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GCSE Higher · grades 4–9 · 15% of marks

GCSE Higher — Number

Every number statement a GCSE Higher student may be asked is here; together they are 15% of the assessment. There are 16 number statements to cover. Working through them one at a time beats mixed practice while a topic is still shaky — mixed practice tells you that something is wrong, not what. The list includes ordering numbers and inequality symbols, the four operations and place value, inverse operations and priority of operations, factors, multiples, primes, HCF and LCM, systematic listing and the product rule for counting and powers and roots. No statement in this area is wholly Higher, but 6 of them have a Higher-only part — systematic listing and the product rule for counting, powers and roots, calculating with roots and indices and exact calculation: fractions, surds and π. With 40% AO1 and 60% across AO2 and AO3, fluency alone is not enough — the paper repeatedly asks what your answer means. The bulk of it sits comfortably on the non-calculator paper; a calculator quietly hides the gap until the exam.

  • N1 — Ordering numbers and inequality symbols
  • N2 — The four operations and place value
  • N3 — Inverse operations and priority of operations
  • N4 — Factors, multiples, primes, HCF and LCM
  • N5 — Systematic listing and the product rule for counting (part Higher)
  • N6 — Powers and roots (part Higher)
  • N7 — Calculating with roots and indices (part Higher)
  • N8 — Exact calculation: fractions, surds and π (part Higher)
  • N9 — Standard form
  • N10 — Fractions and decimals, including recurring decimals (part Higher)
  • …and 6 more number statements at this tier

Practise

GCSE Higher · NumberQuestion 1 of 20 · 0 correct
Practice mode· no pressure · hints available

Number

N4

Intermediate

The number 72 can be written as 2³ × 3², and the number 108 can be written as 2² × 3³. Work out the highest common factor of 72 and 108.

💡 Hints:
Printable worksheetNon-calculator sheetSample Paper 1Sample Paper 2

The 16 DfE statements in number at Higher

N1Ordering numbers and inequality symbolsnon-calculator
30 questions
N2The four operations and place valuenon-calculator
30 questions
N3Inverse operations and priority of operationsnon-calculator
30 questions
N4Factors, multiples, primes, HCF and LCMnon-calculator
30 questions
N5Systematic listing and the product rule for countingpart Highereither paper
Higher-only part: "including use of the product rule for counting"30 questions
N6Powers and rootspart Highernon-calculator
Higher-only part: "estimate powers and roots of any given positive number"30 questions
N7Calculating with roots and indicespart Highernon-calculator
Higher-only part: "and fractional"30 questions
N8Exact calculation: fractions, surds and πpart Highernon-calculator
Higher-only parts: "surds"; "simplify surd expressions involving squares and rationalise denominators"30 questions
N9Standard formeither paper
30 questions
N10Fractions and decimals, including recurring decimalspart Highernon-calculator
Higher-only part: "change recurring decimals into their corresponding fractions and vice versa"30 questions
N11Fractions in ratio problemsnon-calculator
30 questions
N12Fractions and percentages as operatorseither paper
30 questions
N13Standard and compound unitseither paper
30 questions
N14Estimation and checkingnon-calculator
30 questions
N15Rounding, significant figures and error intervalseither paper
30 questions
N16Limits of accuracy and boundspart Highercalculator
Higher-only part: "upper and lower bounds"30 questions

Related

Number at Foundation25% of Higher marksRatio, proportion and rates of changeHigher · 20% of marksAlgebraHigher · 30% of marksGeometry and measuresHigher · 20% of marks

Questions people ask

How much of the GCSE Higher paper is number?

15% of the total marks, and the three papers each carry an equal share of the qualification, so it is spread across all of them rather than concentrated in one.

How many topics are there in number at GCSE Higher?

16 DfE content statements, coded N1 to N16 within this area. Every question in the bank is tagged to one of them.

Which number topics are Higher only?

No number statement is wholly Higher, though 6 of them have a Higher-only part. The difference between the tiers here is the demand of the questions rather than the list of topics.

Can I use a calculator for number questions?

Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 16 statements in this area, 10 are naturally non-calculator and 1 naturally calculator, with the rest workable either way — so practise both.

What kind of marks does number carry?

The GCSE Higher split is 40% AO1 (use and apply standard techniques), 30% AO2 (reason, interpret and communicate) and 30% AO3 (solve problems in and out of context). Questions in this area are set across all three.

Are these past paper questions?

No. Every question at /gcse-higher is original, written to the DfE content statements and checked before it is published. We do not host past papers or mark schemes.

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