Indices C (Path)
Mathematics K–10 (2022) · Stage 5 · View this focus area on the NESA NSW Curriculum website ↗
Outcomes
MA5-IND-P-02 describes and performs operations with surds and fractional indices (Path: Adv)Content dot points
Each dot point has its own page with resources matched to it.
Describe surds
- Describe a real number as a number that can be represented by a point on the number line
- Examine the differences between rational and irrational numbers and recognise that all rational and irrational numbers are real 4 resources · 1 interactive/game
- Convert between recurring decimals and their fractional form using digital tools 4 resources
- Describe the term surd as referring to irrational expressions of the form n√(x) where x is a rational number and n is an integer such that n ≥ 2, and x > 0 when n is even 2 resources
- Recognise that a surd is an exact value that can be approximated by a rounded decimal
- Demonstrate that √x is undefined for x √x = 0 when x = 0 using digital tools
- Describe √x as the positive square root of x for x > 0 and √0 = 0
Apply knowledge of surds to solve problems
- Establish and apply the following results for x > 0 and y > 0: (√x)² = x = √(x²), √(xy) = √x × √y and √(x/y) = √x/√y 3 resources
- Apply the 4 operations to simplify expressions involving surds 4 resources
- Expand and simplify expressions involving surds 3 resources
- Rationalise the denominators of surds of the form (a√b)/(c√d) 3 resources
Describe and use fractional indices
- Apply index laws to describe fractional indices as: a^(1/n) = n√(a) and a^(m/n) = n√(a^m) = (n√(a))^m 3 resources · 1 interactive/game
- Translate expressions in surd form to expressions in index form and vice versa 2 resources · 1 interactive/game
- Evaluate numerical expressions involving fractional indices including using digital tools 3 resources
Focus area resources
- Unit/PlanningStage 5 Unit 2 – working with triangles (sample unit of learning)
- Unit/PlanningStage 5 Unit 4 – index laws (sample unit of learning)
- Unit/PlanningStage 5 Year 10 – the unit circle 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