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Edexcel 1MA1 GCSE Maths · 4 Worked Solutions

Edexcel GCSE Maths: Geometry Worked Solutions

Real mark-scheme-derived worked solutions for Edexcel GCSE Maths Geometry questions. Every solution includes step-by-step working, the correct final answer, marks awarded, and a common mistake callout — with question-level AO breakdown from the official 1MA1 spec.

Q1 Foundation 2 marks
Edexcel 1MA1 · 2022

Question

Here is a right-angled triangle. 8.5 cm, x cm, 4 cm. Work out the value of x.

Worked Solution

  1. Identify the sides: 8.5 cm is the hypotenuse (the longest side, opposite the right angle), 4 cm and x cm are the two shorter sides.

  2. Apply Pythagoras' theorem: x² + 4² = 8.5². So x² = 8.5² – 4² = 72.25 – 16 = 56.25.

  3. Take the square root: x = √56.25 = 7.5.

Final Answer

7.5

Common Mistake

Squaring the sides incorrectly (e.g. computing 8.5 – 4 = 4.5 and squaring that) instead of subtracting the squares. Always square each side first, then subtract.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 50%
AO2 Reason and communicate — 25%
AO3 Solve problems — 25%
Q2 Higher 4 marks
Edexcel 1MA1 · 2024

Question

A paddling pool is in the shape of a cylinder. The pool has radius 100 cm. The pool has depth 30 cm. The pool is empty. It is then filled with water at a rate of 250 cm³ per second. Work out the number of minutes it takes to fill the pool completely. Give your answer correct to the nearest minute. You must show all your working.

Worked Solution

  1. Find the volume of the cylindrical pool using V = πr²h: V = π × 100² × 30 = 300 000π ≈ 942 478 cm³.

  2. Find how long it takes to fill at 250 cm³/s: time = 942 478 ÷ 250 ≈ 3769.9 seconds.

  3. Convert to minutes: 3769.9 ÷ 60 ≈ 62.8 minutes.

  4. Rounded to the nearest minute: 63 minutes.

Final Answer

63

Common Mistake

Forgetting to convert seconds to minutes at the end, or rounding intermediate values too early (use the full unrounded value of π throughout).

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%
Q3 Higher 3 marks
Edexcel 1MA1 · 2023

Question

Solid A and solid B are similar. The ratio of the height of solid A to the height of solid B is 2 : 5. The volume of solid A is 12 cm³. Work out the volume of solid B.

Worked Solution

  1. For similar solids, if the linear scale factor from A to B is k, the volume scale factor is k³.

  2. The ratio of heights is 2 : 5, so the linear scale factor k = 5/2 = 2.5.

  3. Volume scale factor = k³ = 2.5³ = 15.625.

  4. Volume of B = 12 × 15.625 = 187.5 cm³.

Final Answer

187.5

Common Mistake

Using the linear scale factor (2.5) or the square scale factor (6.25) instead of the cube scale factor (15.625) — volumes scale with the cube of the linear ratio, not the ratio itself.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%
Q4 Higher 4 marks
Edexcel 1MA1 · 2022

Question

ABDE is a cyclic quadrilateral. ABC and EDC are straight lines. Angle DBC = 60°. Given that size of angle EAB : size of angle BCD = 2 : 1, work out the size of angle BCD. You must show all your working.

Worked Solution

  1. Opposite angles in a cyclic quadrilateral sum to 180°. So angle EAB + angle BDE = 180°.

  2. Angle DBC = 60° is an exterior angle to the cyclic quadrilateral. Use the exterior angle theorem: angle BDE = angle BCD + 60° (exterior angle of triangle BCD equals sum of the two non-adjacent interior angles, one of which is angle DBC).

  3. Let angle BCD = x. Then angle EAB = 2x (given ratio 2 : 1). Also angle BDE = x + 60°.

  4. From the cyclic quadrilateral: EAB + BDE = 180°, so 2x + (x + 60°) = 180°, giving 3x + 60° = 180°, so 3x = 120°, x = 40°.

Final Answer

40°

Common Mistake

Forgetting that opposite angles in a cyclic quadrilateral sum to 180° (not 90°) — this property is essential to set up the equation.

Assessment Objectives (question level, Edexcel 1MA1 spec — not per step)

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%

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More Edexcel GCSE Maths Worked Solutions

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