# 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 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

#### 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

### Mr Mathematics Blog

#### 3D Vectors – Year 2

A-Level Scheme of work: Edexcel A-Level Mathematics Year 2: Pure 2: 3D Vectors

#### Parametric Equations

Edexcel A-Level Mathematics Year 2: Pure 2: Parametric Equations