1. spatial-reasoning-s01-q01
A rectangular flag has a red top half and a blue bottom half. If the flag is rotated 180° (turned upside down), what color is now on top?
- Red
- Blue
- Half red, half blue
- White
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This is untimed educational practice for one cognitive skill. It is not a clinical, diagnostic, employment, or professionally recognized assessment, and it does not produce an IQ score or credential.
One hundred text-described visualisation exercises in ten themed sections, from simple flips to multi-step 3D challenges. Work untimed and picture each move carefully. Every answer comes with a short explanation of the method.
Choose one answer for each item. For a delayed-recall item, read its study text, cover it, and then answer without looking back.
Simple flips and quarter or half turns of flat shapes and letters, picture the move before answering.
1. spatial-reasoning-s01-q01
A rectangular flag has a red top half and a blue bottom half. If the flag is rotated 180° (turned upside down), what color is now on top?
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2. spatial-reasoning-s01-q02
The capital letter N is rotated 180° on the page. What does it look like now?
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3. spatial-reasoning-s01-q03
An arrow points to the right. After the arrow is rotated 90° clockwise, which way does it point?
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4. spatial-reasoning-s01-q04
A square card has a dot in its top-left corner. The card is flipped over left-to-right, like turning the page of a book. Viewed from the new front, where is the dot?
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5. spatial-reasoning-s01-q05
The lowercase letter b is rotated 180° on the page. Which letter does it now resemble?
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6. spatial-reasoning-s01-q06
A triangle points straight upward. It is rotated 180°. Which way does it now point?
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7. spatial-reasoning-s01-q07
A rectangular photo shows a person standing upright. The photo is rotated 90° anticlockwise. In the rotated photo, the person now appears to be…
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8. spatial-reasoning-s01-q08
A square tile has a dark stripe running from its bottom-left corner to its top-right corner. After the tile is rotated 90° clockwise, the stripe runs from…
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9. spatial-reasoning-s01-q09
How many degrees are in three-quarters of a full turn?
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10. spatial-reasoning-s01-q10
The digit 6 is rotated 180° on the page. Which digit does it now resemble?
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Track which compass direction you face after each described turn.
11. spatial-reasoning-s02-q01
You are facing North. You turn 90° clockwise, then another 90° clockwise. Which direction do you now face?
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12. spatial-reasoning-s02-q02
You are facing East. You turn 90° anticlockwise. Which direction are you now facing?
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13. spatial-reasoning-s02-q03
You face South and make a three-quarter turn (270°) clockwise. Which direction do you now face?
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14. spatial-reasoning-s02-q04
A weathervane arrow points North-East. The wind swings it 90° clockwise. Where does it point now?
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15. spatial-reasoning-s02-q05
You are facing West. You turn 180°, then 90° clockwise. Which direction are you facing?
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16. spatial-reasoning-s02-q06
You stand facing North. Which compass direction is directly to your right?
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17. spatial-reasoning-s02-q07
You face North and turn clockwise through 450°. Which direction do you face?
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18. spatial-reasoning-s02-q08
Facing South-West, you turn 180°. Which direction do you now face?
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19. spatial-reasoning-s02-q09
You make four 90° clockwise turns in a row. Compared with your starting direction, which way are you now facing?
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20. spatial-reasoning-s02-q10
You face East. You turn 90° clockwise, then 180°, then 90° clockwise again. Which direction do you face?
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Follow each route step by step and work out the finishing position relative to the start.
21. spatial-reasoning-s03-q01
You walk 3 blocks north, then 4 blocks east, then 3 blocks south. Relative to your starting point, where are you now?
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22. spatial-reasoning-s03-q02
You walk 5 blocks east, then 2 blocks west. How far are you from your starting point, and in which direction?
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23. spatial-reasoning-s03-q03
A delivery cyclist rides 2 km north, then 2 km east, then 2 km south, then 2 km west. Where does she finish relative to her start?
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24. spatial-reasoning-s03-q04
You walk 6 metres south, then 8 metres west. Measured in a straight line, how far are you from your starting point?
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25. spatial-reasoning-s03-q05
Starting at her front door, Amara walks 4 blocks north, then 1 block east, then 1 more block north. How many blocks north of her door is she?
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26. spatial-reasoning-s03-q06
You walk 3 blocks west, 2 blocks north, 3 blocks east, and 2 blocks north. Where are you relative to your starting point?
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27. spatial-reasoning-s03-q07
A robot on a square grid starts facing north. It repeats this loop twice: move forward 2 squares, turn 90° clockwise, move forward 1 square, turn 90° clockwise. Where does it finish relative to its starting square?
