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GCSE Maths · Edexcel 1MA1 · Grade Ladder · Number

Grade Ladder: Number

18 questions climbing from grade 1 to grade 9 across the number content of the Edexcel GCSE, two at each grade. Each question shows its grade, its specification code and whether it is non-calculator.

How to use this ladderFoundation students: work through Grades 1–5. Higher students: start at Grade 4 and push on to 9. Questions marked Non-calculator should be done without a calculator, as in Paper 1.
Grades 1–3 · Foundation
  1. (1 mark)
    Grade 1N1Non-calculator
    Write these numbers in order, smallest first: −3, 5, −7, 0, 2
  2. (1 mark)
    Grade 1N3Non-calculator
    Work out 7 × 8 − 6.
  3. (1 mark)
    Grade 2N15Non-calculator
    Round 3.476 to 1 decimal place.
  4. (2 marks)
    Grade 2N4Non-calculator
    List all the factors of 18.
  5. (2 marks)
    Grade 3N12Non-calculator
    Work out 35 of 45.
  6. (2 marks)
    Grade 3N10Non-calculator
    Write 0.35 as a fraction in its simplest form.
Grades 4–5 · Foundation and Higher
  1. (2 marks)
    Grade 4N4Non-calculator
    Write 360 as a product of its prime factors in index form.
  2. (2 marks)
    Grade 4N14Non-calculator
    Estimate the value of 61.8 × 0.49.
  3. (2 marks)
    Grade 5N9Non-calculator
    Work out (3.2 × 10⁴) × (5 × 10³). Give your answer in standard form.
  4. (3 marks)
    Grade 5N4Non-calculator
    Find the HCF and the LCM of 24 and 36.
Grades 6–7 · Higher
  1. (2 marks)
    Grade 6N15Non-calculator
    x = 4.7 correct to 1 decimal place. Write down the error interval for x.
  2. (2 marks)
    Grade 6N7Non-calculator
    Evaluate 272/3.
  3. (3 marks)
    Grade 7N10Non-calculator
    Write 0.4̇7̇ as a fraction.
  4. (2 marks)
    Grade 7N8Non-calculator
    Simplify √75 − √12.
Grades 8–9 · Higher
  1. (2 marks)
    Grade 8N8Non-calculator
    Rationalise the denominator of 6√3. Simplify your answer.
  2. (3 marks)
    Grade 8N16
    a = 5.3 and b = 2.1, both correct to 1 decimal place. Calculate the upper bound of a ÷ b. Give your answer to 3 significant figures.
  3. (3 marks)
    Grade 9N8Non-calculator
    Show that 43 − √5 simplifies to 3 + √5.
  4. (3 marks)
    Grade 9N10Non-calculator
    Prove algebraically that 0.13̇ = 215.
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Worked solutions

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GCSE Maths · Edexcel 1MA1 · Grade Ladder · Number

Grade Ladder: Number — Worked Solutions

Full worked solutions to all 18 questions (38 marks).

Grades 1–3 · Foundation
  1. (1 mark)
    Grade 1N1Non-calculator
    Write these numbers in order, smallest first: −3, 5, −7, 0, 2
    Solution
    1. The most negative is smallest.
    −7, −3, 0, 2, 5
  2. (1 mark)
    Grade 1N3Non-calculator
    Work out 7 × 8 − 6.
    Solution
    1. Multiply first: 56 − 6.
    50
  3. (1 mark)
    Grade 2N15Non-calculator
    Round 3.476 to 1 decimal place.
    Solution
    1. The second decimal digit is 7, so round up.
    3.5
  4. (2 marks)
    Grade 2N4Non-calculator
    List all the factors of 18.
    Solution
    1. Find factor pairs: 1×18, 2×9, 3×6.
    1, 2, 3, 6, 9, 18
  5. (2 marks)
    Grade 3N12Non-calculator
    Work out 35 of 45.
    Solution
    1. 45 ÷ 5 = 9, then 9 × 3.
    27
  6. (2 marks)
    Grade 3N10Non-calculator
    Write 0.35 as a fraction in its simplest form.
    Solution
    1. 0.35 = 35100; divide by 5.
    720
Grades 4–5 · Foundation and Higher
  1. (2 marks)
    Grade 4N4Non-calculator
    Write 360 as a product of its prime factors in index form.
    Solution
    1. 360 = 2 × 180 = 2 × 2 × 90 = 2 × 2 × 2 × 45 = 2³ × 3² × 5.
    2³ × 3² × 5
  2. (2 marks)
    Grade 4N14Non-calculator
    Estimate the value of 61.8 × 0.49.
    Solution
    1. Round to 1 s.f.: 60 × 0.5.
    ≈ 30
  3. (2 marks)
    Grade 5N9Non-calculator
    Work out (3.2 × 10⁴) × (5 × 10³). Give your answer in standard form.
    Solution
    1. 3.2 × 5 = 16 and 10⁴ × 10³ = 10⁷.
    2. 16 × 10⁷ = 1.6 × 10⁸.
    1.6 × 10⁸
  4. (3 marks)
    Grade 5N4Non-calculator
    Find the HCF and the LCM of 24 and 36.
    Solution
    1. 24 = 2³ × 3 and 36 = 2² × 3².
    2. HCF = 2² × 3 = 12. LCM = 2³ × 3² = 72.
    HCF 12, LCM 72
Grades 6–7 · Higher
  1. (2 marks)
    Grade 6N15Non-calculator
    x = 4.7 correct to 1 decimal place. Write down the error interval for x.
    Solution
    1. Half of 0.1 is 0.05 either side.
    4.65 ≤ x < 4.75
  2. (2 marks)
    Grade 6N7Non-calculator
    Evaluate 272/3.
    Solution
    1. ∛27 = 3, then 3² = 9.
    9
  3. (3 marks)
    Grade 7N10Non-calculator
    Write 0.4̇7̇ as a fraction.
    Solution
    1. x = 0.474747…; 100x = 47.4747…
    2. 99x = 47, so x = 4799.
    4799
  4. (2 marks)
    Grade 7N8Non-calculator
    Simplify √75 − √12.
    Solution
    1. √75 = 5√3 and √12 = 2√3.
    3√3
Grades 8–9 · Higher
  1. (2 marks)
    Grade 8N8Non-calculator
    Rationalise the denominator of 6√3. Simplify your answer.
    Solution
    1. Multiply top and bottom by √3: 6√33.
    2√3
  2. (3 marks)
    Grade 8N16
    a = 5.3 and b = 2.1, both correct to 1 decimal place. Calculate the upper bound of a ÷ b. Give your answer to 3 significant figures.
    Solution
    1. Upper bound of a ÷ b = (upper bound of a) ÷ (lower bound of b).
    2. = 5.35 ÷ 2.05 = 2.60976…
    2.61
  3. (3 marks)
    Grade 9N8Non-calculator
    Show that 43 − √5 simplifies to 3 + √5.
    Solution
    1. Multiply by 3 + √53 + √5.
    2. Denominator: (3 − √5)(3 + √5) = 9 − 5 = 4.
    3. Numerator: 4(3 + √5). Divide by 4.
    3 + √5
  4. (3 marks)
    Grade 9N10Non-calculator
    Prove algebraically that 0.13̇ = 215.
    Solution
    1. x = 0.1333…, 10x = 1.333…
    2. 9x = 1.2, so x = 1.29 = 1290 = 215.
    Proved
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