Alevel Maths elibrary
In this section, you will find resources that will support your teaching of our Alevel Maths specification, including resources for AS.
Use the menu links on the lefthand side to find resources for a particular topic.

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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Absurd!♥ (12)
An activity on rationalising denominators.
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Acceleration due to gravity♥ (1)
Strobe image showing a ball falling allowing students to see acceleration due to gravity.
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Addition formulae♥ (1)
Worksheets for practising the addition formulae.
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Additional integrals♥ (2)
Rich task looking at combinations of definite integrals.
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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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Analysing scatter plots♥ (3)
Notes and exercises (using US vocabulary) on scatter graphs, including identifying outliers.
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Antiderivative worksheet♥ (1)
Simple worksheet for thinking about antiderivatives.
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Antiderivatives and indefinite integrals
Examples and exercises.
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AP proof sorter♥ (3)
This is a selfchecking 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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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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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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Basics of vectors
Worksheet using Cartesian components.
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Become friends with logarithms
Mixed exercises using logs.
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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 3digit code.
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Binomial expansion questions♥ (1)
Fluency practice for binomial expansions.
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Binomial expansion worksheets♥ (1)
Notes, examples and a summary activity for binomial expansions where n is negative or a noninteger.
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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 cardbased puzzle for binomial distribution.
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Breaking Strain♥ (1)
Contextual activity for resolving forces.
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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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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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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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Can you find... trigonometry edition♥ (1)
Activity for combined transformations of sine graphs
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Can you find… chain rule edition♥ (1)
A rich task finding functions to meet certain criteria.
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Cartesian components of vectors♥ (1)
Notes and exercises on writing vectors in Cartesian component form
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Cartesian components of vectors 2
Notes and exercises on writing vectors in Cartesian component form.
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Cartesian components of vectors powerpoint
Slides giving an introduction of i and j components in vectors.
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Census or sample?
An activity looking at types of sampling and sample size.
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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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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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Change one thing
Rich task exploring arithmetic sequences.
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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.
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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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Composite and inverse functions
Worksheets on composite and inverse functions.
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Conditional probability puzzler
Scaffolded tree diagram activity.
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Constant acceleration equations♥ (1)
Notes, examples and exercises.
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Coordinate Geometry Group Cards♥ (1)
Tasks for solving linear graph problems.
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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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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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Currency
A geometric progression activity involving logs.
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Curve Match
Rich task for thinking about curve sketches.
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Data types and sampling methods
A gap fill on data collection and sampling
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Defining vectors
Activity for developing fluency in vector addition.
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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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Describing motion with words
Notes and examples on the vocabulary of kinematics.
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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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Differential equations textbook chapter
Textbook chapter with detailed explanations.
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Differentiating logarithmic and exponential functions
Notes on differentiating e and ln from first principles.
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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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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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Differentiation revision
Mixed worksheet on differentiation.
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Differentiation worksheets
Worksheets to practice basic differentiation.
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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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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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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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Evaluating Statements about Radicals
Always, sometimes, never activity.
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Ever wondered why?♥ (2)
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'
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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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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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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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First steps into differentiation♥ (1)
An IT task investigating gradient.
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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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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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Graph transforms♥ (1)
Activities for developing fluency in graph transformations.
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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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Graphing exponential functions
Notes and practice problems for drawing exponential graphs.
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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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Guessing correlations game
Online game looking at correlation coefficients.
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Haircut Costs
A box plot comparison activity.
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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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Hit the spot♥ (2)
Rich task involving magnitude, direction and Cartesian component form.
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How Far Did the Earth Move?
Task using logs to model magnitude and energy.
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Hypothesis testing♥ (1)
Notes and example including testing for the sample mean.
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Hypothesis testing
Notes and examples on how to conduct hypothesis tests.
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Hypothesis testing for the binomial distribution
Video explaining how to conduct binomial hypothesis tests.
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Hypothesis testing topic mat
Template to complete the stages of hypothesis testing.
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Hypothesis testing using the binomial distribution
Geogebra tool for binomial hypothesis tests.
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Hypothesis testing worksheets
Worksheets including binomial testing.
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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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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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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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Identifying outliers
Task involving constructing a box plot and considering outliers.
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Implicit circles
Task looking at various approaches for finding the gradient of a circle.
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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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Increasing and decreasing functions
Worksheets looking at increasing and decreasing functions.
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Increasing, decreasing and not monotonic sequences
Video explaining the different types of sequence.
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Indefinite integration
Examples, worksheets and activities on indefinite integration.
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Indefinite integration
Examples, worksheets and activities on indefinite integration.
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Independence, dependence, mutually exclusive or not?
Worksheet using set notation to look at independence and related concepts.
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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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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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Inequalities
Examples and exercises for linear, quadratic and graphical inequalities.
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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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Inequations: Regions
Fluency practice for graphical inequalities.
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Integral chasing
Rich task for developing fluency in definite integration.
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Integral sorting
Card match activity for integration by substitution.
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Integrating algebraic fractions
Notes and exercises for integrating with partial fractions
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Integrating basic functions
Worksheet for practising integration
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Integration
Slides and worksheet for area under curve.
