Operations with Functions & Domains Worksheet Rational and Radical Practice

A worksheet on adding, subtracting, multiplying and dividing functions and determining the domain of the functions produced. Detailed solutions are included.

Looking for a rigorous Operations with Functions Worksheet that moves past basic arithmetic? This print-and-go practice booklet challenges KS5 Maths and A-Level Mathematics students to add, subtract, multiply, and divide equations while analyzing complex domain restrictions. It covers linear, rational, and radical (square root) functions, forcing students to calculate domain intersections and handle points where functions are undefined. A complete step-by-step teacher answer key is included!

Mastering operations with functions requires a deep structural understanding of overlapping domains. This comprehensive 4-page booklet moves smoothly from basic polynomial operations to complex radical intersections and fractional undefined points.
Whether you need a targeted homework assignment, rigorous cover lessons, a classroom activity, or an intensive exam revision aid, this resource ensures deep concept mastery.

Key Skills & Topics Covered
• Arithmetic Operations: Find clear, simplified formulas for adding, subtracting, multiplying, and dividing expressions.
• Domain Intersections: Determine why certain combined functions are not defined by assessing empty intersection sets.
• Radical Function Restrictions: Analyze square root boundaries to find exactly where combined radical graphs exist.
• Rational Exclusions: Factor denominators and solve for points of discontinuity when computing quotient combinations like f/g and g/f.

What’s Included in the Download
• 1-Page Student Practice Worksheet: Features 6 high-quality, scaffolded multi-part problems.
• 3-Page Detailed Answer Key: Includes complete, line-by-line mathematical layouts and intersection breakdowns for every single problem to save you hours of marking or allow for easy student self-assessment.

Perfect For
• KS5 Maths / A-Level Mathematics (Pure Mathematics modules covering functions and algebra)
• GCSE Further Maths / Advanced GCSE extension groups
• Suitable for all major UK exam boards (Edexcel, AQA, OCR)