11th Grade Calculus Resources

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Calculus worksheet with QR code to a video explanation. Worked solutions are included.

This uses finding derivatives of functions to find maximum and minimum points in the context of practical problems.

For example, a manufacturer wants a cardboard box to have volume of 500 cm^3 but wants to minimise the amount of cardboard used.

PowerPoint with an example

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Differentiation from first principles

Calculus - Derivative Treasure Hunt (Scavenger Hunt)

Calculus Gradient Match - Card sort activity

Calculus - Differentiating using the chain rule Treasure Hunt (Scavenger Hunt)

Calculus - Algebra - Differentiation - Exploring Graphs

Applying integration to the motion of a particle in a straight line.

Worked solutions are included.

This follows on from

Contextual Applications of differentiation - motion in a straight line

Use this Treasure / Scavenger Hunt to practice differentiating logarithms and exponentials. Also practices the product rule, quotient rule, chain rule and rules of logarithms

Instructions

• Print off the twenty question pages and put them up around the room
• Each question is in the middle of the page and the solution is at the top of another page.
• Answers are correct to two decimal places where appropriate
• A student begins on a given question, solves it and finds the answer on another sheet. The question on this sheet will be the next question they answer. Once they have answered all twenty, they will return to their starting question
• Depending on numbers, students can all start on different questions
• There is a student answer sheet included plus the correct sequence

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Differentiation from first principles

Derivatives of powers of x Scavenger Hunt

Calculus Gradient Match card sort

Calculus - Exploring graphs

Calculus - Differentiation using the chain rule Scavenger Hunt

Calculus - Optimization using differentiation

Worksheet on implicit differentiation

Include questions on finding gradients, the equations of tangents and normals and finding stationary points.

Worked solutions included for ease with marking and/or sharing with students.

College Board Unit 3.2 Implicit Differentiation

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Differentiation from first principles

Derivatives of powers of x Scavenger Hunt

Calculus Gradient Match card sort

Calculus - Exploring graphs

Calculus - Differentiation using the chain rule Scavenger Hunt

Calculus - Optimization using differentiation

Scavenger Hunt - Differentiating logarithms and exponentials

Calculus - Contextual applications of differentiation - motion in a straight line

Calculus - Contextual applications of integration - motion in a straight line

Calculus - Differentiation - The Product and Quotient Rules

Calculus - Differentiating Inverse Trigonometric Functions

Calculus - Contextual Applications of Differentiation: straight line motion connecting position, velocity and acceleration.

9 questions of increasing difficulty using differentiation to find velocity and acceleration. Also finding maximum/minimum velocities and where a particle changes direction.

Worked solutions are included

No prep lesson for finding the equation of the tangent and normal to a curve using differentiation (Power Rule)

• PowerPoint asking students to sketch a cubic, find the gradient at a point then find the equation of a tangent and a normal
• Question sheet including basic finding the equation of a tangent or normal. More challenging questions involve finding where normals intersect axes and finding areas of triangles.
• Black and white version as well as color version included.
• Worked solutions that can be shared with students to help them review their own work
• All functions of the form ax^n

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

Calculus worksheet on differentiating using the product rule and the quotient rules. Follows on from the chain rule and only looks at expressions involving exponents. I always teach this before I move on to differentiating trigonometric functions, logs and exponentials so I can include more complex expressions.

There are 20 questions which are quite meaty which could be split over two lessons, one for product and one for quotient. There are questions on finding equations of normals and tangents at the end.

A black and white version is included

Worked solutions are included plus a QR code for a video on the Chimp-a-roo Maths You Tube Channel. The video derives the rules from first principles and has an example of each.

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Differentiation from first principles

Derivatives of powers of x Scavenger Hunt

Calculus Gradient Match card sort

Calculus - Exploring graphs

Calculus - Differentiation using the chain rule Scavenger Hunt

Calculus - Optimization using differentiation

Scavenger Hunt - Differentiating logarithms and exponentials

Calculus - Contextual applications of differentiation - motion in a straight line

Calculus - Contextual applications of integration - motion in a straight line

Worksheet for finding the derivatives of inverse trigonometric functions.

