Transum Maths Software

Calculus

There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Calculus. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

Main Page

Calculus Starters:

 

Fence Optimisation: Find the length of a rectangle enclosing the largest possible area.

Maximum Product: Two numbers add up to 10. What's the largest possible product they could have?

Road Connections: Design roads to connect four houses that are on the corners of a square, side of length one mile, to minimise the total length of the roads.

Index of Advanced Starters


Suggested

Integration

Integration

Exercises on indefinite and definite integration of basic algebraic and trigonometric functions.

The short web address is:

Transum.org/go/?to=integration

 

Curriculum for Calculus:

Years 12 and 13

Pupils should be taught to 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, sketching the gradient function for a given curve, second derivatives, differentiation from first principles for small positive integer powers of x and for sin x and cos x. Understand and use the second derivative as the rate of change of gradient; connection to convex and concave sections of curves and points of inflection more...

Pupils should be taught to know and use the Fundamental Theorem of Calculus more...

Pupils should be taught to differentiate xn, for rational values of n, and related constant multiples, sums and differences. Differentiate ekx and akx, sin kx, cos kx, tan kx and related sums, differences and constant multiples. Understand and use the derivative of ln x more...

Pupils should be taught to integrate xn (excluding n = -1) and related sums, differences and constant multiples.
Integrate ekx, 1/x, sin kx , cos kx and related sums, differences and constant multiples more...

Pupils should be taught to apply differentiation to find gradients, tangents, normals, maxima, minima and points of inflection. Identify where functions are increasing or decreasing more...

Pupils should be taught to evaluate definite integrals; use a definite integral to find the area under a curve and the area between two curves more...

Pupils should be taught to differentiate using the product rule, the quotient rule and the chain rule, including problems involving connected rates of change and inverse functions more...

Pupils should be taught to Understand and use integration as the limit of a sum. more...

Pupils should be taught to 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 more...

Pupils should be taught to differentiate simple functions and relations defined implicitly or parametrically, for first derivative only more...

Pupils should be taught to 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) more...

Pupils should be taught to construct simple differential equations in pure mathematics and in context, (contexts may include kinematics, population growth and modelling the relationship between price and demand) more...

Pupils should be taught to integrate using partial fractions that are linear in the denominator more...

Pupils should be taught to 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.) more...

Pupils should be taught to interpret the solution of a differential equation in the context of solving a problem, including identifying limitations of the solution; includes links to kinematics more...

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"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access the whole month so I can use favourites with classes I see at different times of the week. Thanks."

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"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

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"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

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Could we have some on angles too please?"

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Thanks"

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Thanks again"

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"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

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Notes:

It is said that the word calculus comes from the Latin word for the small pebble used for counting and calculations. The two major branches, differentiation and integration, are studied by pupils only towards the end of their school days but does then form a major part of their studies. A course in calculus is a prerequisite for other, more advanced courses in mathematical analysis.

Calculus Activities:

Differentiation: Practise the technique of differentiating polynomials with this self marking exercise.

Integration: Exercises on indefinite and definite integration of basic algebraic and trigonometric functions.

Alternatively, for the more advanced student, there is an ever-growing collection of Exam-Style Questions with worked solutions on the topic of Calculus.

Calculus Videos:

Introduction to Calculus: This video will give you a brief introduction to calculus. It does this by explaining that calculus is the mathematics of change. A couple of examples are presented, and then limits, derivatives, and integrals are introduced.

The Birth Of Calculus: A fascinating BBC Two television programme from 1986. A documentary on Leibniz and the calculus.

Calculus External Links:

Links to other websites containing resources for Calculus are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

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Suggested

Differentiation

Differentiation

Practise the technique of differentiating polynomials with this self marking exercise.

The short web address is:

Transum.org/go/?to=differentiation

 

Homepage

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