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This is a SET 11+ Stage 2 Maths practice paper. Unlike Stage 1, this is NOT multiple choice — you must show your working and write your answers clearly. Stage 2 Maths tests deeper problem-solving and the ability to explain your reasoning.
Q1. (3 marks) A school has 480 pupils. 3/8 of them have packed lunch, 1/4 have school dinners, and the rest go home. How many pupils go home?
Q2. (3 marks) A shop sells pens in packs of 6 for 2.70 pounds, or individually for 50p each. Mr Davies needs 20 pens. What is the cheapest way to buy them, and how much does it cost?
Q3. (3 marks) The mean of four numbers is 15. Three of the numbers are 12, 18, and 14. What is the fourth number?
Q4. (4 marks) A rectangular garden is 12 m long and 8 m wide. A path 1 m wide runs around the inside edge. What is the area of the path?
Q5. (3 marks) A train leaves London at 09:35 and arrives in Manchester at 12:08. The return train takes 15 minutes longer. If it departs at 14:20, what time does it arrive in London?
Q6. (3 marks) In a sale, all prices are reduced by 20%. A pair of trainers now costs 44 pounds. What was the original price?
Q7. (4 marks) Here are the scores of 10 students in a test: 56, 72, 48, 65, 72, 81, 39, 72, 58, 67. Find: (a) the mode, (b) the median, (c) the range.
Q8. (3 marks) A cuboid has length 10 cm, width 6 cm, and height 4 cm. What is its volume? What is its surface area?
Q9. (4 marks) Solve these equations: (a) 5x - 3 = 22, (b) 2(x + 4) = 18
Q10. (3 marks) A map has a scale of 1:25,000. Two towns are 8 cm apart on the map. What is the real distance in kilometres?
Q11. (4 marks) A jar contains red, blue, and green sweets. The probability of picking red is 1/3 and the probability of picking blue is 5/12. There are 60 sweets in total. How many green sweets are there?
Q12. (3 marks) A number sequence starts: 5, 8, 11, 14, 17... (a) What is the rule? (b) What is the 20th term?
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