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28. spatial-reasoning-s03-q08
From camp, a hiker walks 5 km east, then 3 km north, then 5 km west. In a straight line, how far and in which direction must she walk to return to camp?
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29. spatial-reasoning-s03-q09
A taxi drives 1 km south, 2 km east, 3 km north, 2 km west, and finally 1 km south. Where does it finish relative to where it started?
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30. spatial-reasoning-s03-q10
A square walking trail has corners at its north-west, north-east, south-east, and south-west. You start at the south-west corner and walk clockwise around the trail exactly three-quarters of the way. At which corner do you stop?
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Decide how letters, words, and objects appear when reflected in a mirror.
31. spatial-reasoning-s04-q01
Which of these capital letters looks exactly the same when reflected left-to-right in a vertical mirror?
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32. spatial-reasoning-s04-q02
The capital letter E is reflected in a vertical mirror. Which way do its three horizontal arms now point?
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33. spatial-reasoning-s04-q03
You raise your right hand while facing a mirror. Which hand does your reflection appear to raise?
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34. spatial-reasoning-s04-q04
Which pair of lowercase letters are mirror images of each other across a vertical mirror line?
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35. spatial-reasoning-s04-q05
The word BOX is painted on the outside of a shop window. Read from inside the shop, what does it look like?
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36. spatial-reasoning-s04-q06
An analogue clock with no numerals shows exactly 3:00 (minute hand at the 12 position, hour hand at the 3 position). Viewed in a mirror, what time does it appear to show?
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37. spatial-reasoning-s04-q07
Which of these capital letters does NOT look the same after being reflected in a vertical mirror?
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38. spatial-reasoning-s04-q08
A left-hand glove is reflected in a mirror. What does the reflection show?
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39. spatial-reasoning-s04-q09
The word MUM is written in capital letters. Reflected in a vertical mirror, it reads…
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40. spatial-reasoning-s04-q10
The lowercase letter p is reflected in a horizontal mirror (flipped top-to-bottom). Which letter does it now resemble?
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Fold the paper in your mind, punch or cut, then unfold to count and place the holes.
41. spatial-reasoning-s05-q01
A square sheet of paper is folded in half left-to-right, then folded in half again top-to-bottom. A hole is punched through all layers at the folded corner. How many holes appear when the paper is fully unfolded?
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42. spatial-reasoning-s05-q02
A sheet of paper is folded in half once. A hole is punched through both layers. How many holes are there when the sheet is unfolded?
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43. spatial-reasoning-s05-q03
A square sheet is folded in half three times, then a hole is punched through every layer. How many holes appear when the sheet is fully unfolded?
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44. spatial-reasoning-s05-q04
A square sheet is folded in half left-to-right. A hole is punched close to the folded (creased) edge. When the sheet is unfolded, the two holes will be…
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45. spatial-reasoning-s05-q05
A square sheet is folded in half top-to-bottom, so the fold crease lies along the top of the folded rectangle. A hole is punched through both layers near the top-right of the folded rectangle. When unfolded, where are the holes?
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46. spatial-reasoning-s05-q06
A square sheet is folded in half twice, making four layers. A hole is punched through only the top two of the four layers. How many holes are there when the sheet is unfolded?
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47. spatial-reasoning-s05-q07
A square sheet of paper is folded along its diagonal to make a triangle. A hole is punched through both layers at the centre of the triangle. When unfolded, how many holes are there and how are they arranged?
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48. spatial-reasoning-s05-q08
Each fold of a sheet doubles the number of layers. After four folds, a hole is punched through every layer. How many holes appear when the sheet is unfolded?
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49. spatial-reasoning-s05-q09
A square sheet is folded in half by bringing its left edge across to its right edge. A small triangle is then snipped off the top corner on the creased side. What does the cut look like when the sheet is opened out flat?
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50. spatial-reasoning-s05-q10
A square sheet is folded in half top-to-bottom, then in half left-to-right, giving four layers. One hole is punched through all four layers away from any fold or edge. Then a second hole is punched in a different spot through the top layer only. How many holes are in the sheet once it is fully unfolded?
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Keep track of a cube's faces as it spins, tips, and rolls.
51. spatial-reasoning-s06-q01
A cube has letter A on top, letter B on the front face, and letter C on the right face. If the cube is rotated 90° clockwise around the vertical axis (viewed from above), which letter is now on the front face?
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52. spatial-reasoning-s06-q02
On a standard die, opposite faces always add up to 7. If the 3 is on top, which number is on the bottom face?
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53. spatial-reasoning-s06-q03
A cube has a star on its top face. The cube is tilted toward you by 90°, so the top face swings down to face you directly. Where is the star now?
