Non-linear relationships C (Path)
Mathematics K–10 (2022) · Stage 5 · View this focus area on the NESA NSW Curriculum website ↗
Outcomes
MA5-NLI-P-01 interprets and compares non-linear relationships and their transformations, both algebraically and graphically (Path: Adv)Content dot points
Each dot point has its own page with resources matched to it.
Graph parabolas and describe their features and transformations
- Use graphing applications to compare parabolas of the form y = (kx)², y = (kx)² + c,y = k(x - b)² and y = k(x - b)² + c, and describe their features and transformations 4 resources · 3 interactive/game
- Find x- and y-intercepts algebraically, where appropriate, for the graph of y = (ax)² + bx + c, given a,b and c 1 resource · 1 interactive/game
- Determine the equation of the axis of symmetry of a parabola using either the formula x = - b/(2a) or the midpoint of the x-intercepts 2 resources
- Find the coordinates of a parabola’s vertex using a variety of methods 4 resources · 1 interactive/game
- Graph quadratic relationships of the form y = (ax)² + bx + c by identifying and applying features of parabolas and their equations without graphing software 4 resources · 3 interactive/game
Graph exponentials and describe their features and transformations
- Use graphing applications to graph exponential relationships of the form y = k(a)^x + c and y = k(a)^(- x) + cfor integer values of k, a and c (where a > 0 and a≠1), and compare and describe any relevant features 2 resources · 2 interactive/game
Graph hyperbolas and describe their features and transformations
- Use graphing applications to graph, compare and describe hyperbolic relationships of the form y = k/x for integer values of k 4 resources · 2 interactive/game
- Use graphing applications to graph and describe a variety of hyperbolas, including where the equation is given in the form y = k/x + c or y = k/(x - b) for integer values of k,b and c 3 resources · 2 interactive/game
Graph circles and describe their features and transformations
- Derive the equation of a circle x² + y² = r² with centre (0,0) and radius r using the distance formula 3 resources · 1 interactive/game
- Identify and describe equations that represent circles with centre at the origin and radius of the circle r 2 resources
- Graph circles of the form x² + y² = r², where r is the radius of the circle using graphing applications 3 resources · 2 interactive/game
- Establish the equation of the circle with centre (a,b) and radius r, and graph equations of the form (x - a)² + (y - b)² = r² 2 resources · 1 interactive/game
- Find the centre and radius of a circle with the equation in the form x² + y² + ax + by + c = 0 by completing the square 2 resources · 1 interactive/game
Distinguish between different types of graphs by examining their algebraic and graphical representations and solve problems
- Identify and describe features of different types of graphs based on their equations
- Identify a possible equation from a graph and verify using graphing applications 2 resources · 2 interactive/game
- Find points where a line intersects with a parabola, hyperbola or circle, both graphically and algebraically 2 resources
Graph and compare polynomial curves and describe their features and transformations
- Use graphing applications to graph and compare features of cubic equations of the form y = ax³ + c, where a and c are integers 4 resources · 2 interactive/game
- Use graphing applications to graph a variety of equations of the form y = (kx)ⁿ, where n is an integer and n ≥ 2, and describe the effect on the shape of the curve where n is an odd or an even number 2 resources · 2 interactive/game
- Use graphing applications to graph curves of the form y = (kx)ⁿ + c and y = k(x - b)ⁿ where n is an integer and n ≥ 2, and describe the transformations from y = (kx)ⁿ 2 resources · 2 interactive/game
Focus area resources
- 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)
Stage 5 planning resources
Stage- or course-wide documents (scope and sequences, guides) that cover this focus area alongside others.
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 03)
- Unit/PlanningSample scope and sequence: Stages 4–5 core and selected paths (NESA no. 04)
- Unit/PlanningSample scope and sequence: Stage 5 core and all paths (NESA no. 05)
- Unit/PlanningSample scope and sequence: Stage 5 core (NESA no. 02)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 06)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 01)
- Unit/PlanningSample scope and sequence: Stages 4–5 stage based (NESA no. 08)
- Unit/PlanningStage 5 – sample scope and sequence
- Unit/PlanningStage 5 – stage based – sample scope and sequence