Mathematics (Syllabus D) 4024/22 — May/June 2021

Walkthrough

1. Identify the original price and the percentage decrease: The original price of the drill is $78 and it is reduced by $15\%$.
2. Calculate the reduction (discount): Find $15\%$ of $78 by multiplying $\frac{15}{100} \times 78 = 11.70$. This means the price is reduced by $11.70.
3. Find the sale price: Subtract the reduction from the original price:

Alternatively, you can multiply directly by the multiplier for a $15\%$ decrease:

Key Takeaways

• A percentage decrease can be found either by calculating the decrease amount and subtracting it, or by multiplying directly by $(1 - \text{rate})$.
• Currency answers with one decimal place like $66.3$ are conventionally written with two decimal places as $66.30$, although both $66.3$ and $66.30$ are accepted.

Common Mistakes

• Adding the $15\%$ instead of subtracting it (giving $89.70).
• Leaving the discount amount ($11.70) as the final answer instead of finding the sale price.

Things to Be Careful About

• Ensure the discount is subtracted from the original price, not added.
• Since this is a money problem, keep track of decimal points carefully.

Walkthrough

1. Convert dollars to euros: The exchange rate is $1 = €0.85. To convert $100 to euros, multiply by $0.85$:

1. Deduct the cost of the clock: Michael spends €58.99, so calculate the remaining money in euros:

1. Convert the remaining euros back to dollars: Since $1 = €0.85, to convert from euros back to dollars, divide by the exchange rate $0.85$:

Alternatively, convert the cost of the clock to dollars first ($\frac{58.99}{0.85} = 69.40$) and subtract from $100:

Key Takeaways

• To convert from the base currency (dollars) to the target currency (euros), multiply by the rate.
• To convert from the target currency (euros) back to the base currency (dollars), divide by the rate.

Common Mistakes

• Multiplying instead of dividing when converting euros back to dollars (e.g., computing $26.01 \times 0.85$).
• Mixing units by subtracting euros directly from dollars ($100 - 58.99$).

Things to Be Careful About

• Ensure you perform the conversion before or after the subtraction using the correct operation (multiply to get euros, divide to get dollars).

Walkthrough

1. Calculate Pietro's total (Simple Interest):
   • Principal $P = 3500$, Rate $R = 2.1\%$, Time $T = 4$ years.
   • Simple interest earned:

• Total amount in Pietro's account:

1. Calculate Eliana's total (Compound Interest):
   • Principal $P = 3500$, Rate $R = 2\%$, Time $n = 4$ years.
   • Total amount using the compound interest formula $A = P\left(1 + \frac{r}{100}\right)^n$:

1. Determine who has more and find the difference:
   • Pietro has $3794 and Eliana has $3788.51.
   • Pietro has more money.
   • Difference in amounts:

Key Takeaways

• Simple interest is calculated on the original principal every year: $I = \frac{PRT}{100}$. The total is $P + I$.
• Compound interest adds the interest to the principal at each compounding period: $A = P\left(1 + \frac{r}{100}\right)^n$, which directly gives the total amount.

Common Mistakes

• Adding the principal again to the compound interest formula result (i.e. computing $3500 + 3500(1.02)^4$).
• Using simple interest for both accounts or compound interest for both accounts.
• Premature rounding during compound interest calculation which might lead to inaccurate final differences.

Things to Be Careful About

• Ensure you state both parts of the required answer: the person's name (Pietro) and the numerical difference ($5.48 or $5.49).