IGCSE Rate: Complete Guide for Cambridge IGCSE Mathematics

IGCSE rate calculations are practical topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering rate formulas, unit rates, and rate comparisons is essential for solving real-world problems involving rates of change, efficiency, and productivity.

This comprehensive IGCSE rate guide covers everything you need to know, including calculating rates, finding unit rates, comparing rates, step-by-step worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to calculate various types of rates, find unit rates, compare rates, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Rate Matters

IGCSE rate calculations are practical topics with real-world applications. Here’s why they’re so important:

• High frequency topic: Rate questions appear regularly in IGCSE maths papers
• Real-world applications: Used in work rates, flow rates, consumption rates, and efficiency calculations
• Exam weight: Typically worth 4-8 marks per paper
• Foundation for advanced topics: Essential for understanding rates of change and calculus
• Problem-solving skills: Develops proportional reasoning and unit conversion abilities

Key insight from examiners: Students often confuse different types of rates or make errors with unit conversions. This guide will help you master these systematically.

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Understanding Rates

A rate is a ratio that compares two different quantities with different units.

General form: Rate = Quantity 1 / Quantity 2

Examples:

• Speed: km/h (distance per time)
• Flow rate: liters per minute
• Work rate: tasks per hour
• Consumption rate: km per liter

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Calculating Rates

Basic Rate Formula

Formula: Rate = Amount / Time (or appropriate units)

Example 1: A factory produces 1,200 items in 8 hours. Find the production rate.

Solution: Rate = 1200 items / 8 hours = 150 items/hour

Answer: 150 items per hour

Example 2: A tap fills a 60-liter tank in 4 minutes. Find the flow rate.

Solution: Rate = 60 liters / 4 minutes = 15 liters/minute

Answer: 15 liters per minute

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Unit Rates

A unit rate is a rate with a denominator of 1. It answers “how much per one unit?”

Finding Unit Rates

Method: Divide the quantity by the number of units.

Example 1: Find the unit rate: 300 km in 5 hours

Solution: Unit rate = 300 km / 5 hours = 60 km/hour

Answer: 60 km per hour

Example 2: Find the unit rate: $45 for 3 kg

Solution: Unit rate = $45 / 3 kg = $15/kg

Answer: $15 per kg

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Comparing Rates

To compare rates, convert them to the same units and find unit rates.

Example: Which is better value?

• Option A: 500 ml for $4.50
• Option B: 750 ml for $6.00

Solution:

1. Option A: $4.50 / 500 ml = $0.009/ml = $9/liter
2. Option B: $6.00 / 750 ml = $0.008/ml = $8/liter

Option B is better value (lower cost per liter).

Answer: Option B

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Work Rates

Work rate problems involve people or machines working together.

Formula

Combined work rate: If person A works at rate r₁ and person B works at rate r₂, their combined rate is r₁ + r₂.

Time to complete work: Time = Work / Combined Rate

Example: Person A can complete a job in 6 hours, and Person B can complete it in 4 hours. How long will it take if they work together?

Solution:

1. Person A’s rate: 1 job / 6 hours = 1/6 job/hour
2. Person B’s rate: 1 job / 4 hours = 1/4 job/hour
3. Combined rate: 1/6 + 1/4 = 2/12 + 3/12 = 5/12 job/hour
4. Time together: 1 job / (5/12 job/hour) = 12/5 hours = 2.4 hours = 2 hours 24 minutes

Answer: 2 hours 24 minutes

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Consumption Rates

Consumption rate problems involve using resources at a certain rate.

Example: A car travels 450 km using 30 liters of fuel. Find the fuel consumption rate.

Solution: Rate = 450 km / 30 liters = 15 km/liter

Answer: 15 km per liter

Example: If the consumption rate is 12 km/liter, how far can the car travel on 25 liters?

Solution: Distance = 12 km/liter × 25 liters = 300 km

Answer: 300 km

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Flow Rates

Flow rate problems involve liquids or gases flowing.

Example: Water flows from a tap at 8 liters per minute. How long will it take to fill a 200-liter tank?

