Content:
MA5-IND-P-01
Apply index laws to algebraic expressions involving negative-integer indices
- Apply index notation, patterns and index laws to establish a−1=1a, a−2=1a2, a−3=1a3 and a−n=1an
- Represent expressions involving negative-integer indices as expressions involving positive-integer indices and vice versa
- Apply the index laws to simplify algebraic products and quotients involving negative-integer indices
- Describe and use x−1 as the reciprocal of x and generalise this relationship to expressions of the form (ab)−1
- Use knowledge of the reciprocal to simplify expressions of the form (ab)−n
MA5-IND-P-02
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
- Convert between recurring decimals and their fractional form using digital tools
- 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
- Recognise that a surd is an exact value that can be approximated by a rounded decimal
- Demonstrate that √x is undefined for x<0 and that √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 √xy=√x√y
- Apply the 4 operations to simplify expressions involving surds
- Expand and simplify expressions involving surds
- Rationalise the denominators of surds of the form a√bc√d
Describe and use fractional indices
- Apply index laws to describe fractional indices as: a1n=n√a and amn=n√am=(n√a)m
- Translate expressions in surd form to expressions in index form and vice versa
- Evaluate numerical expressions involving fractional indices, including using digital tools