Indices, Standard Form and Surds

Scheme of work: GCSE Higher: Year 10: Term 3: 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, and 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 x 10-2 they assume,  to have a value of -120.
  • Multiplying out brackets involving surds is often attempted incorrectly.
  • 2(52) is often confused with 102

Indices, Standard Form and Surds Resources

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