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54. spatial-reasoning-s06-q04
A cube has the number 1 on its front face and 2 on its top face. The cube is rotated 180° about its vertical axis. Where is the 1 now?
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55. spatial-reasoning-s06-q05
A die shows 5 on top and 3 on the face toward you. The die is rolled one face to the right, tipping over its bottom-right edge. Which number now faces you?
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56. spatial-reasoning-s06-q06
A cube has a red top face, a blue bottom face, and a green face toward you. The cube is rolled 90° away from you, tipping over its far bottom edge. Which colour is now on top?
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57. spatial-reasoning-s06-q07
On a standard die (opposite faces sum to 7), the 2 faces you and the 6 is on top. Which number is on the face pointing directly away from you?
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58. spatial-reasoning-s06-q08
A cube has a different letter on each of its six faces, with P on top. If the cube is only ever spun about its vertical axis (P stays on top), how many different faces can be brought round to face you?
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59. spatial-reasoning-s06-q09
A cube shows 4 on top and 1 on the face toward you. It is first rotated 90° clockwise about its vertical axis (viewed from above), then tilted toward you by 90° so the top face swings down to face you. Which number faces you now?
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60. spatial-reasoning-s06-q10
Two opposite faces of a cube are painted red and the remaining four faces are painted white. How many of the cube's 12 edges lie between one red face and one white face?
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Fold flat nets into cubes and reason about which faces touch or oppose each other.
61. spatial-reasoning-s07-q01
A cube net is a vertical strip of four squares numbered 1 to 4 from top to bottom, with square 5 attached to the left of square 2 and square 6 attached to the right of square 2. When it is folded into a cube, which face is opposite face 2?
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62. spatial-reasoning-s07-q02
A cube net is a vertical strip of four squares numbered 1 to 4 from top to bottom, with square 5 attached to the left of square 2 and square 6 attached to the right of square 2. When it is folded into a cube, which face is opposite face 5?
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63. spatial-reasoning-s07-q03
Six identical squares are joined edge-to-edge in one straight row. Can this shape fold up into a cube?
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64. spatial-reasoning-s07-q04
A cube net has a horizontal row of three squares (L (left), C (centre), R (right)) with a column of three more squares C1, C2, C3 hanging directly below C, in that order. After folding into a cube, which face does NOT share an edge with face L?
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65. spatial-reasoning-s07-q05
On a flat cube net, a heart is printed on one square and an arrow on a square that shares an edge with it. After the net is folded into a cube, the heart face and the arrow face will…
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66. spatial-reasoning-s07-q06
Six squares are arranged in a solid 2×3 rectangle (two rows of three). Can this shape fold up into a cube?
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67. spatial-reasoning-s07-q07
A cross-shaped cube net has a centre square X with squares N, E, S, and W attached to its four sides, and one more square B attached below S. When folded, which face ends up opposite X?
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68. spatial-reasoning-s07-q08
A cross-shaped cube net has a centre square X with squares N, E, S, and W attached to its four sides, and one more square B attached below S. When folded, which face ends up opposite E?
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69. spatial-reasoning-s07-q09
Eight identical small cubes are glued together into one larger 2×2×2 cube. How many faces of each small cube are visible on the outside of the large cube?
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70. spatial-reasoning-s07-q10
A die is folded from a net so that 1 is opposite 6, 2 is opposite 5, and 3 is opposite 4. The faces 1, 2, and 3 meet at one corner of the die. Which three faces meet at the diagonally opposite corner?
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Count cubes, painted faces, and visible surfaces in assembled block shapes.
71. spatial-reasoning-s08-q01
A cube is painted red on all six faces, then cut into 27 equal smaller cubes (a 3×3×3 grid). How many of the small cubes have paint on exactly two faces?
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72. spatial-reasoning-s08-q02
A cube is painted on all six faces and cut into 27 equal smaller cubes (a 3×3×3 grid). How many of the small cubes have paint on exactly three faces?
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73. spatial-reasoning-s08-q03
A 4×4×4 cube is painted on all six faces and cut into 64 equal small cubes. How many small cubes have paint on exactly two faces?
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74. spatial-reasoning-s08-q04
A cube is painted on all six faces and cut into 27 equal smaller cubes (a 3×3×3 grid). How many of the small cubes have paint on exactly one face?
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75. spatial-reasoning-s08-q05
A staircase shape is built from identical cubes: a bottom row of 3 cubes, a row of 2 cubes stacked on the back two, and 1 cube on top of the back one. How many cubes are used in total?
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76. spatial-reasoning-s08-q06
A staircase shape is built from identical cubes: a bottom row of 3 cubes running away from you, 2 cubes stacked on the two farthest, and 1 cube on top of the farthest one. Looking straight down from above, how many squares do you see?
