This study notes covers Worked Examples within Compound Measures for GCSE Mathematics. Revise Compound Measures in Number for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 7 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 5 of 7
Practice
12 questions
Recall
22 flashcards
Worked Examples
Example 1: Basic Speed Calculation
Problem: A car travels 150 km in 2.5 hours. Calculate its average speed.
Solution:
Using S = D ÷ T
Speed = 150 km ÷ 2.5 hours = 60 km/h
Answer: 60 km/h
Example 2: Finding Time with Unit Conversion
Problem: A runner maintains a speed of 8 m/s. How long does it take to run 2.4 km?
Solution:
First convert 2.4 km to metres: 2.4 × 1000 = 2400 m
Using T = D ÷ S
Time = 2400 m ÷ 8 m/s = 300 seconds = 5 minutes
Answer: 5 minutes
Example 3: Density with Unit Conversion
Problem: A gold bar has mass 150 g and volume 7.8 cm³. Calculate its density in both g/cm³ and kg/m³.
Solution:
Using D = M ÷ V
Density = 150 g ÷ 7.8 cm³ = 19.23 g/cm³
Converting to kg/m³: 19.23 × 1000 = 19,230 kg/m³
Answer: 19.23 g/cm³ or 19,230 kg/m³
Example 4: Pressure Calculation
Problem: A force of 500 N is applied over an area of 0.25 m². Calculate the pressure.
Solution:
Using P = F ÷ A
Pressure = 500 N ÷ 0.25 m² = 2000 N/m² = 2000 Pa
Answer: 2000 Pa (or 2 kPa)
Example 5: Multi-Step Journey
Problem: A train travels 80 km in the first hour at 80 km/h, then 120 km in the next 1.5 hours. Calculate the average speed for the whole journey.
Solution:
Total distance = 80 km + 120 km = 200 km
Total time = 1 hour + 1.5 hours = 2.5 hours
Average speed = 200 km ÷ 2.5 hours = 80 km/h
Answer: 80 km/h