Includes a worked example on differentiating arcsin x and then students can show how to get the results for arccos x and arctan x.

Questions then rely on using the chain rule and product rule and increase in difficulty.

Worked solutions are included for ease with marking or to give students to review their own work.

Black and White version also included

College Board Unit 3.4 Differentiating Inverse Trigonometric Functions

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Differentiation from first principles

Derivatives of powers of x Scavenger Hunt

Calculus Gradient Match card sort

Calculus - Exploring graphs

Calculus - Differentiation using the chain rule Scavenger Hunt

Calculus - Optimization using differentiation

Scavenger Hunt - Differentiating logarithms and exponentials

Calculus - Contextual applications of differentiation - motion in a straight line

Calculus - Contextual applications of integration - motion in a straight line

Calculus - Differentiation - The Product and Quotient Rules

Calculus matching activity. There are 12 graphs. 6 are graphs of functions and 6 are graphs of their corresponding gradient. However they have been mixed up.

Student task is to match up the graphs with their gradient function.

Extension task to suggest equations of the graphs. Actual equations are given in the solution however the extension can create some great discussion.

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

You may also like

Differentiation from first principles

Derivatives of powers of x Scavenger Hunt

Calculus - Exploring graphs

Calculus - Differentiation using the chain rule Scavenger Hunt

Calculus - Optimization using differentiation

Scavenger Hunt - Differentiating logarithms and exponentials

Calculus - Contextual applications of differentiation - motion in a straight line

Calculus - Contextual applications of integration - motion in a straight line

Calculus - Differentiation - The Product and Quotient Rules

Calculus - Differentiating Inverse Trigonometric Functions

Calculus - Differentiation - Maximum and Minimum points

This activity is designed to relate calculus and sketching graphs. Using first and second derivatives to find and identify the nature of stationary points.

Students can work in pairs or individually to suit your class.

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

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Calculus - differentiation from first principles

Calculus - Gradient Match card sort activity

Calculus Derivatives of powers of x Treasure Hunt (Scavenger Hunt)

Calculus - Chain Rule Treasure Hunt (Scavenger Hunt)

Calculus - Differentiation from first principles (Defining the derivative of a function) and finding the derivative using the limit definition of the derivative

PowerPoint introducing gradients of chords and worked examples.

Questions on differentiating powers of x from first principles. Increase in difficulty with a juicy proof at the end.

Black and white version included for printing

Answers are included in the form of my worked solutions

QR code for a link to a video explanation

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

You may also like:

Derivatives of powers of x Scavenger Hunt

Calculus Gradient Match card sort

Calculus - Exploring graphs

Calculus - Differentiation using the chain rule Scavenger Hunt

Calculus - Optimization using differentiation

Scavenger Hunt - Differentiating logarithms and exponentials

Calculus - Contextual applications of differentiation - motion in a straight line

Calculus - Contextual applications of integration - motion in a straight line

Calculus - Differentiation - The Product and Quotient Rules

Calculus - Differentiating Inverse Trigonometric Functions

Calculus - Differentiation - Maximum and Minimum points

Two worksheets involving differentiation of trigonometric functions

1. 40 + questions involving chain rule, product and quotient rule. Also finding equations of tangents and normals to trigonometric curves. Worked solutions are included. There is enough to last a couple of lessons
2. Homework sheet with a selection of questions on the topics listed above

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

You may also like

Differentiation from first principles

Derivatives of powers of x Scavenger Hunt

Calculus Gradient Match card sort

Calculus - Exploring graphs

Calculus - Differentiation using the chain rule Scavenger Hunt

Calculus - Optimization using differentiation

Use this Treasure / Scavenger Hunt to practice the chain rule by differentiating, trigonometric functions, logarithms and exponentials.

Instructions

• Print off the twenty question pages and put them up around the room
• Each question is in the middle of the page and the solution is at the top of another page.
• A student begins on a given question, solves it and finds the answer on another sheet. The question on this sheet will be the next question they answer. Once they have answered all twenty, they will return to their starting question
• Depending on numbers, students can all start on different questions
• There is a student answer sheet included plus the correct sequence

A fun activity to keep students moving whilst differentiating using the chain rule. This focuses on functions that are powers of x.

