Indices, Standard Form and Surds

Prerequisite Knowledge

• Apply the four operations, including formal written methods, to integers
• Use and interpret algebraic notation
• Count backwards through zero to include negative numbers
• Use negative numbers in context, and calculate intervals across zero

Success Criteria

• Use the concepts and vocabulary of highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem
• Calculate with roots, and with integer and fractional indices
• Calculate with and interpret standard form A x 10n, where 1 ≤ A < 10 and n is an integer.
• Simplify and manipulate algebraic expressions
• Simplifying expressions involving sums, products and powers, including the laws of indices
• Calculate exactly with surds
• Simplify surd expressions involving squares and rationalise denominators

Key Concepts

• To decompose integers into their prime factors students may need to review the definition of a prime.
• A base raised to a power of zero has a value of one.
• Students need to have a secure understanding in the difference between a highest common factor and lowest common multiple.
• Standard index form is a way of writing and calculating with very large and small numbers. A secure understanding of place value is needed to access this.
• Surds are square roots that cannot exactly in fraction form.
• Students need to generalise the rules of indices.

Common Misconceptions

• One is not a prime number since it only has one factor.
• x² is often incorrectly taken with 2x.
• Students often have difficulty when dealing with negative powers. For instance, 1.2 × 10^-2 they assume,  to have a value of -120.
• Multiplying out brackets involving surds is often attempted incorrectly.
• √(5²) is often confused with 2√5