Numbers and the Number System

Worked examples (7)

• 1Write a number as a product of prime factors in index form
• 2Find the HCF and LCM from prime factorisations
• 3Use the HCF × LCM identity
• 4Classify numbers as prime, square or cube
• 5Use divisibility rules to find a missing digit
• 6Order of operations with negative integers
• 7Real-life LCM word problem

Worked examples (6)

• 1Convert a recurring decimal to a fraction
• 2Percentage increase and decrease
• 3Reverse percentage problem
• 4Mixed-fraction arithmetic with division
• 5Compound percentage problem
• 6Compare fractions, decimals and percentages

Worked examples (6)

• 1Apply index laws to simplify
• 2Evaluate a negative index
• 3Evaluate a fractional index
• 4Anything to the power of zero
• 5Combine multiple index laws
• 6Estimate a square root without a calculator

Worked examples (4)

• 1Read set notation
• 2Use a 2-set Venn diagram with overlap
• 3Three-set Venn diagram
• 4Read set-builder notation

Worked examples (6)

• 1Share an amount in a ratio
• 2Direct proportion problem
• 3Direct proportion using $y \\propto x$
• 4Inverse proportion
• 5Ratio to fraction conversion
• 6Simplify a ratio with units

Worked examples (5)

• 1Round to a given accuracy
• 2Find upper and lower bounds
• 3Bounds with multiplication
• 4Bounds with subtraction
• 5Truncate vs round

Worked examples (5)

• 1Convert to standard form
• 2Convert from standard form
• 3Multiplying in standard form
• 4Adding in standard form (different powers)
• 5Order of magnitude estimate

Worked examples (5)

• 1Convert units in a multi-step problem
• 2Convert time and combine
• 3Money calculation with rate
• 4Compare best buys with bonus offers
• 5Currency conversion

Worked examples (5)

• 1Simplify a surd
• 2Add and subtract surds
• 3Multiply and expand surds
• 4Rationalise a simple denominator
• 5Rationalise using a conjugate

Worked examples (5)

• 1Simple interest calculation
• 2Compound interest calculation
• 3Compare simple vs compound interest
• 4Compound depreciation
• 5Find the interest rate