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Edexcel 1MA1 GCSE Maths · 2 Worked Solutions

Edexcel GCSE Maths: Density, Mass and Volume Worked Solutions

Real mark-scheme-derived worked solutions for Edexcel GCSE Maths Density, Mass and Volume 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 Higher 5 marks
Edexcel 1MA1 · 2022

Question

The pyramid P is formed from two parts made of different materials. The top part of P has a mass of 92.8 g and is made from material with a density of 2.9 g/cm³. The bottom part of P has a mass of 972.8 g. The average density of P is 4.7 g/cm³. Calculate the volume of the top part of P as a percentage of the total volume of P. Give your answer correct to 1 decimal place. You must show all your working.

Worked Solution

  1. Find the volume of the top part: volume = mass ÷ density = 92.8 ÷ 2.9 = 32 cm³.

  2. Find the total mass of pyramid P: 92.8 + 972.8 = 1065.6 g.

  3. Find the total volume of pyramid P using the average density: total volume = total mass ÷ average density = 1065.6 ÷ 4.7 ≈ 226.72 cm³.

  4. Express the volume of the top part as a percentage: (32 ÷ 226.72) × 100 ≈ 14.1%.

Final Answer

14.1

Common Mistake

Using the wrong density for the total volume calculation — the average density 4.7 g/cm³ applies to the whole pyramid, not just one part. Make sure to use total mass and average density together.

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

AO1 Use standard techniques — 40%
AO2 Reason and communicate — 30%
AO3 Solve problems — 30%
Q2 Higher 3 marks
Edexcel 1MA1 · 2022

Question

Here are two cubes, A and B. Cube A has edges of 3 cm and a mass of 81 g. Cube B has edges of 4 cm and a mass of 128 g. Work out the density of cube A : the density of cube B. Give your answer in the form a : b, where a and b are integers.

Worked Solution

  1. Find the volume of cube A: volume = 3³ = 27 cm³.

  2. Find the density of cube A: density = mass ÷ volume = 81 ÷ 27 = 3 g/cm³.

  3. Find the volume of cube B: volume = 4³ = 64 cm³.

  4. Find the density of cube B: density = mass ÷ volume = 128 ÷ 64 = 2 g/cm³.

  5. Ratio of density A to density B = 3 : 2.

Final Answer

3 : 2

Common Mistake

Using the edge length as the volume (3 and 4) rather than cubing them (27 and 64) — the volume of a cube is edge³, not edge.

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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