Speed as well as accuracy is important in this section. Work quickly, or you might not finish the paper. There are no penalties for incorrect responses, only marks for correct answers, so you should attempt all questions. Each question is worth one mark.

Calculators are NOT permitted.

Here you will find all TSA Cube questions that have been written 2008-2019.

The cut out below was folded together to make a cube.

14. Which of the following cubes was formed from this cut-out?
1
1

## Explanation

If we rotate the net shown by 180 degrees, fold it keeping the face with the cross facing towards us, and then tilt the cube 45 degrees clockwise so the face with the cross is facing slightly to the left, the cube would look the same as in E, which is the answer.

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Three views of the same die with unusual symbols are shown below:

38. Which one of the following dice is not identical to the die above?
1
0

## Explanation

Let the 3 cubes shown in the diagram be cube 1, 2 and 3 from left to right. A is cube 1 rotated 180 degrees so that the arrow is pointing down, is cube 2 when the top face is rotated so it is the front facing face and cube 3 when it is rotated to the right so the face with the arrow is on the right-facing face. Similarly, cubes B, C and D can be rotated to give each of the 3 cubes. Whereas, E can be rotated to give cube 1 and 3, but not cube 2 because if the face with the moon was in the same position as in cube 2, the front-facing face would have the arrow on it rather than the two horizontal lines showed on cube 2.

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On a normal die, opposing faces add up to 7. Four views of the same die on which the numbers are arranged differently from a normal die are shown below. The unseen face has the number two on it.

50. How many spots are on the face opposite the two on this die?
1
0

## Explanation

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anon Medicmind Tutor

Fri, 06 Oct 2023 19:57:00

why A?

The die shown below is a conventional die, i.e. the total number of spots on any two opposite faces is always seven.

44. Which one of the following could not be the appearance of the die shown above after a subsequent throw?
1
3

## Explanation

If dice D is rotated so that the face with 5 dots takes the lower right position (currently occupied by the face with 6 dots), the 3 dots would not match up with those on the dice given in the question. In dice D, a dot on the face with 3 dots would occupy the upper left corner of the face, whereas in the dice given in the question the face with 3 dots would have a dot occupying the upper right corner of that face.

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A cube is labelled with six letters and, when viewed in two positions, looks like this:

8. Which one of the following nets could be folded to make the above cube?
1
1

## Explanation

We can rule out options C and E because the ‘bottom’ of the letter A points to the cube face with the letter B, whereas in the examples we can see that it should be the top of the letter A. We can rule out B because we can see that while the letter F is upright, the letter A is upside-down, whereas in the examples we can see that they have the same orientation so either both should be upright or both should be upside down on the net. Option A can also be ruled out because if we were to fold the net, the base of the letters F and E will be adjacent to the letter A – rather then their sides, so yet again the orientation of the letters relative to A is incorrect. Hence, we are left with D as the only correct net that can be folded to give the example cube shown.

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The following net is folded up to make a cube.

26. At how many corners of the cube do exactly two of the diagonal lines on the faces meet?
2
1

## Explanation

This is a very difficult question to explain without visualisation. I would recommend drawing your best 3D cube, maybe expanding the faces separated from each other so you can visualise all six sides at one. Carefully then work out what each line from the net would sit on the 3D cube, and cross out any corners that meet with just a two-line intersection. This will be 4 (option C). Alternatively you could draw the cube from a few different perspectives to visualise how all the sides interact with each other.

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The diagram below shows the net of a cube.

The following diagrams show five suggested views of the cube once it has been assembled.

20. Which two of the above are possible views of the cube?
0
0

## Explanation

Cube questions can be hard to work through if you have difficulty visualising the nets. To make it easier to approach, start off with the nets that require the least amount of visualisation, in this case we can see that the options 3 and 4 focus on the letters A, N and D, which are right next to each other on the 2D net. Hence to work out which of the options is correct out of 3 and 4 we only need to observe the orientation of the letters on the net rather than trying to visualise what would happen when we fold the net. The orientation of the letter A is the wrong way round relative to N in option 4, so we can rule out answer options C, D and E. We can also see that cube 3 is accurate as the letters are all orientated the right way round relative to each other, and cube 2 is also correct so we can select the answer option B.

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Here is a diagram of a cube.

1                                                          2                                                       3

44. Which one of the following nets could be folded to make this cube?
1
0

## Explanation

For this question you only need to look at the cube faces with a single coloured-in triangle and consider their orientation compared to each other. We can see that the resulting cubes for nets 1,2,3 and 5 therefore do not give the same cube and the correct answer is therefore D.

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A solid cube has 6 different shapes drawn on each of its 6 faces. A plan view showing all the shapes is given below. It is placed on the path drawn below with the triangular shape facing up. The cube is rolled, one face at a time, forward along the route shown, from start position until it reaches the end position.

26. Which one of the following shapes is facing up when it reaches the end position?
0
20

## Explanation

This question requires spatial reasoning. Importantly, rolling the cube 2ce to the right (1st step) will result in the fact opposite to the triangle facing up, which is the rectangle. When rolling the dice 2x down, one again the opposite side to the rectangle is facing up, which is the triangle. The final step is the same as the first one, 2x to the right, which again results in the rectangle facing up – the answer is therefore D. To put this differently, whenever a cube is roles 2ce (each role is one face at a time), the face now up is the one opposite to the original. This process is repeated 3 times in this question. The only additional thing is to determine which face is opposite to the triangle, which is most easily done by looking at the cube plan – the face which is 2 squares away from the triangle is the one opposite to it.

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Pyke Medicmind Tutor

Tue, 19 Apr 2022 18:05:10

"the answer is therefore D" which I put wtf

The net below can be folded to make a Roman numerical dice.

50. Which one of the following dice could have been made as a result of folding the net?
0
0

## Explanation

Cube questions can be difficult to visualise so try to focus on patterns that allow you to rule out the incorrect options. Here we can rule out A as the roman numeral I is in the wrong place (it should be replaced by VI as we can see that the base of V points to VI in the net). B is incorrect as we can see from the net that the open part of V in the numeral IV faces I not II. C can be ruled out as the numeral III is orientated incorrectly (the side of III should be facing II rather than the top of III facing II) and E is incorrect as we can see from the net that the side of V faces the side of III. Having ruled out A, B, C and E, we can see that the correct answer option is D.

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## Official TSA Cube Questions (2008-2019) Section

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