet
     (1)

    Questions on Newton's first law.

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    Type(s):
  • Newton's first law of motion
     (1)

    Video explaining Newton's first law of motion.

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    Type(s):
  • Newton's laws of motion
     (1)

    A sheet for summarising and testing knowledge of Newton's laws of motion.

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    Type(s):
  • Newton's second law
     (1)

    Video explaining Newton's second law.

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    Type(s):
  • Newton's third law activities
     (1)

    Discussion points for making sense of Newton's third law.

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    Type(s):
  • Newton's third law of motion
     (1)

    Lesson ideas and practical activities for exploring Newton's third law.

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    Type(s):
  • Newton's third law of motion
     (1)

    Examples and exercises

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    Type(s):
  • Newton's third law of motion
     (1)

    Overview video.

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    Type(s):
  • Newton, Leibniz, and Usain Bolt
     (2)

    An introductory video about some of the concepts underlying calculus.

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    Type(s):
  • Normal distribution matching activity
     (1)

    A card sort activity where students match questions to graphs and solutions.

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    Type(s):
  • Normal distribution question sheets
     (2)

    A set of contextual normal distribution questions with answers.

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    Type(s):
  • Normal distributions worksheet
     (1)

    A worksheet including a range of normal distribution questions.

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    Type(s):
  • Numerical Methods
     (1)

    Numerical methods exam questions and slides.

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    Type(s):
  • Numerical Methods
     (1)

    Brief notes and examples for location of roots, iterative procedures, cobweb diagrams and staircase diagrams.

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    Type(s):