CSSE Essex Style Problem Solving Paper 1
Within the CSSE-style maths test, problem-solving questions differ from routine calculation questions in that the pupil must first decide what the question is actually asking and which operations are needed, rather than being told directly to add, multiply or find a percentage, with the numbers needed often buried inside a longer worded scenario alongside numbers that are not needed at all. Problem Solving Paper 1 focuses on this planning step across multi-step worded problems drawn from everyday contexts such as shopping, travel and sharing.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole problem once through before doing any calculation, to understand the situation before hunting for numbers.
- Underline only the numbers and facts that are actually needed to answer the question, since worded problems often include extra detail that is not needed.
- Decide what the final answer needs to look like, such as a total, a difference, or an amount each, before choosing your first calculation.
- Break a multi-step problem into a numbered list of smaller calculations, and complete them in order.
- Label each stage of your working with what it represents, such as 'cost per person', so you do not lose track of what a number means partway through.
- Once you have a final answer, reread the original question and check your answer actually answers what was asked, not an earlier stage of the working.
- Check that your answer is a sensible size for the situation described, for example an amount of change should be smaller than the amount paid.
Worked example
Three friends, Priya, Sam and Tom, share the cost of a meal equally. The total bill is 46.50 pounds, but Priya also orders a dessert costing 4.20 pounds which she pays for herself on top of her share. (a) Find the amount each friend pays towards the shared bill. (b) Find the total amount Priya pays altogether.
- (a) Divide the total bill by the number of friends: 46.50 / 3.
- 46.50 / 3 = 15.50, so each friend pays 15.50 towards the shared bill.
- (b) Priya pays her share plus the dessert: 15.50 + 4.20.
- 15.50 + 4.20 = 19.70, so Priya pays 19.70 (19.70 pounds) altogether.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A shop sells notebooks at 1.60 pounds each. A pupil buys 3 notebooks and pays with a 10-pound note. How much change do they get?Show answer
Answer: 5.20 pounds (3 x 1.60 = 4.80; 10 - 4.80 = 5.20).
Q2A car travels 180 miles using 6 gallons of fuel. How many miles does it travel per gallon?Show answer
Answer: 30 miles per gallon.
Q3A class of 32 pupils is split into equal groups of 4 for a project. How many groups are there?Show answer
Answer: 8 groups.
Q4A ribbon 3.6m long is cut into pieces 0.4m long. How many pieces can be cut?Show answer
Answer: 9 pieces.
Q5A school buys 15 footballs at 8 pounds each and gets a 12-pound discount on the total order. How much does the school pay?Show answer
Answer: 108 pounds (15 x 8 = 120; 120 - 12 = 108).
Q6A jug holds 2 litres of juice. If 350ml is poured out, how many millilitres remain?Show answer
Answer: 1,650ml (2,000 - 350).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A family of 2 adults and 3 children visits a theme park. Adult tickets cost 22 pounds and child tickets cost 15 pounds. They also spend 18 pounds on lunch in total. (a) Find the total cost of the tickets. (b) Find the total amount spent by the family, including lunch. (c) If they had a voucher giving 5 pounds off the total ticket cost, how much would they have spent altogether including lunch?
Show mark scheme
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A gardener plants bulbs in rows. Each row has 14 bulbs, and the gardener plants 9 full rows. Bulbs are sold in bags of 20 for 6.50 pounds per bag. (a) How many bulbs does the gardener plant in total? (b) How many bags of bulbs must be bought, given that a part-used bag still has to be bought whole? (c) Find the total cost of the bags bought.
Show mark scheme
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Free printable worksheet
Want more practice on paper? Download the csse essex style problem solving paper 1 worksheet pack - 8 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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