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Integration
Slides introducing integration.
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Integration by parts
Integration by parts questions.
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Integration by substitution
Integration questions that require substitution.
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International System of Units (SI)
Website defining the SI base units and providing information about their historical context.
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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 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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Introduction to algebra♥ (1)
Fluency exercise for simplifying algebra.
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Introduction to series
Straightforward worksheet on sigma notation, to develop fluency.
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Introduction to vectors
Notes, examples and worksheets on component vectors.
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Inverse functions notes and solutions
Lecture notes and exercises for inverse functions.
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Inverse trignometric functions
Simple worksheet for developing fluency in inverse trigonometric functions.
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Inverse, composite, domain and range of functions
Gap fill activity designed for pairs or groups
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Is the gradient function increasing or decreasing on this curve?
Task looking at where functions are increasing and decreasing .
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Is the Serpentine Lake really 40m acres?
Approximation task linked to introducing calculus.
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Is the Serpentine Lake really 40m?
Rich task looking at approximating areas.
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Iteration♥ (2)
Video on how to solve an equation using iteration.
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Iteration♥ (1)
Slides and activities for iteration.
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Iteration♥ (4)
Slides and activities for iteration.
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Kangaroo lovers
A activity to explore the sum to infinity of convergent geometric progressions.
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Kinematics workbook
Comprehensive workbook containing a wide range of questions on topics in kinematics.
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Kinematics: describing motion
Notes and examples on the vocabulary of kinematics.
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Laws of Logarithms
Matching activity for log laws.
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Least squares regression simulation
Online interactive tool for exploring least squares regression.
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Linear equations and Mr Venn♥ (1)
Rich task for classifying equations of straight lines.
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Linear Functions
Rich tasks for linear graphs.
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Linearising Data
Textbook chapter with investigations and exercises.
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Linking the properties and forms of quadratic functions
Card sort for quadratic functions.
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Logarithm dominoes  simplifying logs
Matching activity involving log laws.
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Logarithm lattice♥ (1)
Rich task sorting log expressions by size
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Logarithm worksheets
Log law worksheets to develop fluency.
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Logarithmic equations maze activity
Fun worksheets for solving equations using logs and ln.
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Magnitude and angle of the resultant force
Overview video.
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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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Make it stop!
Rich task involving applying forces to particles.
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Make it stop!
Rich task involving applying forces to particles.
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Making predictions and reliability of predicted values
Video on using regression lines.
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Making sense of differentiation
Notes and exercises for introducing calculus.
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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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Manipulating Surds
Card sort, dominoes and exercises for simplifying surds.
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Matching differential equations to descriptions
Card match activity in which students match descriptions to equations.
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Mathematical Modelling
Teacher package of articles and lesson ideas.
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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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Meaningful areas
Task looking at the area between two curves.
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Mechanics 1 PowerPoints
A set of PowerPoints including one on vectors for mechanics which includes magnitude/direction form.
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Mechanics 1 Videos
A set of videos including vectors.
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Mechanics PowerPoint♥ (1)
PowerPoint and workbook for mechanics topics.
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Methods of sampling♥ (1)
A series of activities on sampling methods.
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Modulus always, sometimes, never♥ (1)
Activity in which students classify statements about modulus graphs and transformations.
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Modulus function worksheets♥ (1)
Worksheets for Modulus equations, inequalities, graphs and transformations.
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Moments♥ (1)
Moments puzzle challenge.
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Moments revision sheet and problems♥ (1)
A set of problems on moments.
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Moments worksheets♥ (1)
Worksheets and examples for moments.
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Money matters♥ (1)
Contextual worksheet to practise calculating terms and sums from an arithmetic series.
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Muddled trig♥ (1)
A matching activity involve trigonometric graphs.
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Nested Surds♥ (1)
A rich task to explore surds.
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Newton's first law conceptual worksheet♥ (1)
Questions on Newton's first law.
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Newton's first law conceptual worksheet♥ (1)
Questions on Newton's first law.
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Newton's first law of motion♥ (1)
Video explaining Newton's first law of motion.
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Newton's laws of motion♥ (1)
A sheet for summarising and testing knowledge of Newton's laws of motion.
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Newton's second law♥ (1)
Video explaining Newton's second law.
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Newton's third law activities♥ (1)
Discussion points for making sense of Newton's third law.
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Newton's third law of motion♥ (1)
Lesson ideas and practical activities for exploring Newton's third law.
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Newton's third law of motion♥ (1)
Examples and exercises
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Newton's third law of motion♥ (1)
Overview video.
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Newton, Leibniz, and Usain Bolt♥ (2)
An introductory video about some of the concepts underlying calculus.
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Normal distribution matching activity♥ (1)
A card sort activity where students match questions to graphs and solutions.
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Normal distribution question sheets♥ (2)
A set of contextual normal distribution questions with answers.
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Normal distributions worksheet♥ (1)
A worksheet including a range of normal distribution questions.
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Numerical Methods♥ (1)
Numerical methods exam questions and slides.
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Numerical Methods♥ (1)
Brief notes and examples for location of roots, iterative procedures, cobweb diagrams and staircase diagrams.
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