Many of the Core Maths qualifications involve preliminary material that students need to gain familiarity with before the exam. In a non-Covid year, lots of teachers think about these materials, consider what their students need to know and create potential questions for them to answer.
The summer 2021 exam papers are being used by a small number of students who will be doing the (inaccurately named) resit option in October. A group of us (Tom, Chloe, Sue, Jane, Zoe and Mark) explored the AQA materials and gathered some ideas.
Paper 1
Preliminary materials
- The reduction of the personal allowance is new here.
- This reduction is only challenging for people who earn between £100,000 and £125,000. Below that amount the personal allowance applies in full, while above that there is no allowance at all.
- Students should note the figures that are here and use them; they are different from those that were in use in previous years.
Possible questions:
- Choose salary amounts that fall into the lowest rate only, that cross into the middle band and that cross £100,000. Calculate the amount of tax paid each time.
- See the image about lorry drivers. If you and your partner both earn £53,000 per year, how much tax do you pay? What if one member of the family earns £106,000 per year? How much tax would they pay?
- There is no ‘allowance’ to be subtracted before working out the NI that is due (but there is a zero-rated band).
- You start paying NI before you start paying income tax.
- Income tax is progressive, in that the more you earn, the higher the percentage rate becomes, whereas higher earners pay a lower percentage on their highest earnings in NI.
- National Insurance is paid on your original salary (don’t subtract the tax first!).
- Student Loan repayment is also done on your original salary (the ‘gross income’).
- There are three separate things going on with Student Loans:
- You pay 9% of your income, regardless of how much you owe.
- There are two different thresholds at which you start paying, depending on when you started university.
- Interest is added to the amount you owe: using the figures that are given, this is 5.4%.
Possible
questions:
1) Kadir is a senior foreign exchange broker and earns £120
000 per annum.
He has paid off his student loans.
a)
What is his personal allowance for income tax?
b)
Calculate his net monthly pay.
2) Beyza is a real estate lawyer.
She graduated in 2005 and now earns £65 000 as a Senior
Counsel.
a)
Calculate her monthly student loan repayment.
b)
How much money does she have left per week after
paying her tax, NI and student loan?
3) You owe £29,000 on your student loan. At the end of a year you need to add on the
interest and then make a payment of 9% of your salary (assuming it is over the
threshold). If you earn £40,000 per
year, how much will you still owe on your student loan after three years?
Points to ensure the students understand:
- The plot sizes include the garden, and are given for a 4-bed house (presumably it will be smaller for a house with fewer bedrooms).
- 1 hectare is equivalent to the area of a square of side 100 metres.
Possible questions:
This information could be used as the starting point for an extended project. For example, students could be given a number of houses to plan for and could be asked to create a map of the new estate (perhaps on a hectare of land). (This could be extended to include building costs and prices of houses.)
- Estimate the scale of the given photograph.
- In the middle of the photograph there is a park. Estimate the area of the park, clearly stating all your assumptions.
- Estimate how many houses could reasonably be built on 1 hectare of land.
There is a lot of material here about the same topic. It is broken down here.
Blue: How much came from households? What might have produced the rest of the
plastic waste?
Pink: What is/isn’t included? What is a “waste stream”? What does “packaging” refer to?
Green: What is the difference between the government estimates and the WWF estimates? Why might they be different? How might these estimates have been reached?
Yellow: 9% (of the plastic waste “which was sent to treatment”) is 53,400 tonnes. How much plastic waste does this mean there is altogether? What is the problem here?
Blue: Calculate the amount that is recycled and
landfilled using the WWF figures.
Possible
questions:
1)
What is the life-cycle of a bottle of soft
drink?
2)
Estimate how many kg of plastic each person in
the UK is responsible for each year (using the WWF figures).
3) A newspaper article says that the WWF calculation for the plastic waste generated in 2014 was 4 times as much as the government-estimated amount. Use the figures in the briefing to determine whether this is true.
There are lots of issues with this graph! (Some of these overlap with the questions below.
- ‘EU28’ is presumably the value for all EU countries (including, at the time, the UK). This could have been highlighted to show it encompasses the whole EU.
- The scale is difficult to read and to apply to countries further up the list.
- The size of the country is surely relevant. Malta has a population of under 0.5 million, so is less of a concern than France, which is now the second biggest country in the EU (pop: 67 million).
- It doesn’t mention whether each country produces the same amount of waste per person (just the percentage of that which is produced which is then recycled).
- What does “recycling/recovery” actually mean?
Possible questions
- What might be misleading about the graph?
- Suggest two ways the graph could be improved
Possible questions
- Using the graph, estimate the amounts of plastic waste exported to China/Hong Kong in 2017 and 2018. Calculate the % fall in the amount.
- A newspaper article suggests that the plastic waste that is exported for recycling does not actually get recycled and may end up as landfill overseas or polluting the oceans. Using the graph on page 4 and the UK government estimates on page 2, work out a new estimate for the proportion of the UK’s plastic waste that was actually recycled in 2016.
Other links
Here are some other links that might be of use:
https://www.youtube.com/watch?v=B_PAK4aMQ14 Chap on Question Time talking about tax
https://www.bbc.co.uk/news/uk-57139474 News story about recycling
https://commonslibrary.parliament.uk/research-briefings/cbp-8515/ Updated version of this information. What has changed?
Final thought
I got lots out of talking to others about this. I would encourage all teachers of Core Maths to take the opportunity to talk to colleagues about the preliminary material ... and then to blog about their ideas!
