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This is your second CEM 11+ Maths and Non-Verbal Reasoning practice paper. It covers algebra, ratio, data handling, and more advanced spatial reasoning — all interleaved as in the real CEM exam.
Q1. What are the next two numbers in this sequence: 5, 11, 17, 23, 29, ___, ___? (1 mark)
Q2. Solve: 3x + 8 = 29 (2 marks)
Q3. If p = 4 and q = 7, find the value of 3p + 2q - 5. (2 marks)
Q4. Share 90 pounds between two friends in the ratio 2:3. How much does each person get? (2 marks)
Q5. A recipe for 6 people requires 450 g of pasta. How much pasta is needed for 10 people? (2 marks)
Q6. The mean of four numbers is 15. Three of the numbers are 12, 14, and 18. What is the fourth? (2 marks)
Q7. A pie chart shows how 80 pupils travel to school. The "bicycle" sector has an angle of 72 degrees. How many pupils cycle? (1 mark)
Q8. The range of a set of numbers is 19. The largest number is 31. What is the smallest? (2 marks)
Q9. A white triangle is to a black triangle as a white circle is to ___? (1 mark)
Q10. A shape with 3 sides and 1 dot is to a shape with 4 sides and 2 dots. A shape with 5 sides and 3 dots is to ___? (2 marks)
Q11. Using shape codes: Triangle=T, Square=S, Circle=C; Large=L, Small=s; Black=B, White=W. What is the code for a large white circle? (1 mark)
Q12. The code is S, s, B. Describe the shape. (1 mark)
Q13. Two shapes have codes T, L, B and T, L, W. What is the only difference? (1 mark)
Q14. A pattern has three independent features. Outer shape: 4-cycle (triangle, square, pentagon, hexagon). Dot position: 2-cycle (top, bottom). Shading: 3-cycle (black, grey, white). Frame 1: triangle, dot at top, black. What is frame 7? (3 marks)
Q15. Four shapes in a row: a small circle, a medium circle, a large circle, a small square. Which is the odd one out? (1 mark)
Q16. A right-pointing arrow is reflected in a vertical mirror line. What direction does the reflected arrow point? (1 mark)
Q17. A cube has a star on top and a circle on the front. It is rotated 90 degrees to the right. What shape is now on the front? (1 mark)
Q18. A circle has a radius of 7 cm. Using pi = 22/7, what is the circumference? (2 marks)
Q19. Two angles of a triangle are 55 degrees and 70 degrees. What is the third angle? (1 mark)
Q20. Convert 3,750 millilitres to litres. (1 mark)
Q21. A train leaves at 10:48 and arrives at 13:15. How long is the journey? (2 marks)
Q22. Tickets cost 7 pounds for adults and 4 pounds for children. A group of 3 adults and 5 children buys tickets. What is the total cost? (2 marks)
Q23. A shop sells pencils at 45p each. Emma has 4 pounds. How many pencils can she buy, and how much change will she get? (2 marks)
Q24. A car travels at 50 miles per hour. How far does it travel in 1 hour 48 minutes? (2 marks)
Q25. A rectangular garden is 20 m long and 14 m wide. A path 2 m wide runs around the outside. What is the total area including the path? (2 marks)
| Section | Marks available |
|---|---|
| A: Algebra, Ratio & Data | 14 |
| B: NVR — Analogies & Codes | 12 |
| C: Geometry, Measurement & Problem Solving | 14 |
| Total | 40 |
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