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77. spatial-reasoning-s08-q07
A staircase shape is built from identical cubes: a bottom row of 3 cubes running away from you, 2 cubes stacked on the two farthest, and 1 cube on top of the farthest one. Viewed exactly side-on, how many unit squares make up its silhouette?
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78. spatial-reasoning-s08-q08
A 2×2×2 cube built from 8 small cubes is painted on all outside faces. How many of the small cubes have paint on exactly three faces?
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79. spatial-reasoning-s08-q09
A 3×3×3 cube of 27 small cubes sits on a table and is painted on every face except the bottom, which stays unpainted against the table. How many small cubes end up with no paint at all?
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80. spatial-reasoning-s08-q10
A shape is built from unit cubes: a flat 3×3 layer of 9 cubes on a table, with 1 more cube placed on the centre of the top. Counting every visible cube face (the faces against the table are hidden), how many faces can be seen from outside?
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Match solids to their top, front, and side views, and predict cross-section shapes.
81. spatial-reasoning-s09-q01
A cylindrical tin stands upright on a table. Viewed from directly above, what shape do you see?
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82. spatial-reasoning-s09-q02
A cylindrical tin stands upright on a shelf. Viewed straight on from the side, what is the outline of its silhouette?
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83. spatial-reasoning-s09-q03
A pyramid with a square base sits on that base. Viewed straight on from the front at table height, what is its silhouette?
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84. spatial-reasoning-s09-q04
A cone is sliced by a flat cut parallel to its base, partway up. What is the shape of the newly cut surface?
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85. spatial-reasoning-s09-q05
A cube is cut exactly in half by a vertical plane passing through two opposite vertical edges (so the cut runs along the diagonals of the top and bottom faces). What is the shape of the cut surface?
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86. spatial-reasoning-s09-q06
A solid sphere is cut by a flat plane, anywhere and at any angle. The cut surface is always…
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87. spatial-reasoning-s09-q07
A solid object's view from directly above is a circle, and its view from the front is a triangle. Which solid fits both views?
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88. spatial-reasoning-s09-q08
A solid object's views from above, from the front, and from the side are all identical squares. Which solid fits?
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89. spatial-reasoning-s09-q09
One corner of a cube is sliced off by a flat cut passing through the three vertices nearest that corner. What is the shape of the cut surface?
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90. spatial-reasoning-s09-q10
A ring doughnut (torus) lies flat on a table. Viewed from directly above, what do you see?
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Combined, multi-step visualisation problems. Take them one transformation at a time.
91. spatial-reasoning-s10-q01
A standard die (opposite faces always sum to 7) rests with 1 on top and 2 on the face nearest you. It is rolled 90° away from you twice, tipping over its far bottom edge each time. Which number is on top after the second roll?
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92. spatial-reasoning-s10-q02
You are reading a map with north at the top. You rotate the map 90° anticlockwise. Which compass direction now points toward the top of the map?
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93. spatial-reasoning-s10-q03
An ant walks on the outside of a cube with 1-metre edges, from one corner to the corner diagonally opposite (through the cube's centre if it could tunnel). Staying on the surface and taking the shortest possible route, how far does it walk?
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94. spatial-reasoning-s10-q04
A cube shows a different symbol on each face. From your viewpoint you can see the star (front face), the moon (top face), and the sun (right face). The cube is rotated 180° about its vertical axis. Which of those three symbols can you still see?
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95. spatial-reasoning-s10-q05
An analogue clock shows exactly 3:00. If you turn the whole clock upside down (rotate it 180°), what time does it appear most like?
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96. spatial-reasoning-s10-q06
A transparent sheet of film is printed with the letter R. The film is flipped over left-to-right, then rotated 180°. What does the R look like now?
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97. spatial-reasoning-s10-q07
You start facing north. You walk 10 m forward, turn 90° clockwise, walk 10 m, turn 90° clockwise again, and walk 10 m. Which direction are you facing, and where are you relative to your start?
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98. spatial-reasoning-s10-q08
A cube with 3 cm edges is dipped fully in paint, dried, then cut into 1 cm cubes, and all 27 small cubes are dropped into a bag. Among the cubes in the bag, which number of painted faces is the most common?
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99. spatial-reasoning-s10-q09
A cube is rotated 90° clockwise about its vertical axis three times in a row. This has the same result as which single rotation?
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100. spatial-reasoning-s10-q10
A cube has 1 on top, 6 on the bottom, 2 facing north, 5 facing south, 3 facing east, and 4 facing west. It rolls one face-length toward the east, then one face-length toward the north. Which number is on top after both rolls?
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