11+ Practice Test

11+ Entrance Non-Verbal Reasoning: Cube Nets Questions and Answers — Questions and Answers

Question 1: Which of the following cubes can be made from the net shown? <img src='https://i.imgur.com/8Q9f2Yt.png' alt='Cube net with a black circle, a horizontal arrow, a plus sign, a white square, a black triangle, and a white circle.'/>

<img src='https://i.imgur.com/kL5j3Pz.png' alt='Cube A showing a black circle, a horizontal arrow, and a plus sign.'/>
<img src='https://i.imgur.com/dM2n1Fv.png' alt='Cube B showing a black triangle, a white square, and a white circle.'/>
<img src='https://i.imgur.com/G7w7sXh.png' alt='Cube C showing a horizontal arrow, a plus sign, and a white square.'/> (Correct answer)
<img src='https://i.imgur.com/A6fXo4v.png' alt='Cube D showing a black circle, a black triangle, and a horizontal arrow.'/>

Correct answer: <img src='https://i.imgur.com/G7w7sXh.png' alt='Cube C showing a horizontal arrow, a plus sign, and a white square.'/>

To solve this, we can analyse the relationships between the faces on the net. The horizontal arrow, plus sign, and white square are all adjacent to each other. If we take the plus sign as the top face, the arrow can be folded to be the front face, and the white square can be the right-hand face. This matches cube C. Cube A is incorrect because the arrow and the black circle are on opposite faces in the net, so they cannot be seen together. Cube B is incorrect because the black triangle and the white square are on opposite faces. Cube D is incorrect because of the orientation; when the arrow is on the front and the black circle is on the left, the black triangle should be on top, not adjacent in that configuration.

Question 2: Look at the net below. Which cube can be formed by folding it? <img src='https://i.imgur.com/tN8oP5E.png' alt='Cube net with three grey shaded faces, one face with vertical stripes, one with diagonal stripes, and one white face.'/>

<img src='https://i.imgur.com/J3hYx4a.png' alt='Cube A showing two grey faces and a vertically striped face.'/>
<img src='https://i.imgur.com/yO8v3wZ.png' alt='Cube B showing a grey face, a vertically striped face, and a diagonally striped face.'/> (Correct answer)
<img src='https://i.imgur.com/cR6sE9t.png' alt='Cube C showing a white face, a grey face, and a vertically striped face.'/>
<img src='https://i.imgur.com/U2rW8Xv.png' alt='Cube D showing three grey faces together.'/>

Correct answer: <img src='https://i.imgur.com/yO8v3wZ.png' alt='Cube B showing a grey face, a vertically striped face, and a diagonally striped face.'/>

In the net, the vertically striped face, the diagonally striped face, and the central grey face are all adjacent. If you fold the net with the central grey face at the front, the vertically striped face will be on the right, and the diagonally striped face will be on top. This configuration matches cube B. Cube A is incorrect because the two grey faces shown would be opposite each other when folded. Cube C is incorrect as the white face and the vertically striped face are opposites. Cube D is impossible because the three grey faces cannot all meet at one corner; two of them are opposite each other.

Question 3: Which of the cubes shown could be made from the 2D net provided? <img src='https://i.imgur.com/wVjX4yJ.png' alt='Cube net with a lightning bolt, a star, a moon, a sun, a cloud, and a raindrop.'/>

<img src='https://i.imgur.com/qR7f1yS.png' alt='Cube A showing a star, a moon, and a sun.'/>
<img src='https://i.imgur.com/E5dY4zW.png' alt='Cube B showing a lightning bolt, a star, and a raindrop.'/>
<img src='https://i.imgur.com/M6fJ9zT.png' alt='Cube C showing a cloud, a raindrop, and a sun.'/>
<img src='https://i.imgur.com/sX0p0vF.png' alt='Cube D showing a lightning bolt, a sun, and a cloud.'/> (Correct answer)

Correct answer: <img src='https://i.imgur.com/sX0p0vF.png' alt='Cube D showing a lightning bolt, a sun, and a cloud.'/>

By examining the net, we can determine the relationships between the faces. The lightning bolt, sun, and cloud are all adjacent to the star face. If we imagine the star as the base (bottom face), the lightning bolt, sun, and cloud would form three of the side faces. Cube D correctly shows the lightning bolt, sun, and cloud meeting at a vertex. Cube A is incorrect because the moon and the sun are opposite faces on the net. Cube B is incorrect as the lightning bolt and raindrop are on opposite faces. Cube C is incorrect because the cloud and the sun are not adjacent in the way depicted; the star or lightning bolt should be between them depending on the fold.

