Non-linear relationships & functions
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Focus areas in this topic
Stage 5: Functions and other graphs (Path) · Stage 5: Non-linear relationships A · Stage 5: Non-linear relationships B · Stage 5: Non-linear relationships C (Path) · Mathematics Advanced 11–12 – Year 11: Exponential and logarithmic functions · Mathematics Advanced 11–12 – Year 11: Graph transformations · Mathematics Advanced 11–12 – Year 11: Working with functions · Mathematics Advanced 11–12 – Year 12: Further graph transformations and modelling · Mathematics Extension 1 11–12 – Year 11: Further work with functions · Mathematics Extension 1 11–12 – Year 12: Inverse trigonometric functions
Stage 4 (Year 7, 8)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
- PhET Function BuilderUse it for: Input-output machines for writing rules and functions.
Stage 5 (Year 9, 10)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
- Mathigon: Exponential decay and carbon datingUse it for: Real-world exponential decay context for extension.
- Interactive toolStarterMathigon: Quadratic equationsUse it for: Visual introduction to parabolas and solving quadratics.
- Interactive toolStarterMaths Is Fun: Domain and rangeUse it for: Domain and range explained with examples.
- Interactive toolStarterMaths Is Fun: Equation of a circleUse it for: Derives x² + y² = r² from Pythagoras, with an interactive.
- Interactive toolStarterMaths Is Fun: Exponential growth and decayUse it for: Real-world exponential growth and decay explained.
- Interactive toolStarterMaths Is Fun: Graphing quadratic equationsUse it for: How to sketch parabolas from intercepts and vertex.
- Interactive toolStarterMaths Is Fun: What is a function?Use it for: Functions vs relations explained with mapping diagrams.
- Interactive toolDrillMathsisfun: Function grapherUse it for: Plot functions quickly.
- PhET Function BuilderUse it for: Input-output machines for writing rules and functions.
- PhET Graphing QuadraticsUse it for: See how coefficients change a parabola and locate the vertex.
- Corbettmaths practice questions: Algebra: equation of a circleUse it for: Free printable graded practice questions (with answers) on algebra: equation of a circle for drill or a quick check.
- Corbettmaths practice questions: Composite functionsUse it for: Free printable graded practice questions (with answers) on composite functions for drill or a quick check.
- Corbettmaths practice questions: Function MachinesUse it for: Free printable graded practice questions (with answers) on function machines for drill or a quick check.
- Corbettmaths practice questions: Inequalities: graphical y>x+aUse it for: Free printable graded practice questions (with answers) on inequalities: graphical y>x+a for drill or a quick check.
- Corbettmaths practice questions: Quadratic graphs: drawingUse it for: Free printable graded practice questions (with answers) on quadratic graphs: drawing for drill or a quick check.
- Corbettmaths practice questions: Quadratic graphs: finding turning pointUse it for: Free printable graded practice questions (with answers) on quadratic graphs: finding turning point for drill or a quick check.
- Corbettmaths practice questions: Types of graph: cubicsUse it for: Free printable graded practice questions (with answers) on types of graph: cubics for drill or a quick check.
- Corbettmaths practice questions: Types of graph: exponentialUse it for: Free printable graded practice questions (with answers) on types of graph: exponential for drill or a quick check.
- Corbettmaths practice questions: Types of graph: reciprocalUse it for: Free printable graded practice questions (with answers) on types of graph: reciprocal for drill or a quick check.
- WorksheetDrillKuta free worksheet: Equations of circlesUse it for: Printable skills-practice sheet with answer key on equations of circles; good for drill or homework.
- WorksheetDrillKuta free worksheet: Evaluating and graphing functionsUse it for: Printable skills-practice sheet with answer key on evaluating and graphing functions; good for drill or homework.
- WorksheetDrillKuta free worksheet: Evaluating functionsUse it for: Printable skills-practice sheet with answer key on evaluating functions; good for drill or homework.
- WorksheetDrillKuta free worksheet: Exponential functions and graphsUse it for: Printable skills-practice sheet with answer key on exponential functions and graphs; good for drill or homework.
- WorksheetDrillKuta free worksheet: Graphing circlesUse it for: Printable skills-practice sheet with answer key on graphing circles; good for drill or homework.
- WorksheetDrillKuta free worksheet: Graphing hyperbolasUse it for: Printable skills-practice sheet with answer key on graphing hyperbolas; good for drill or homework.
- WorksheetDrillKuta free worksheet: Graphing linear inequalitiesUse it for: Printable skills-practice sheet with answer key on graphing linear inequalities; good for drill or homework.
- WorksheetDrillKuta free worksheet: Line-parabola/circle intersectionsUse it for: Printable skills-practice sheet with answer key on line-parabola/circle intersections; good for drill or homework.
- WorksheetDrillKuta free worksheet: Properties of parabolasUse it for: Printable skills-practice sheet with answer key on properties of parabolas; good for drill or homework.
- NRICH: Parabolic PatternsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- NRICH: Quadratic PatternsUse it for: Low-floor, high-ceiling NRICH task extending this dot point; use for extension or a problem-solving lesson.
- VideoStarterCorbettmaths video: Algebra: equation of a circleUse it for: Short worked-example video on algebra: equation of a circle to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Composite functionsUse it for: Short worked-example video on composite functions to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Function MachinesUse it for: Short worked-example video on function machines to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Inequalities: graphical y>x+aUse it for: Short worked-example video on inequalities: graphical y>x+a to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Inequalities: regionsUse it for: Short worked-example video on inequalities: regions to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Quadratic graphs: drawingUse it for: Short worked-example video on quadratic graphs: drawing to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Quadratic graphs: finding turning pointUse it for: Short worked-example video on quadratic graphs: finding turning point to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Quadratic graphs: line of symmetryUse it for: Short worked-example video on quadratic graphs: line of symmetry to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Quadratic graphs: sketching using key pointsUse it for: Short worked-example video on quadratic graphs: sketching using key points to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Simultaneous equations (advanced)Use it for: Short worked-example video on simultaneous equations (advanced) to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Types of graph: cubicsUse it for: Short worked-example video on types of graph: cubics to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Types of graph: exponentialUse it for: Short worked-example video on types of graph: exponential to model the method before practice or for flipped revision.
- VideoStarterCorbettmaths video: Types of graph: reciprocalUse it for: Short worked-example video on types of graph: reciprocal to model the method before practice or for flipped revision.
- Unit/PlanningStage 5 Unit 11 – applying exponentials (sample unit of learning)
- Unit/PlanningStage 5 Unit 12 – investigating parabolas (sample unit of learning)
- Unit/PlanningStage 5 Unit 9 – surveying (sample unit of learning)
- Unit/PlanningStage 5 Year 10 – maths in science elective (sample unit of learning)
Standard Year 11 (Year 11)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Advanced Year 11 (Year 11)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Standard Year 12 (Year 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Extension 1 (Year 11, 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Advanced Year 12 (Year 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.
Extension 2 (Year 12)
- Desmos Graphing CalculatorUse it for: Graph lines, parabolas and exponentials live; find intersections to solve simultaneous equations.
- Interactive toolEnrichmentGeoGebra ClassicUse it for: Dynamic geometry and graphing for constructions and proofs.