A worksheet on evaluating the limit of a polynomial at infinity. The exercises aim to teach students that in order to find the limit of such functions you consider the term in which the variable has the highest degree and how to find the limit using the graph of the function. Detailed solutions are provided.

Master evaluating limits at infinity with this comprehensive, no-prep calculus maths worksheet pack featuring polynomial functions. Designed specifically for A-Level Mathematics, Further Maths, and advanced secondary calculus lessons, this print-and-go resource pack contains both algebraic calculations and graphical end behaviour analysis. 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 at Infinity?
In calculus, a limit at infinity examines the end behaviour of a function as the input variable increases or decreases without bound (as x approaches positive or negative infinity). Evaluating these limits for polynomial functions allows pupils to determine whether the graph rises or falls on its far ends. Mastering this skill is a crucial prerequisite for understanding curve sketching, global function behaviour, and horizontal asymptotes.

What is Included in This Resource Pack:
• Constant & Monomial Questions – Foundational evaluation practice focusing on constant functions and single-variable power terms as x approaches positive or negative infinity.
• Multi-Term Polynomials – Core calculation problems requiring pupils to identify the dominant leading term to evaluate complex cubic, quartic, and higher-degree functions.
• Graphical Analysis Problems – Visual questions where pupils study a printed function graph to determine its exact behaviour on the far left and far right ends of the coordinate plane.
• Complete Step-by-Step Solutions Guide – A full, line-by-line worked math answers section showcasing the exact phase of isolation, leading coefficient behaviour, and final infinite outcomes 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 basic constants to multi-term equations and graphical representations.
• 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.