• Print off the twenty question pages and put them up around the room
• Each question is in the middle of the page and the solution is at the top of another page.
• A student begins on a given question, solves it and finds the answer on another sheet. The question on this sheet will be the next question they answer. Once they have answered all twenty, they will return to their starting question
• Depending on numbers, students can all start on different questions
• There is a student answer sheet included plus the correct sequence

This can be used when introducing the chain rule. No knowledge of derivatives of trigonometric functions, exponentials and logarithms needed.

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

You may also like

Derivatives - Powers of x Treasure Hunt

Differentiation from first principles

Calculus - Gradient Match card sort activity

Early Calculus scavenger hunt

A good activity once the topic of differentiating powers of x has been introduced.

Instructions

• Print off the twenty question pages and put them up around the room
• Each question is in the centre of the page and the solution is at the top of another page.
• A student begins on a given question, solves it and finds the answer on another sheet. The question on this sheet will be the next question they answer. Once they have answered all twenty, they will return to their starting question
• Depending on numbers, students can all start on different questions
• There is a student answer sheet included plus the correct sequence

Depending on ability of the group this may take longer than 45 minutes. Good algebraic manipulation will determine the length of time needed.

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

You may also like:

Differentiation from first principles

Calculus Gradient Match card sort

Calculus - Exploring graphs

Calculus - Differentiation using the chain rule Scavenger Hunt

Calculus - Optimization using differentiation

Scavenger Hunt - Differentiating logarithms and exponentials

Calculus - Contextual applications of differentiation - motion in a straight line

Calculus - Contextual applications of integration - motion in a straight line

Calculus - Differentiation - The Product and Quotient Rules

Calculus - Differentiating Inverse Trigonometric Functions

Calculus - Differentiation - Maximum and Minimum points

A no prep lesson practising finding derivatives of powers of x (power rule)

• PowerPoint slide with three examples
• Students will practice (a) Writing expressions in exponent form before differentiating, (b) Multiplying out expressions and using laws of exponents before differentiating (c) Simplifying algebraic fractions and turning expressions into exponent form
• Worksheet 1 - 54 functions to differentiate
• Worksheet 2 - 30 questions similar to first sheet. Ideal for a homework task or revision at a later date.
• B&W and color versions included
• Worked solutions to model answers
• Writing expressions in exponent form before differentiating
• Multiplying out expressions and using laws of exponents before differentiating
• Simplifying algebraic fractions and turning expressions into exponent form

This follows from the following lesson:

Differentiation from First Principles

where students derive the power rule

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

Use this Treasure / Scavenger Hunt after introducing the reverse of differentiation.

These are all definite integrals for powers of x. Some questions need to be rewritten in exponent form and others require some simple algebraic manipulation first.

Instructions

• Print off the twenty question pages and put them up around the room
• Each question is in the middle of the page and the solution is at the top of another page.
• Answers are correct to two decimal places where appropriate
• A student begins on a given question, solves it and finds the answer on another sheet. The question on this sheet will be the next question they answer. Once they have answered all twenty, they will return to their starting question
• Depending on numbers, students can all start on different questions
• There is a student answer sheet included plus the correct sequence

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable, meaning they cannot be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

A worksheet using the first and second derivatives to find stationary points. Mainly maximum and minimum but does have a couple of examples of stationary points of inflection. All curves are functions involving powers of x.

*Points of inflection will be looked at in more detail in an upcoming shapes of curves worksheet/activity.

Answers are included as detailed work solutions.

Black and White version included

College Board Unit

5.4 Using the first derivative test to determine local extrema

5.7 Using the second derivative test to determine extrema

You may also like:

Differentiation from first principles

Derivatives of powers of x Scavenger Hunt

Calculus Gradient Match card sort

Calculus - Exploring graphs

Calculus - Differentiation using the chain rule Scavenger Hunt

Calculus - Optimization using differentiation

Scavenger Hunt - Differentiating logarithms and exponentials

Calculus - Contextual applications of differentiation - motion in a straight line

Calculus - Contextual applications of integration - motion in a straight line

Calculus - Differentiation - The Product and Quotient Rules

Calculus - Differentiating Inverse Trigonometric Functions