A worksheet on examining whether a function is one-to-one, given its equation, mapping diagram, set of ordered pairs or graph. Detailed solutions are included.

Looking for a comprehensive One-to-One Functions Worksheet to master multiple mathematical representations? This print-and-go practice booklet challenges KS5 Maths and A-Level Mathematics students to identify injective relationships using ordered pairs, algebraic equations, and arrow mapping diagrams. It features extensive practice utilizing the Horizontal Line 91¶¶Òõt across quadratic, cubic, and rational graphs. A complete 6-page step-by-step teacher answer key is included!

Mastering the structural boundaries of one-to-one functions is vital before students move on to inverse operations and advanced calculus modules. This comprehensive 9-page booklet smoothly bridges the gap between discrete coordinate data sets, conceptual visual arrow diagrams, and continuous graph equations.
Whether you need a targeted homework task, clear cover lesson plans, an entry check, or an end-of-unit revision tool, this multi-method practice resource saves hours of secondary maths preparation.

Key Skills & Topics Covered
• Algebraic Proofs: Prove or disprove one-to-one parameters from linear, quadratic, cubic, and literal equations using formal algebraic steps.
• Discrete Coordinate Sets: Scan sets of ordered pairs to verify distinct range mappings and identify duplicated outputs.
• Visual Mapping Diagrams: Track numerical paths through structural arrow domains to locate duplicated outputs.
• Horizontal Line 91¶¶Òõt: Analyze 6 different graph configurations (parabolas, cubics, polynomials, hyperbola curves) to pinpoint exact coordinate intersection points.

What’s Included in the Download
• 3-Page Student Practice Worksheet: Features clean spacing and crisp, uncrowded graph plots for direct student markings and sketches.
• 6-Page Detailed Answer Key: Includes full line-by-line algebraic explanations and graphical callouts to show exactly why a function passes or fails the horizontal line test.

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