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GCSE Maths · Edexcel 1MA1 · Grade Ladder · Ratio and proportion

Grade Ladder: Ratio, Proportion and Rates

18 questions climbing from grade 1 to grade 9 across the ratio and proportion 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 1R4Non-calculator
    Write the ratio 12 : 18 in its simplest form.
  2. (1 mark)
    Grade 1R1Non-calculator
    Change 3.5 km to metres.
  3. (2 marks)
    Grade 2R5Non-calculator
    Share £40 in the ratio 3 : 5.
  4. (2 marks)
    Grade 2R7Non-calculator
    4 pens cost £3.20. How much do 7 pens cost?
  5. (2 marks)
    Grade 3R9Non-calculator
    Increase £80 by 15%.
  6. (2 marks)
    Grade 3R11Non-calculator
    A train travels 150 km in 2.5 hours. Work out its average speed.
Grades 4–5 · Foundation and Higher
  1. (3 marks)
    Grade 4R11
    Which is better value: 500 g for £2.40 or 750 g for £3.45?
  2. (2 marks)
    Grade 4R7Non-calculator
    A recipe for 4 people uses 300 g of flour. How much flour is needed for 10 people?
  3. (3 marks)
    Grade 5R9
    In a sale, prices are reduced by 20%. A jacket costs £64 in the sale. What was its original price?
  4. (2 marks)
    Grade 5R11
    A metal block has mass 540 g and volume 200 cm³. Work out its density.
Grades 6–7 · Higher
  1. (3 marks)
    Grade 6R16
    £5000 is invested at 3% compound interest per year. Work out its value after 4 years.
  2. (3 marks)
    Grade 6R10Non-calculator
    y is directly proportional to x. y = 12 when x = 4. Find y when x = 7.
  3. (3 marks)
    Grade 7R13Non-calculator
    y is directly proportional to x². y = 45 when x = 3. Find y when x = 4.
  4. (2 marks)
    Grade 7R1
    Change 15 m/s to km/h.
Grades 8–9 · Higher
  1. (3 marks)
    Grade 8R13Non-calculator
    y is inversely proportional to x². y = 4 when x = 3. Find the positive value of x when y = 1.
  2. (3 marks)
    Grade 8R16
    A car worth £12 000 loses 15% of its value each year. After how many whole years is it first worth less than £6000?
  3. (3 marks)
    Grade 9R4Non-calculator
    a : b = 3 : 4 and b : c = 6 : 5. Find a : b : c in its simplest form.
  4. (3 marks)
    Grade 9R11
    The force on an object increases by 20% and the area it acts on decreases by 20%. Find the percentage change in the pressure.
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Worked solutions

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GCSE Maths · Edexcel 1MA1 · Grade Ladder · Ratio and proportion

Grade Ladder: Ratio, Proportion and Rates — Worked Solutions

Full worked solutions to all 18 questions (43 marks).

Grades 1–3 · Foundation
  1. (1 mark)
    Grade 1R4Non-calculator
    Write the ratio 12 : 18 in its simplest form.
    Solution
    1. Divide both by 6.
    2 : 3
  2. (1 mark)
    Grade 1R1Non-calculator
    Change 3.5 km to metres.
    Solution
    1. 1 km = 1000 m.
    3500 m
  3. (2 marks)
    Grade 2R5Non-calculator
    Share £40 in the ratio 3 : 5.
    Solution
    1. 8 parts → £5 per part.
    2. 3 × 5 and 5 × 5.
    £15 and £25
  4. (2 marks)
    Grade 2R7Non-calculator
    4 pens cost £3.20. How much do 7 pens cost?
    Solution
    1. 1 pen = £0.80.
    2. 7 × 0.80.
    £5.60
  5. (2 marks)
    Grade 3R9Non-calculator
    Increase £80 by 15%.
    Solution
    1. 10% = 8, 5% = 4, so 15% = 12.
    £92
  6. (2 marks)
    Grade 3R11Non-calculator
    A train travels 150 km in 2.5 hours. Work out its average speed.
    Solution
    1. Speed = distance ÷ time.
    60 km/h
Grades 4–5 · Foundation and Higher
  1. (3 marks)
    Grade 4R11
    Which is better value: 500 g for £2.40 or 750 g for £3.45?
    Solution
    1. £2.40 ÷ 5 = 48p per 100 g.
    2. £3.45 ÷ 7.5 = 46p per 100 g.
    750 g is better value
  2. (2 marks)
    Grade 4R7Non-calculator
    A recipe for 4 people uses 300 g of flour. How much flour is needed for 10 people?
    Solution
    1. 75 g per person × 10.
    750 g
  3. (3 marks)
    Grade 5R9
    In a sale, prices are reduced by 20%. A jacket costs £64 in the sale. What was its original price?
    Solution
    1. £64 is 80% of the original.
    2. 64 ÷ 0.8.
    £80
  4. (2 marks)
    Grade 5R11
    A metal block has mass 540 g and volume 200 cm³. Work out its density.
    Solution
    1. Density = mass ÷ volume.
    2.7 g/cm³
Grades 6–7 · Higher
  1. (3 marks)
    Grade 6R16
    £5000 is invested at 3% compound interest per year. Work out its value after 4 years.
    Solution
    1. 5000 × 1.03⁴.
    £5,627.54
  2. (3 marks)
    Grade 6R10Non-calculator
    y is directly proportional to x. y = 12 when x = 4. Find y when x = 7.
    Solution
    1. y = kx → 12 = 4k → k = 3.
    2. y = 3 × 7.
    21
  3. (3 marks)
    Grade 7R13Non-calculator
    y is directly proportional to x². y = 45 when x = 3. Find y when x = 4.
    Solution
    1. 45 = k × 9 → k = 5.
    2. y = 5 × 16.
    80
  4. (2 marks)
    Grade 7R1
    Change 15 m/s to km/h.
    Solution
    1. 15 m/s = 15 × 3600 m per hour = 54 000 m/h.
    2. = 54 km/h.
    54 km/h
Grades 8–9 · Higher
  1. (3 marks)
    Grade 8R13Non-calculator
    y is inversely proportional to x². y = 4 when x = 3. Find the positive value of x when y = 1.
    Solution
    1. y = k/x² → 4 = k/9 → k = 36.
    2. 1 = 36/x² → x² = 36.
    x = 6
  2. (3 marks)
    Grade 8R16
    A car worth £12 000 loses 15% of its value each year. After how many whole years is it first worth less than £6000?
    Solution
    1. Multiplier 0.85 each year.
    2. After 4 years: £6,264.07; after 5 years: £5,324.46.
    5 years
  3. (3 marks)
    Grade 9R4Non-calculator
    a : b = 3 : 4 and b : c = 6 : 5. Find a : b : c in its simplest form.
    Solution
    1. Make b the same: 3 : 4 = 9 : 12 and 6 : 5 = 12 : 10.
    9 : 12 : 10
  4. (3 marks)
    Grade 9R11
    The force on an object increases by 20% and the area it acts on decreases by 20%. Find the percentage change in the pressure.
    Solution
    1. P = F/A. New pressure = (1.2F)/(0.8A) = 1.5 × F/A.
    An increase of 50%
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