# Calculus Practice

Practice questions

This page has a variety of tasks designed for practise and revision. Practice questions are an important part consolidating students' understanding of a concept. They can be found from numerous sources and the following is not intended as a 'fix all' solution. Most teachers appreciate that questions gathered from numerous different sources make the best diet!

### Worksheets

Below are links to a series of focussed worksheets for this topic. The worksheets consist largely of 'Practise Questions' but most finish with more open ended questions to extend. Ultimately, students need to be able to answer questions from a variety of topics and contexts, but often it is necessary to spend some time focussing on particular skills whilst still in the process of learning them. The worksheets are clearly titled according to the particular sub-topic and come complete with answers.

**The Concept**

Concept of Calculus - Practise using the concept and terminology associated with functions. answers

Deriving 1 - Application of general formula without negative powers. answers

Deriving 2 - Application of general formula including negative powers. answers

Differentiating puzzle - This is one of the well known 'Tarsia' puzzles that is ideal for engaging students in practising how to differentiate expressions including negative indices. It is quite challenging so some clues at the ready might be useful. Here are the solutions.

Gradients at a given point - Calculating the value of gradients at a given point by differentiating and substituting. answers

Tangents and Normals - Practise using the process of finding their equations with and without calculators answers

### Revision Notes

This is a series of 'Fill in the Gaps' notes that I have created to help students keep useful records of the course. The rationale is explained in more detail on the 'Exams and Revision pages. Essentially the aim is bridge the gap between Students making their own notes on a blank canvas and being given detailed notes that they did not create.

1 - Concept 1 - **Syllabus ref*** 7.1*, Calculus as rate of change

2 - Differentiating Polynomials * Syllabus ref 7.2*, applying the general formula with positive and negative indices.

3-Gradients, tangents and normals Syllabus ref 7.3, exploring the process behind finding gradients, tangents and normals at a given point. Students are given the elements of the process jumbled up and asked to put them together in a coherent manner. In doing so they will have to revisit all of the key ideas.

4 Increasing and Decreasing functions (* New* 7.4,

*7.4)*

**Previous**5 - f'(x) = 0 Syllabus reference 7.5 about recognising and finding the points on a function where the gradient = 0.

6 - Optimisation Optimisation problems (* New* 7.6,

*7.5)*

**Previous**IB style questions

Here are some exam style questions on the topic of Calculus for students to practice with.

Calculus concept - These questions test the basic ideas behind the calculus topic. Ten questions and 80 marks. Here are the solutions.

Calculus - Tangents and Normals Ten questions worth 80 marks on tangents and normals. The solutions.

Calculus - Optimisation Ten questions worth 110 marks on optimisation. Here are the solutions.

Calculus - General - This is a set of general questions on the Calculus topic that make for a challenging summary of the unit. Here are the solutions.

### Errors - an appeal to users!

Few are infallible and we have all experienced frustration in finding errors in shiny new textbooks that we have just paid lots of money for! The advantage of online resources should be that as soon as errors are found they can be pointed out and corrected! When you find errors, please accept my apologies for the inevitable frustration it can cause but please also **tell me as soon as you can on jamesn@inthinking.co.uk** so that I can correct it as soon as possible! Thank you!

## Comments 10

Grant Fossum22 February 2018 - 13:36Two of the Calculus notes sheets are missing. Optimization and Increasing/Decreasing

Rosa Carbajal27 February 2018 - 06:01The solutions to Calculus - Optimisation are missing. Will they be posted soon?

Jon Datta1 March 2018 - 16:24Same question

Jim Noble27 February 2018 - 17:21Hi Grant, I have just added those two calculus notes sheets!

Rosa, sorry, I don't have those just yet. I will need them for my own students in the next couple of weeks though.... so hopefully I'll be able to post them soon.

Jim Noble5 March 2018 - 18:14OK, working on some solutions - will put them up soon.....

Jim Noble6 March 2018 - 08:37Rosa, Jon, I have added a set of solutions to the optimisation questions. I corrected a couple of errors I found in the questions along the way. Apologies for those.

Grant Fossum8 March 2018 - 15:57On Calculus Optimization, I found the following possible corrections.

Problem # 3 says to take x= 2cm because it was the only one in the "range" you actually get x=2 and x=6 as solutions, both of which fit in the domain, so not sure you could discount one without a sign diagram etc?

Problem #4a a should equal 8 not 3.

Grant Fossum8 March 2018 - 16:10Sorry a couple more questions, on # 5, since we have points and not arrows shouldn't decrease be .8
And on number 6d I think the max and min are mixed up.

Jim Noble8 March 2018 - 20:07Thanks Grant - its first on my list for tomorrow to check it out

Jim Noble9 March 2018 - 11:13Thanks so much for time taken to point that out Grant. I have made the corrections, Jim

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