A worksheet on evaluating the limit of a polynomial or rational function. The exercises aim to teach students that in order to find the limit of such functions you substitute the value of the limit and in the cases where the denominator is zero you simplify the function if possible and then substitute. Detailed solutions are provided.

Master evaluating limits algebraically with this comprehensive, no-prep calculus maths worksheet pack featuring polynomial and rational functions. Designed specifically for A-Level Mathematics, Further Maths, and advanced secondary calculus lessons, this print-and-go resource pack contains 16 progressive practice problems. A complete, step-by-step worked solutions guide is included for every question to entirely eliminate your marking time and provide easy diagnostic scoring.

What is a Limit in Calculus?
In calculus, a limit is the fundamental value that a function approaches as the input variable gets closer and closer to a specific number. Evaluating limits algebraically allows pupils to analyze the behavior of a function near a given point—even when the function is undefined or results in an indeterminate form (like zero divided by zero) at that exact value. Mastering this skill is a crucial prerequisite for understanding derivatives and integration.

What is Included in This Resource Pack:
• Direct Substitution Questions (1–8) – Core calculation practices focusing on finding the limit of polynomials and basic rational functions where the denominator does not equal zero.
• Indeterminate Forms & Factoring (9–14) – Challenging problems requiring pupils to factorise quadratics and difference of cubes expressions to cancel common factors and resolve 0/0 indeterminate forms.
• Greatest Common Factor Limits (15–16) – Advanced rational function expressions requiring pupils to factorise out x to evaluate the limit successfully as x approaches zero.
• Complete Step-by-Step Solutions Guide – A full, line-by-line worked math answers section showcasing every single algebraic phase, factorisation step, and final substitution for easy student self-correction or quick marking.

Why Secondary Maths Teachers Love This Pack:
• Zero Planning Required: Simply download the high-quality PDF files, print the ready-made worksheets, and hand them directly to your class.
• Scaffolded Learning Flow: Problems naturally build in difficulty—moving from simple polynomials to complex rational expressions requiring advanced factoring.
• Versatile Classroom Implementation: An ideal choice for independent homework packs, classroom maths starter activities, sixth-form revision folders, early finishers, or end-of-unit exam preparation.