# Factors, Multiples, Indices, Roots and Standard Form

Prior learning: Year 7 Autumn 2; Year 8 Autumn 2

 Topic Foundation Higher Factors, Multiples, Indices, Roots and Standard Form Exemplification questions Calculate factors and multiples List the prime factors of a number as a product Calculate the HCF and LCM of numbers or expressions Calculate powers and roots Use the three laws of indices Change between normal notation and standard form Calculate with numbers in standard form Use the laws of indices for fractional and negative powers Simplify surds and expressions involving surds Rationalise the denominator of fractions Perform harder calculations with numbers in standard form

Notes:

Students should be able to:

• identify multiples, factors and prime numbers from lists of numbers
• write out lists of multiples and factors to identify common multiples or common factors of two or more integers
• write a number as the product of its prime factors and use formal (eg using Venn diagrams) and informal methods (eg trial and error) for identifying highest common factors (HCF) and lowest common multiples (LCM)
• work out a root of a number from a product of prime factors.

Students will be expected to apply index laws to simplify numerical and algebraic expressions.