Pearson Edexcel GCSE (9-1) Mathematics revision notes
Structure and calculation Revision Notes
Review revision notes for Structure and calculation in Edexcel Mathematics.
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Structure and calculation
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Fractional indices and roots Revision Notes
Interpreting the index
In a fractional index a^(m/n), the denominator n indicates the root and the numerator m indicates the power. Thus 27^(2/3) means the cube root of 27, squared: 3^2 = 9.
A reliable calculation method
For positive numerical bases, first evaluate the root indicated by the denominator, then apply the power indicated by the numerator. For instance, 32^(2/5) = (fifth root of 32)^2 = 2^2 = 4. Check that the root and power have not been reversed.
Assessment focus
The objective concerns interpreting and calculating with fractional indices and is within the Higher tier for Papers 1, 2 and 3. Show intermediate steps when working out a value so the root interpretation and subsequent power are clear.
Operations, inverses and priority Revision Notes
Inverse operations and cancellation
Inverse operations reverse one another. Addition and subtraction form a pair, as do multiplication and division. The reciprocal of a non-zero number reverses its multiplicative effect; for example, the reciprocal of 5/8 is 8/5. Common factors can be cancelled in suitable fractions.
Priority of operations
Evaluate brackets before anything outside them. Then calculate powers and roots, followed by multiplication and division from left to right. Complete addition and subtraction last, also from left to right. Brackets can make the intended order explicit and prevent a different calculation.
Checking calculations
Use an inverse operation to check a result: add back after subtracting, multiply after dividing, or divide after multiplying. For a multi-step expression, check each stage against the stated priority. Keep exact values such as square roots where they are straightforward, and recalculate numerical comparisons independently.
Operations with numbers Revision Notes
Integers and decimals
For integers, apply the sign rules consistently: adding a negative is equivalent to subtracting its positive value, while subtracting a negative is equivalent to adding. For decimals, align place values for addition and subtraction, and count decimal places when multiplying.
Fractions and mixed numbers
For fraction addition and subtraction, use a common denominator before combining numerators. For multiplication, multiply numerators and denominators, simplifying where possible. For division, multiply by the reciprocal. Convert mixed numbers to improper fractions before calculating.
Checking calculations
Estimate first using convenient rounded values, then compare the estimate with the exact answer. Check that the sign, place value and size of the result are sensible, and simplify fractional answers where appropriate.
Ordering numbers and inequalities Revision Notes
Comparing different forms
Convert fractions to decimals, or use equivalent fractions, when this makes comparison easier. For example, 3/4 = 0.75 and 2/5 = 0.4, so 2/5 < 3/4. Keep track of place value when comparing decimals.
Ordering negative numbers
On a number line, values increase from left to right. Among negative numbers, the value closer to zero is greater: -0.2 > -0.6. Therefore, when arranging negative numbers in ascending order, the number with the larger absolute value comes first.
Inequality symbols
The symbol < means ‘is less than’, > means ‘is greater than’, and = means ‘is equal to’. The wider part of < or > faces the greater value. Check the relationship by comparing both sides before choosing a symbol.
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