Power Rule Differentiation & Curve Gradients Calculus Worksheet with Solutions

Intro to Derivatives, Turning Points & Kinematics Calculus Bundle GCSE 9-1

A collection of 5 worksheets on Calculus based on the GCSE 9-1 specification. In these worksheets students are taught to understand the concept of a variable rate of change, differentiate integer powers of x, determine gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs, distinguish between maxima and minima by considering the general shape of the graph and apply calculus to linear kinematics and to other simple practical problems). Detailed solutions are included. Master differentiation, turning points, and kinematics with this complete calculus worksheet bundle! Perfectly optimized for GCSE Further Maths, IGCSE, and AS-Level Pure Mathematics revision, this print-and-go pack covers the power rule, curve gradients, velocity, and acceleration with full step-by-step worked solutions. ________________________________________ Looking for a rigorous, print-and-go resource to help your secondary and sixth-form students master the fundamentals of calculus? This GCSE 9-1 & AS-Level Introduction to Calculus & Kinematics Bundle contains a comprehensive set of structured practice problems designed to build fluency and algebraic confidence. Moving from basic power rule applications to multi-step particle motion and stationary point proofs, this resource is perfect for formal classroom lessons, independent exam revision, structured homework assignments, cover work, or university preparation! Every question includes an uncrowded, student-friendly layout and comes paired with a complete, step-by-step worked solution key showing every single algebraic step, index law conversion, and derivative rule required to find the final answers. ________________________________________ **What's Included in This Practice Pack?** • **The Power Rule & Index Laws:** Extended practice differentiating standard polynomials alongside functions requiring manipulation of negative and fractional indices (e.g., handling variables in denominators or under radicals). • **Gradients of Curves:** Calculating the exact gradient of a curve at a specified coordinate point, or finding coordinates matching a given slope value. • **Stationary Points (Turning Points)**: Solving equations where the rate of change is zero (dy/dx = 0) to locate turning point coordinates, alongside identifying maximum or minimum turning states. • **Calculus Kinematics (Particle Motion):** Multi-step contextual problems analyzing position/displacement equations to derive velocity (v = ds/dt) and acceleration (a = dv/dt) expressions, including solving for exact displacement and time criteria. ________________________________________ **Perfect For:** • GCSE Further Maths / IGCSE Additional Maths: High-tier extension work and rigorous preparation for upper-level secondary exams. • AS-Level Mathematics (Year 12): Targeted Pure Maths and Mechanics practice for students laying down foundational calculus skills. • Cover Lessons & Homework: Structured, self-explanatory layout that requires zero preparation from you or a cover teacher. ________________________________________