# IGCSE Higher: Compound Measures

## Scheme of work: IGCSE Higher: Year 10: Term 2: Compound Measures

#### Prerequisite Knowledge

1. Understanding Units of Measurement
• Concept: Knowing common units of measurement for distance (meters, kilometers), time (seconds, hours), and speed (meters per second, kilometers per hour).
• Example: $\text{Distance: } 5 \text{ km}, \quad \text{Time: } 2 \text{ hours}, \quad \text{Speed: } 60 \text{ km/h}$
2. Basic Algebraic Manipulation
• Concept: Rearranging formulas to solve for a specific variable.
• Example: Given $$\text{distance} = \text{speed} \times \text{time}$$, solve for speed: $\text{speed} = \frac{\text{distance}}{\text{time}}$

#### Success Criteria

1. Understand and Use the Relationship Between Average Speed, Distance, and Time
• Objective: Students should be able to calculate average speed, distance, and time using the formula $$\text{speed} = \frac{\text{distance}}{\text{time}}$$.
• Example: Calculate the average speed if a car travels 150 km in 3 hours: $\text{speed} = \frac{150 \text{ km}}{3 \text{ hours}} = 50 \text{ km/h}$
2. Use Compound Measures Such as Speed, Density, and Pressure
• Objective: Students should be able to use and calculate compound measures like speed, density, and pressure.
• Example: Calculate the density of an object with mass 200 grams and volume 50 cubic centimeters: $\text{density} = \frac{\text{mass}}{\text{volume}} = \frac{200 \text{ g}}{50 \text{ cm}^3} = 4 \text{ g/cm}^3$
3. Convert Units Appropriately
• Objective: Students should be able to convert between different units of measurement appropriately.
• Example: Convert a speed of 72 km/h to meters per second: $72 \text{ km/h} = 72 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 20 \text{ m/s}$

#### Key Concepts

1. Relationship Between Speed, Distance, and Time
• Concept: Understanding the formula $$\text{speed} = \frac{\text{distance}}{\text{time}}$$ and its rearrangements: $$\text{distance} = \text{speed} \times \text{time}$$ and $$\text{time} = \frac{\text{distance}}{\text{speed}}$$.
• Example: $\text{If distance} = 100 \text{ km and time} = 2 \text{ hours, then speed} = \frac{100 \text{ km}}{2 \text{ hours}} = 50 \text{ km/h}$
2. Compound Measures
• Concept: Understanding that compound measures like density and pressure are derived from basic physical quantities.
• Example: Density is defined as mass per unit volume: $\text{density} = \frac{\text{mass}}{\text{volume}}$
3. Unit Conversion
• Concept: Knowing how to convert between different units of measurement (e.g., kilometers to meters, hours to seconds).
• Example: Convert 5 km to meters: $5 \text{ km} = 5 \times 1000 = 5000 \text{ meters}$

#### Common Misconceptions

1. Incorrect Application of the Speed Formula
• Common Mistake: Students might confuse the formula for speed, distance, and time, leading to incorrect calculations.
• Example: Given distance = 120 km and time = 3 hours, a student might incorrectly calculate speed as: $\text{Incorrect: speed} = \frac{3 \text{ hours}}{120 \text{ km}} = 0.025 \text{ km/h}$ Correct calculation: $\text{speed} = \frac{120 \text{ km}}{3 \text{ hours}} = 40 \text{ km/h}$
2. Confusion in Unit Conversion
• Common Mistake: Students might incorrectly convert units, especially when dealing with compound measures.
• Example: Converting 90 km/h to m/s incorrectly: $\text{Incorrect: } 90 \text{ km/h} = 90 \times 1000 = 90000 \text{ m/s}$ Correct conversion: $90 \text{ km/h} = 90 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 25 \text{ m/s}$
3. Misinterpreting Compound Measures
• Common Mistake: Students might misunderstand the relationships in compound measures, leading to incorrect calculations.
• Example: Calculating density with incorrect units: $\text{Incorrect: density} = \frac{200 \text{ g}}{0.05 \text{ m}^3} = 4000 \text{ g/m}^3$ Correct calculation: $\text{density} = \frac{200 \text{ g}}{50 \text{ cm}^3} = 4 \text{ g/cm}^3$

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