11+ Practice (England) · Numerical and Spatial Reasoning

Sequences, Number Puzzles and Spatial Reasoning in Words

22 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 22 questions

  1. What is the next number in the sequence 2, 4, 8, 16, ...?
  2. What is the next number in the sequence 100, 93, 86, 79, ...?
  3. What is the next number in the sequence 3, 6, 11, 18, 27, ...?
  4. In the Fibonacci-style sequence 1, 1, 2, 3, 5, 8, 13, ..., what is the next number?
  5. What is the next number in the sequence 2, 3, 5, 9, 17, ...?
  6. What is the next number in the sequence 5, 2, 9, 4, 13, 6, 17, ...?
  7. In each row, the third number follows the same rule from the first two numbers. Row 1: 3, 4, 11. Row 2: 5, 2, 9. Row 3: 6, 3, ?. What is the missing number?
  8. A number machine doubles the input, adds 3, then halves the result. The output is 9.5. What was the input?
  9. A square piece of paper is folded in half, then in half again, then in half a third time. One hole is punched through all the layers. How many holes appear when the paper is fully unfolded?
  10. A 3 by 3 by 3 cube is painted blue on the outside and then cut into 27 small cubes. How many small cubes have exactly two painted faces?
  11. An arrow points north. It is turned 270 degrees clockwise. Which way does it point now?
  12. A letter b is held up to a vertical mirror on its right-hand side. Which letter does the reflection look like?
  13. On a standard dice, opposite faces add up to 7. A dice is placed with 2 on the top and 3 facing you. It is then tipped forward over its bottom front edge, so the front face becomes the bottom. What nu…
  14. A 4 by 4 grid is made of 16 small squares. How many squares of all sizes can be found in the grid?
  15. A big triangle has four lines drawn from one corner to the opposite side, splitting it into five thin triangles. How many triangles of all sizes are there?
  16. Which solid can be made from a net with one square and four triangles?
  17. A robot faces east. It turns left, moves 3 units, turns left again and moves 3 units. Which way is it facing now?
  18. Three corners of a rectangle are at (1, 1), (5, 1) and (5, 4). What is the perimeter of the rectangle?
  19. A 3 by 3 magic square has rows, columns and diagonals that each add up to 15. The top row reads 2, ?, 6. What is the missing number?
  20. What is the next number in the sequence 2, 5, 10, 17, 26, ...?
  21. What is the angle between the hands of a clock at 3:30?
  22. What is the order of rotational symmetry of an equilateral triangle?

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