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Multi-step problems are the heart of the FSCE 11+ exam. These are questions that cannot be answered in a single calculation — you need to work through several steps, choosing the right operation at each stage. This lesson teaches you a systematic approach to breaking down complex problems, with six fully annotated worked examples that show you exactly how to think through each question.
When you face a multi-step problem, follow this process:
Not all information in a question is immediately useful. Sometimes you need to calculate intermediate values first. Ask yourself: "What do I need to know before I can find the final answer?"
Example: "A shop sells boxes of 12 eggs for £2.40. Mrs Green buys 5 boxes. She uses 8 eggs to bake a cake and gives 1/3 of the remaining eggs to her neighbour. How many eggs does she have left?"
What you need to find: eggs left at the end. What you need to calculate first:
| Clue Words | Operation |
|---|---|
| total, altogether, sum, combined, plus, increased by | Addition |
| difference, less than, fewer, take away, decreased by, change, remaining | Subtraction |
| times, each, every, per, of (with fractions/percentages), product, groups of | Multiplication |
| share, split, divide, per (when finding one), each (when sharing) | Division |
Be careful: some words can indicate different operations depending on context. Always think about what makes sense.
Question: A family goes to a restaurant. Two adults order the roast dinner at £12.50 each, and three children order the children's menu at £7.95 each. They also order drinks totalling £8.60. They leave a 10% tip on the total bill. How much do they spend altogether?
Annotated step-by-step solution:
Step 1: What do I need to find? The total spent, including the tip.
Step 2: Calculate the food costs.
Step 3: Calculate the total bill before tip.
Step 4: Calculate the tip.
Step 5: Calculate the total spent.
Step 6: Check — does this make sense? Two adult meals (≈ £25), three children's meals (≈ £24), drinks (≈ £9) = ≈ £58. Plus 10% (≈ £6) = ≈ £64. Our answer of £63.20 is close. Sensible!
Answer: £63.20
Question: A cyclist rides at 15 km/h for 2 hours, then at 12 km/h for 1 hour 30 minutes. She then rests for 20 minutes before cycling the remaining 8 km at 16 km/h. What is her total journey time (including the rest)?
Annotated step-by-step solution:
Step 1: What do I need? Total time for the whole journey.
Step 2: Time for the first part — already given.
Step 3: Time for the second part — already given.
Step 4: Rest time.
Step 5: Time for the third part — need to calculate.
Step 6: Total time.
Answer: 4 hours 20 minutes.
Question: Tom and Lisa share a bag of 60 marbles in the ratio 2:3. Tom then gives 1/4 of his marbles to his sister. How many marbles does Tom have now?
Annotated step-by-step solution:
Step 1: What do I need? How many marbles Tom has after giving some away.
Step 2: Share 60 marbles in ratio 2:3.
Step 3: Tom gives away 1/4 of his marbles.
Step 4: Tom's remaining marbles.
Answer: Tom has 18 marbles.
Question: A rectangular garden is 12m long and 8m wide. The owner wants to lay turf on the whole garden except for a square flower bed in the corner that measures 3m by 3m. Turf costs £4.50 per square metre. How much will the turf cost?
Annotated step-by-step solution:
Step 1: What do I need? The total cost of the turf.
Step 2: Find the area of the whole garden.
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