Mathematics (Syllabus D) 4024/12 — October/November 2013
Cambridge O-Level · Non-calculator · worked solutions for every part, with the mark scheme
Topics Algebra and Graphs · Number · Geometry · Statistics · Coordinate Geometry · Probability · +3 more
Amy buys 3 drinks at $1.86 each and 1 drink for $2.04.
She pays for the 4 drinks with a $10 note.
How much change should she receive?
$ ______
Approach
Calculate the total cost of all drinks purchased and subtract this amount from the $10 note to find the change.
Working
First, calculate the cost of the 3 drinks at $1.86 each:
Add the cost of the fourth drink ($2.04) to find the total cost:
Subtract the total cost from the $10 note:
Answer
The change received is $2.38.
2.38
Walkthrough
Amy buys several drinks at different prices. To find her change, we first need to know exactly how much she spent in total. We start by multiplying the price of one drink by the quantity bought (). Then we add the price of the single drink she also bought (). Finally, since she paid with a $10 note, we subtract the total spending from 10 to see what is left over.
Key Takeaways
- Always calculate the full cost before determining change.
- When adding currency, ensure decimal places are aligned correctly.
Common Mistakes
- Forgetting to include the fourth drink in the total cost.
- Subtracting the individual drink costs directly from 10 instead of summing them first.
- Arithmetic errors in multiplication or addition of decimals.
Things to Be Careful About
- Ensure the final answer is formatted as currency if required, though here just the number is asked. The mark scheme accepts 'oe' (other equivalent), but standard decimal notation is expected for money.
$180 is shared between Ali and Ben so that Ali’s share : Ben’s share = .
Find Ali’s share.
$ ______
Approach
The total amount is shared in the ratio . We find the total number of parts, divide the total amount by this number to get the value of one part, and then multiply by Ali's number of parts (4).
Working
Total parts in the ratio:
Value of one part:
Ali’s share is 4 parts:
Answer
Ali’s share is $80.
80
Walkthrough
We have a total sum of $180 to split between two people, Ali and Ben, in the ratio . This means for every 4 units Ali gets, Ben gets 5. First, we combine these units to find the total number of shares (). Next, we determine how much one single 'share' or 'part' is worth by dividing the total money by the total parts (). Finally, since Ali owns 4 of those parts, we multiply the value of one part by 4 to get his total share.
Key Takeaways
- Ratio problems often involve finding the 'value of one part' first.
- The total number of parts is the sum of the ratio numbers.
Common Mistakes
- Dividing the total by only one part of the ratio (e.g., ).
- Multiplying the total by the ratio number (e.g., ).
- Confusing whose share corresponds to which number in the ratio (Ali is 4, not 5).
Things to Be Careful About
- Check that the question asks for the correct person's share (Ali, not Ben).
- The mark scheme shows '', meaning 80 or 80.00 are both acceptable.
The rest of this paper
25 more questions- Q2Number2M
- Q3Algebra and Graphs2M
- Q4Number2M
- Q5Geometry2M
- Q6Algebra and Graphs2M
- Q7Number2M
- Q8Algebra and Graphs2M
- Q9Number2M
- Q10Algebra and Graphs2M
- Q11Number · Geometry3M
- Q12Number · Algebra and Graphs3M
- Q13Algebra and Graphs3M
- Q14Statistics3M
- Q15Algebra and Graphs · Coordinate Geometry3M
- Q16Mensuration3M
- Q17Algebra and Graphs4M
- Q18Statistics · Probability4M
- Q19Coordinate Geometry4M
- Q20Transformations and Vectors · [Legacy] Matrices4M
- Q21Probability4M
- Q22Geometry4M
- Q23Algebra and Graphs4M
- Q24Geometry4M
- Q25Algebra and Graphs5M
- Q26Geometry5M