Number

You will be able to

• Write a whole number as a product of its prime factors in index form, using a factor tree.
• Find the highest common factor (HCF) and lowest common multiple (LCM) of two numbers from their prime factors.
• Explain why 1 is not prime, why every factor tree for a number ends in the same primes, and why HCF × LCM = A × B.

You will be able to

• Place the elements of sets in the correct regions of a Venn diagram and list a set in braces.
• Use and interpret the notation ∪, ∩, A′, ∈, ∉, ⊆, ∅ and n(A), and shade the region for a set expression.
• Use n(A ∪ B) = n(A) + n(B) − n(A ∩ B) to find an unknown number in a region.

You will be able to

• Give the upper and lower bounds of a value rounded to a given accuracy, and write the error interval as an inequality.
• Explain why the lower bound is included in the error interval and the upper bound is not.
• Calculate the greatest and least possible values of a sum, difference, product or quotient of rounded quantities.

You will be able to

• Increase or decrease an amount by a percentage in one step using a multiplier.
• Calculate a percentage change, profit or loss as a percentage of the original amount.
• Find the original amount before a percentage change (reverse percentage) and combine two successive changes by multiplying their multipliers.

You will be able to

• Calculate the value after n years of compound interest or depreciation using V = P(1 ± r/100)ⁿ.
• Compare compound and simple interest, explaining why compound growth is a curve and simple interest a straight line.
• Find, by trying whole numbers of years, how long it takes for an amount to reach a given value such as double.