A worksheet on examining whether two given functions are equal by examining their domain and their value at each element of their domain. Detailed solutions are included.

Looking for a rigorous Equal Functions Worksheet that truly tests your students’ algebraic reasoning? This print-and-go practice booklet challenges KS5 Maths and A-Level Mathematics students to determine if functions are mathematically equal by evaluating domain restrictions and simplifying rational expressions. Students will factor polynomials, identify domain exclusions, and find the largest subset where two formulas align. A complete step-by-step teacher answer key is included!

Key Skills & Topics Covered
• Analyzing Rational Functions: Factor quadratic numerators and simplify rational expressions to check for mathematical equivalence.
• Identifying Domain Exclusions: Find restrictions in denominators where an input would make the fraction undefined (removable discontinuities/holes).
• Finding Common Subsets: Determine the largest possible subset of real numbers where two non-equal functions can align.
• Evaluating Discrete Domains: ÌÇÐÄVlogt equality for functions defined only across limited sets of coordinates like {-1, 0, 1}.

What’s Included in the Download
• 2-Page Student Worksheet: Clean layouts with plenty of workspace for students to show their workings.
• 2-Page Detailed Answer Key: Full, line-by-line mathematical 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)