CSSE Essex Style Problem Solving Paper 2
CSSE Essex Problem Solving Paper 2 continues from Paper 1's focus on planning a worded problem before calculating, but introduces ratio, proportion and sharing into the multi-step scenarios, on top of the everyday contexts, such as shopping, travel and sharing, seen in Paper 1. As before, the numbers needed are often mixed in with extra detail that the question does not actually require.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the whole problem once before calculating, and decide what type of answer is needed, such as an amount each, a total, or a difference.
- Where a ratio is involved, find the value of one part or one share before working out any of the amounts the question asks for.
- Underline only the figures that are actually needed for the calculation, since CSSE-style problem-solving questions often include numbers that are not required.
- Break the problem into a numbered sequence of smaller steps, and complete each one before moving to the next.
- Label each intermediate value with what it represents, especially in a sharing or ratio problem, so you do not confuse one person's share with another's.
- Reread the original question once you have an answer, to check it answers exactly what was asked and is a sensible size for the situation.
Worked example
Two friends, Jess and Kim, share 72 pounds of birthday money in the ratio 5:3. Jess then spends 18 pounds of her share on a game. (a) Find how much money Jess receives before spending anything. (b) Find how much money Jess has left after buying the game.
- Find the value of one share: the total ratio parts are 5 + 3 = 8, so 72 / 8 = 9 pounds per part.
- Find Jess's share before spending: 5 x 9 = 45 pounds.
- Subtract what Jess spends on the game: 45 - 18.
- 45 - 18 = 27, so Jess has 27 pounds left.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A total of 60 pounds is shared between two people in the ratio 2:3. Find the larger share.Show answer
Answer: 36 pounds (60 / 5 = 12; 3 x 12 = 36).
Q2A shop sells pens in packs of 8 for 4.80 pounds. A pupil buys 3 packs and pays with a 20-pound note. How much change do they get?Show answer
Answer: 5.60 pounds (3 x 4.80 = 14.40; 20 - 14.40 = 5.60).
Q3A journey of 210 miles is shared equally between 3 drivers, who each drive an equal distance. How far does each driver drive?Show answer
Answer: 70 miles (210 / 3).
Q4A recipe uses flour and butter in the ratio 3:1. If 45g of butter is used, how much flour is needed?Show answer
Answer: 135g (3 x 45).
Q5A ribbon 84cm long is cut in the ratio 4:3. Find the length of the shorter piece.Show answer
Answer: 36cm (84 / 7 = 12; 3 x 12 = 36).
Q6A total bill of 56 pounds is split equally between 4 friends, but one friend also owes an extra 5 pounds for a drink they had alone. Find how much that friend pays in total.Show answer
Answer: 19 pounds (56 / 4 = 14; 14 + 5 = 19).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A charity collection of 180 pounds is shared between two projects in the ratio 5:4. The project receiving the smaller share then receives a further 8 pounds from a separate donation. (a) Find the value of one share. (b) Find the amount each project receives from the original collection. (c) Find the total amount received by the project with the smaller original share, once the extra donation is included.
Show mark scheme
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A minibus of 15 seats is shared between two schools in the ratio 3:2 for a joint trip. Each school pays 6 pounds per seat used towards the minibus hire, plus a fixed 20-pound booking fee split equally between the two schools. (a) Find how many seats each school uses. (b) Find how much the school with fewer seats pays for its seats. (c) Find the total amount, including its share of the booking fee, that the school with fewer seats pays.
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Free printable worksheet
Want more practice on paper? Download the csse essex style problem solving paper 2 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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