# IGCSE Higher: Percentage Changes

## Scheme of work: IGCSE Higher: Year 10: Term 3: Percentage Changes

#### Prerequisite Knowledge

1. Understanding Basic Percentages
• Concept: Knowing how to calculate percentages of a quantity and understand percentage increases and decreases.
• Example: $\text{10% of 200} = \frac{10}{100} \times 200 = 20$
2. Using Multipliers for Percentage Change
• Concept: Understanding how to use multipliers for calculating percentage increase or decrease.
• Example: An increase of 20% can be calculated using the multiplier 1.20: $\text{Original value} \times 1.20 = \text{New value}$

#### Success Criteria

1. Use Repeated Percentage Change
• Objective: Students should be able to calculate the effect of repeated percentage changes on a quantity.
• Example: Calculate the total percentage increase when an increase of 30% is followed by a decrease of 20%: $\text{Initial value} = 100 \\ \text{After 30% increase} = 100 \times 1.30 = 130 \\ \text{After 20% decrease} = 130 \times 0.80 = 104 \\ \text{Total percentage change} = \left( \frac{104 – 100}{100} \right) \times 100 = 4\%$
2. Solve Compound Interest Problems
• Objective: Students should be able to solve problems involving compound interest using the compound interest formula.
• Example: Calculate the compound interest on a principal of $1000 at an annual interest rate of 5% for 3 years: $A = P \left(1 + \frac{r}{100}\right)^n \\ A = 1000 \left(1 + \frac{5}{100}\right)^3 = 1000 \times 1.157625 = 1157.63 \\ \text{Compound interest} = 1157.63 – 1000 = 157.63$ 3. Solve Compound Decay Problems • Objective: Students should be able to solve problems involving compound decay using appropriate formulas. • Example: Calculate the remaining amount of a substance after it decays by 10% annually for 3 years from an initial amount of 500 grams: $A = P \left(1 – \frac{r}{100}\right)^n \\ A = 500 \left(1 – \frac{10}{100}\right)^3 = 500 \times 0.729 = 364.5 \text{ grams}$ #### Key Concepts 1. Using Multipliers for Percentage Change • Concept: Understanding how to use multipliers for calculating percentage increases and decreases efficiently. • Example: An increase of 20% can be calculated using the multiplier 1.20: $\text{New value} = \text{Original value} \times 1.20$ 2. Compound Interest Formula • Concept: Understanding the compound interest formula and its components: $$A = P \left(1 + \frac{r}{100}\right)^n$$, where $$P$$ is the principal, $$r$$ is the rate, and $$n$$ is the number of periods. • Example: $A = 1000 \left(1 + \frac{5}{100}\right)^3 = 1157.63$ 3. Compound Decay Formula • Concept: Understanding the compound decay formula and its components: $$A = P \left(1 – \frac{r}{100}\right)^n$$, where $$P$$ is the initial amount, $$r$$ is the decay rate, and $$n$$ is the number of periods. • Example: $A = 500 \left(1 – \frac{10}{100}\right)^3 = 364.5 \text{ grams}$ #### Common Misconceptions 1. Incorrect Application of Percentage Change • Common Mistake: Students might incorrectly apply the percentage increase or decrease by adding or subtracting the percentage directly from the original value instead of using multipliers. • Example: For a 30% increase followed by a 20% decrease on an initial value of 100: $\text{Incorrect: } 100 + 30 – 20 = 110 \\ \text{Correct: } 100 \times 1.30 = 130 \\ 130 \times 0.80 = 104$ 2. Errors in Compound Interest Calculations • Common Mistake: Students might forget to apply the interest rate for each compounding period, leading to incorrect results. • Example: Calculating compound interest for$1000 at 5% annually for 3 years incorrectly as: $\text{Incorrect: } A = 1000 \left(1 + \frac{5}{100}\right) = 1050 \\ \text{Correct: } A = 1000 \left(1 + \frac{5}{100}\right)^3 = 1157.63$
3. Errors in Compound Decay Calculations
• Common Mistake: Students might incorrectly apply the decay rate or misinterpret the formula.
• Example: Calculating compound decay for 500 grams at 10% annually for 3 years incorrectly as: $\text{Incorrect: } A = 500 \left(1 – 10\right)^3 = -4500 \\ \text{Correct: } A = 500 \left(1 – \frac{10}{100}\right)^3 = 364.5$

### Mr Mathematics Blog

#### Estimating Solutions by Rounding to a Significant Figure

Explore key concepts, FAQs, and applications of estimating solutions for Key Stage 3, GCSE and IGCSE mathematics.

#### Understanding Equivalent Fractions

Explore key concepts, FAQs, and applications of equivalent fractions in Key Stage 3 mathematics.

#### Transforming Graphs Using Function Notation

Guide for teaching how to transform graphs using function notation for A-Level mathematics.