Less than $5 10th Grade Calculus Worksheets

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.

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

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

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Calculus - Differentiation - The Product and Quotient Rules

Calculus - Differentiating Inverse Trigonometric Functions

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

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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.

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Differentiation from first principles

Derivatives of powers of x Scavenger Hunt

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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

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

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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

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Calculus - Differentiating Inverse Trigonometric Functions

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.

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

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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

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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