Indices, Standard Form and Surds

Scheme of work: GCSE Higher: Year 10: Term 3: Indices, Standard Form and Surds

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 â‰¤ 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

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.

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