Derivatives (First Principles) - Harder - Lesson | GSCE Higher / A-level Maths | PPT+W/S+Answers

This resource is perfect for building on an introduction to derivatives using first principles, making it ideal for extending students and further transitioning from algebra to calculus.

Students will develop confidence in:
• Understanding the concept of a derivative
• Applying first principles step-by-step to higher power problems
• Simplifying algebraic expressions
• Preparing for formal differentiation rules

Resource Overview

This download includes:

• ✔ Teaching PowerPoint presentation (clear explanations and fully worked examples)
• ✔ 2 x Structured worksheets (progressive difficulty – 10 Questions each)
• ✔ Fully worked solutions for each worksheet (step-by-step, not just answers)
• ✔ Clear layout for independent learning
• ✔ No prep – ready to print

Learning Objectives

By the end of this lesson, students will be able to:

Extend their use of the first principles method to cubic and quartic functions

Apply algebraic techniques such as expansion and factorisation within the context of calculus

Develop fluency with complex expressions and algebraic manipulation

Strengthen their conceptual grasp of what differentiation means from a foundational level

Teacher Guidance

The PowerPoint slides are fully editable and animated for classroom delivery

Worksheets are ideal for classwork, homework, or revision

Designed for confident students – this lesson assumes strong prior knowledge of basic differentiation from first principles and algebraic fluency

This resource does not include teacher notes or video instruction. If you are seeking a complete video lesson covering the same topic (with worksheets and solutions included), please browse the full video-based resource available in my TES shop.

File Formats

PowerPoint (.pptx) – fully editable

Worksheets and solutions (PDF) – ready to print or distribute digitally

Related Resources

This is Lesson 2 in the Derivatives from First Principles series. For earlier lessons or a bundled version with video content, please visit my TES shop for the full unit.