Mathematics (Syllabus D) 4024/21 — October/November 2020

Walkthrough

The holiday costs 340 dollars per person and there are 2 people, so the normal total is

Because Naseem books before the discount deadline, he pays 8% less than the normal total. That means he pays 100% - 8% = 92% of the total. As a decimal, 92% is 0.92, so the amount paid is

This is 625.60 dollars.

Key Takeaways

A percentage decrease means multiplying by the amount that remains. To find the pay amount after an 8% discount, multiply by 0.92, not by 0.08. This question also tests multiplying a unit price by the number of people.

Common Mistakes

• Using 0.08 instead of 0.92. Multiplying by 0.08 gives the discount amount, not the amount paid.
• Forgetting the second person, which would give 312.80 dollars instead of 625.60 dollars.
• Writing the final money answer without two decimal places, although the mark scheme accepts 625.6 as well as 625.60.

Things to Be Careful About

Show the working as $680 \times 0.92$, since the mark scheme awards M1 for $2 \times 340 \times 0.92$. Keep the units in dollars and give the final money answer to 2 decimal places where appropriate.

Walkthrough

The final price of 241.50 includes the car price plus 15% tax. This means it is not 241.50 dollars before tax; it is 115% of the pre-tax price. If the pre-tax price is $x$, then

so to undo the tax we divide:

The car hire before tax is therefore 210 dollars.

Key Takeaways

When a price has 15% tax added, multiplying the pre-tax price by 1.15 gives the final price. To reverse this, divide the final price by 1.15. The multiplier is always 1 plus the decimal form of the percentage increase.

Common Mistakes

• Subtracting 15% of 241.50 from 241.50. This is wrong because 15% is 15% of the unknown original price, not 15% of the final price.
• Multiplying 241.50 by 1.15 instead of dividing. This would make the answer larger than the price paid.
• Using 0.15 as the divisor instead of 1.15.

Things to Be Careful About

Show the equation $1.15x = 241.50$ or the division $241.50 \div 1.15$ before the answer, since the mark scheme awards M1 when the correct method is seen. Keep the percentage as 115% throughout the working to avoid confusing 15% with the full amount.

Walkthrough

To find how many litres are used per 100 km, divide the total litres by the total kilometres to get litres per kilometre, then multiply by 100:

This means that a typical 100 km stretch of driving uses 3.7 litres of fuel.

Key Takeaways

Rates tell us one quantity per one unit of another. Here the unit is 100 km, so the same division must scaling and rate correctly by multiplying by 100.

Common Mistakes

• Writing 29.6 divided by 800 as 0.037 and forgetting to multiply the result by 100. That gives litres per km, not litres per 100 km.
• Dividing 800 by 29.6, which gives km per litre rather than litres per 100 km.
• Confusing the order: the litres must be the numerator and kilometres the denominator.

Things to be Careful About

Write the unit in the final answer: 3.7 litres per 100 km. The mark scheme awards M1 for $\frac{29.6}{800}\times 100$, so show this as the heading working line. Since this is a calculator component, evaluating the decimal is acceptable, but all work should still be shown.

Walkthrough

First convert the amount he takes to euros: because $1 is worth €0.82, multiply 450 by 0.82 to find how many euros that is:

On holiday he spends €297, so the remaining euros are

When he changes this back, the new rate says each 0.80 euros is equal to 1 dollar, so divide 72 by 0.80:

Therefore Naseem receives 90 dollars.

Key Takeaways

Currency conversion is a direct multiplication or division by an exchange rate. Deciding whether to multiply or divide depends on which currency is being converted to which. Also, two different rates must be used in two exchanges, so each step must use the correct rate.

Common Mistakes

• Using the same exchange rate when converting back. The rate has changed to $1 = €0.80, so the return conversion must use 0.80, not 0.82.
• Multiplying 72 by 0.80 instead of dividing it by 0.80. Since 1 dollar is 0.82 euros at that moment, to turn euros into dollars we divide by 0.80.
• Trying to subtract 297 from 450 directly. These amounts are in different currencies, so both must be in euros first.
• Rounding too early with the decimal exchange rates, which can change the final 90 dollars.

Things to Be Careful About

The mark scheme expects two method steps: one for $450 \times 0.82$ and one for $\frac{(369 - 297)}{0.80}$. Show both clearly. Include all units: dollars, euros, then dollars again. The final answer is exactly 90 dollars.