Question 4: A cube is unfolded to create the net below. Which of the four options shows a possible view of the folded cube? <img src='https://i.imgur.com/P4rX3oF.png' alt='Cube net with a large black dot, a small black dot, a black square, a hollow square, a plus sign, and a minus sign.'/>

<img src='https://i.imgur.com/yF9e7qH.png' alt='Cube A showing a large dot, a small dot, and a plus sign.'/> (Correct answer)
<img src='https://i.imgur.com/lZ6t2sX.png' alt='Cube B showing a black square, a hollow square, and a minus sign.'/>
<img src='https://i.imgur.com/O8tK5bB.png' alt='Cube C showing a large dot, a black square, and a minus sign.'/>
<img src='https://i.imgur.com/xV7g6wR.png' alt='Cube D showing a plus sign, a minus sign, and a small dot.'/>

Correct answer: <img src='https://i.imgur.com/yF9e7qH.png' alt='Cube A showing a large dot, a small dot, and a plus sign.'/>

Let's analyse the adjacencies in the net. The large dot is next to the small dot, the plus sign, the hollow square, and the minus sign. If we take the large dot as the front face, the plus sign can be the top face, and the small dot can be the right face. This view matches cube A. Cube B is incorrect because the black square and the hollow square are opposite faces. Cube C is incorrect because the large dot and the minus sign are adjacent, but their orientation relative to the black square is wrong. Cube D is incorrect because the plus sign and minus sign are on opposite sides of the 'T' junction in the net, making them opposite faces on the cube.

Question 5: Which of the following cubes CANNOT be made from the net shown? <img src='https://i.imgur.com/iI3y6eL.png' alt='Cube net with various black and white patterns. One face has a black half top, one a black half left, one a black half bottom, one a black half right, one a black top-left quadrant, and one a white face.'/>

<img src='https://i.imgur.com/nJ8o7zK.png' alt='Cube A shows the top-left quadrant, top half, and left half faces meeting.'/>
<img src='https://i.imgur.com/cT0s2yF.png' alt='Cube B shows the bottom half, right half, and plain white faces meeting.'/>
<img src='https://i.imgur.com/aE2s3xR.png' alt='Cube C shows the left half, top-left quadrant, and bottom half faces meeting.'/>
<img src='https://i.imgur.com/xJ4r5zW.png' alt='Cube D shows the right half, bottom half, and top half faces meeting.'/> (Correct answer)

Correct answer: <img src='https://i.imgur.com/xJ4r5zW.png' alt='Cube D shows the right half, bottom half, and top half faces meeting.'/>

This question asks which cube CANNOT be made. We need to check each option. A, B, and C are all possible constructions. Let's analyse D. In the net, the face with the black top half is opposite the face with the black bottom half. This means they can never be seen at the same time on the folded cube. Cube D shows these two opposite faces adjacent to each other, which is impossible. Therefore, cube D cannot be made from the net.

Question 6: If the net below is folded into a cube, which of the four cubes would be the result? <img src='https://i.imgur.com/tS9f8vR.png' alt='Cube net with directional arrows. One points up, one down, one left, one right. One face has a circle, and one is blank.'/>

<img src='https://i.imgur.com/Z7sX2vP.png' alt='Cube A shows the up arrow, right arrow, and circle.'/> (Correct answer)
<img src='https://i.imgur.com/F6yW0bT.png' alt='Cube B shows the down arrow, left arrow, and blank face.'/>
<img src='https://i.imgur.com/cW9s3zA.png' alt='Cube C shows the up arrow, down arrow, and right arrow.'/>
<img src='https://i.imgur.com/gO0l4qN.png' alt='Cube D shows the right arrow, left arrow, and circle.'/>

Correct answer: <img src='https://i.imgur.com/Z7sX2vP.png' alt='Cube A shows the up arrow, right arrow, and circle.'/>

Let's analyse the orientation of the arrows. If we use the circle as the front face, the 'up' arrow will be on the top face, and the 'right' arrow will be on the right-hand face. This matches the view shown in cube A. Cube B is incorrect because the blank face is opposite the circle, so they could not be seen with the down and left arrows in that configuration. Cube C is incorrect because the 'up' arrow and 'down' arrow are on opposite faces in the net. Cube D is incorrect because the 'right' arrow and 'left' arrow are on opposite faces and cannot be seen together.

11+ Entrance Non-Verbal Reasoning: Cube Nets Questions and Answers

Which of the following cubes can be made from the net shown?