Mathematics (Syllabus D) 4024/22 — May/June 2022
Cambridge O-Level · Calculator · worked solutions for every part, with the mark scheme
Topics Algebra and Graphs · Number · Statistics · Trigonometry · Coordinate Geometry · Probability · +4 more
In 2021, the cost of posting a letter was 84 cents.
A company posts 1950 letters.
Find the cost, in dollars, to post these letters.
$ ______
Approach
Multiply the number of letters by the cost per letter in cents.
Then divide the total cents by 100 to obtain dollars.
Working
The total is 163800 cents, so in dollars,
Answer
The cost is 1638 dollars.
1638 dollars
Walkthrough
Each letter costs 84 cents, so the total is found by multiplying 84 by 1950. Splitting 84 into 80 and 4 makes the multiplication easier. All 163800 cents is then divided by 100, because 100 cents make one dollar.
Key Takeaways
This part tests multiplying a unit cost by a quantity and converting cents to dollars correctly.
Common Mistakes
The most common mistake is writing 163800 cents as the final answer instead of dividing by 100 to obtain 1638 dollars. Another common mistake is dividing by 10 instead of 100.
Things to Be Careful About
Check the unit requested in the answer line. The total is in cents, but the answer must be given in dollars.
In 2022, the cost of posting a letter is 96 cents.
Calculate the percentage increase in the cost of posting a letter.
______ %
Approach
Subtract the 2021 cost from the 2022 cost to find the increase, then divide by the original 2021 cost and multiply by 100.
Working
Answer
The percentage increase is 14.3% (or 14.28 to 14.29).
14.3%
Walkthrough
The increase in the cost of a letter is 96 - 84 = 12 cents. To express this as a percentage increase, compare the increase with the original cost, 84 cents. So calculate (12/84) × 100. Since 12/84 simplifies to 1/7, the percentage is 14.2857%, usually given as 14.3% on a calculator paper.
Key Takeaways
Percentage increase is always found by dividing the increase by the original amount, not by the new amount.
Common Mistakes
Dividing by 96 instead of 84 would incorrectly give 12.5%. Also, writing 14.2857 without converting to a percentage is wrong.
Things to Be Careful About
The mark scheme allows 14.3 or 14.28 to 14.29. The answer line expects a percentage, so the percentage sign must appear.
| Cost of posting a letter is 96 cents |
|---|
| 15% discount when monthly postage is more than $1000 |
Company posts 1200 letters in one month.
Company posts fewer letters than Company in the same month.
Company and Company each pay the same amount to post their letters that month.
Find the number of letters Company posts in that month.
______
Approach
Company A's monthly postage before discount is 1200 × 96 cents, which exceeds the discount threshold. Apply the 15% discount, then divide the discounted amount by 96 cents to find how many letters Company B posts.
Working
This is 115200 cents, which is 1152 dollars and is above the 1000-dollar threshold, so the discount applies.
After a 15% discount, 85% of the total is paid:
Company B pays the same total, 97920 cents, at 96 cents per letter:
Answer
1020
1020
Walkthrough
Company A posts 1200 letters at 96 cents each, so the full bill is 115200 cents. Since this is 1152 dollars, the 15% discount applies. A 15% discount means paying only 85% of the total. So the final amount is 115200 × 0.85 = 97920 cents.
Company B pays the same final amount, but because B posts fewer letters, its total monthly postage is below the discount threshold. Therefore B pays the ordinary rate of 96 cents per letter. Dividing 97920 by 96 gives 1020 letters.
Key Takeaways
The discount applies to the total monthly postage, and the final amount Company B pays is the same as Company A's discounted amount.
Common Mistakes
A common error is to subtract 15% from the number of letters by calculating 1200 - 180 = 1020 without showing the monetary reasoning; here this gives the correct 1020 but full working must still be shown because the answer is nfww.
Another common error is to apply the 15% discount also to Company B's letters. Since B posts fewer letters, its bill is below the discount threshold, so B pays the ordinary price.
Things to Be Careful About
The mark scheme says nfww, so a correct final answer without correct working may not receive full marks. Show all the steps in the order that explains why 1020 is obtained.
In 2022, the cost of posting a parcel with a mass of or less is $4.60.
The cost increases by $1.10 for each additional .
Find the cost of posting a parcel with a mass of .
$ ______
Approach
Subtract the first 1 kg from the given mass, then find how many 0.5 kg intervals the extra mass represents. Multiply that number by 1.10 and add the initial 4.60.
Working
Extra mass above 1 kg:
Number of 0.5 kg intervals:
Total cost:
Answer
The cost is 10.10 dollars.
10.10 dollars
Walkthrough
The first kilogram costs 4.60. For a 3.5 kg parcel, the mass above that first kilogram is 2.5 kg. Each additional 0.5 kg costs 1.10, so the number of extra intervals is 2.5 ÷ 0.5 = 5. Five intervals cost 5 × 1.10 = 5.50. Adding the initial 4.60 gives 10.10.
Key Takeaways
The key is to exclude the first kilogram from the extra intervals before counting 0.5 kg steps.
Common Mistakes
A common mistake is to divide 3.5 by 0.5 directly and multiply by 1.10, then add 4.60, which gives the wrong amount because the first kilogram is overcounted.
Things to Be Careful About
The answer must be in dollars, so keep the money unit. The exact answer is 10.10, not 10.1 with no units; include two decimal places when giving a money amount.
The cost of posting parcels increases by 7.2%.
After the increase, the cost of posting a parcel is $13.40.
Calculate the original cost of posting this parcel.
$ ______
Approach
Let the original cost be . After a 7.2% increase, the new cost is 107.2% of the original, so . Solve for by dividing.
Working
Answer
The original cost was 12.50 dollars.
12.50 dollars
Walkthrough
The final cost, 13.40, is the cost after a 7.2% increase. That means 13.40 represents 100% + 7.2% = 107.2% of the original cost. To find the original cost, divide the final cost by 1.072. 13.40 ÷ 1.072 = 12.5, so the original parcel cost 12.50.
Key Takeaways
This question tests reverse percentages: the original amount is found by dividing the new amount by the multiplier corresponding to the increase.
Common Mistakes
A common mistake is to multiply 13.40 by 7.2% and subtract the result, giving approximately 12.44 instead of 12.50. Remember that the 7.2% is taken from the original cost, not from 13.40.
Things to Be Careful About
The answer is a price, so give it to two decimal places: 12.50 dollars. Do not round before the division because the exact multiplier 1.072 is needed.
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