Solution: Time = 200 liters / 8 liters/minute = 25 minutes

Answer: 25 minutes

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Step-by-Step Method for Rate Problems

1. Identify the rate type - What quantities are being compared?
2. List given information - Amount, time, or other relevant quantities
3. Use the formula - Rate = Quantity 1 / Quantity 2
4. Convert units if needed - Ensure consistent units
5. Calculate - Show your working clearly
6. Check your answer - Does it make sense?

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Worked Examples

Example 1: Basic Rate

A machine produces 840 items in 7 hours. Find the production rate.

Solution: Rate = 840 items / 7 hours = 120 items/hour

Answer: 120 items per hour

Example 2: Unit Rate

Find the unit rate: $72 for 6 kg

Solution: Unit rate = $72 / 6 kg = $12/kg

Answer: $12 per kg

Example 3: Comparing Rates

Compare:

• Store A: 2 kg for $15
• Store B: 3 kg for $21

Which is better value?

Solution:

1. Store A: $15 / 2 kg = $7.50/kg
2. Store B: $21 / 3 kg = $7.00/kg

Store B is better value.

Answer: Store B

Example 4: Work Rate

Pipe A can fill a tank in 10 hours, Pipe B can fill it in 15 hours. How long if both pipes work together?

Solution:

1. Pipe A rate: 1/10 tank/hour
2. Pipe B rate: 1/15 tank/hour
3. Combined: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 tank/hour
4. Time: 1 tank / (1/6 tank/hour) = 6 hours

Answer: 6 hours

Example 5: Consumption Rate

A car uses 40 liters of fuel to travel 600 km. Find the fuel consumption rate.

Solution: Rate = 600 km / 40 liters = 15 km/liter

Answer: 15 km per liter

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Common Examiner Traps (and How to Dodge Them)

• Unit confusion - Always check units match or convert appropriately
• Rate direction - Make sure you’re calculating the correct rate (e.g., km/liter vs liters/km)
• Work rate errors - For combined work, add the rates, don’t average them
• Unit rate confusion - Unit rate has denominator of 1
• Time conversion - Ensure time units are consistent
• Comparing rates - Convert to same units before comparing

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IGCSE Rate Practice Questions

Question 1: Basic Rate

A printer prints 480 pages in 6 minutes. Find the printing rate.

Solution: Rate = 480 pages / 6 minutes = 80 pages/minute

Answer: 80 pages per minute

Question 2: Unit Rate

Find the unit rate: 350 km in 5 hours

Solution: Unit rate = 350 km / 5 hours = 70 km/hour

Answer: 70 km per hour

Question 3: Comparing Rates

Which is better value?

• Package A: 500 g for $8
• Package B: 750 g for $11

Solution:

1. Package A: $8 / 500 g = $0.016/g = $16/kg
2. Package B: $11 / 750 g = $0.0147/g = $14.67/kg

Package B is better value.

Answer: Package B

Question 4: Work Rate

Worker A completes a task in 8 hours, Worker B in 12 hours. How long if they work together?

Solution:

1. Rate A: 1/8 task/hour
2. Rate B: 1/12 task/hour
3. Combined: 1/8 + 1/12 = 3/24 + 2/24 = 5/24 task/hour
4. Time: 1 / (5/24) = 24/5 = 4.8 hours = 4 hours 48 minutes

Answer: 4 hours 48 minutes

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Frequently Asked Questions About IGCSE Rate

What is a rate?

A rate is a ratio comparing two different quantities with different units, like km/h or liters/minute.

What is a unit rate?

A unit rate is a rate with a denominator of 1, showing how much per one unit (e.g., $15/kg).

How do I calculate a rate?

Divide the first quantity by the second: Rate = Quantity 1 / Quantity 2.

How do I compare rates?

Convert both to the same units and find unit rates, then compare.

How do I solve work rate problems?

Find each person’s rate (work/time), add them for combined rate, then use Time = Work / Rate.

What’s the difference between rate and ratio?

A rate compares different units (e.g., km/h), while a ratio compares same units (e.g., 3:5).

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Speed, Distance and Time: Complete Guide - Master speed calculations
• IGCSE Ratios and Proportions: Complete Guide - Master ratio simplification and proportion problems
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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