CAT4

The shape on the left is hidden in one of the five shapes on the right of the line (and it is exactly the same size and same way round where it is hidden). All of its sides are visible in the shape where it is hiding. Which of the five shapes contains the shape on the left?

• a

• b

• c

• d

• e

Answer explanation

The shape on the left is hidden in one of the five shapes on the right of the line (and it is exactly the same size and same way round where it is hidden). All of its sides are visible in the shape where it is hiding. Which of the five shapes contains the shape on the left?

• a

• b

• c

• d

• e

Answer explanation

The shape on the left is hidden in one of the five shapes on the right of the line (and it is exactly the same size and same way round where it is hidden). All of its sides are visible in the shape where it is hiding. Which of the five shapes contains the shape on the left?

• a

• b

• c

• d

• e

Answer explanation

This question is about folding paper and punching holes in it. You must decide how the paper would look when it is unfolded. Choose which of the five squares beneath the folded squares shows how the paper would look when it is unfolded.

• a

• b

• c

• d

• e

Answer explanation

The first square in the top row shows a grey piece of paper at the start (before it is folded). There are small marks that show where the middle of each side is. The white line shows the crease along which the paper will be folded. The arrow shows the direction that the paper will be folded i.e. from the right side of the paper across towards the centre.

The second square in the top row shows the grey paper after the fold. The folded portion of the paper consists of two layers of paper (one on top of the other) because a single layer of paper has been folded on top of an underlying layer. The second square also shows the direction of the second fold i.e. from three quarters of the way across from the left side to one quarter of the way across from the left side.

The third square in the top row shows the grey paper after the second fold. The folded portion of the paper now consists of three layers of paper (two layers on top of one layer). The third square also shows the direction of the third fold i.e. from the centre towards the left side.

The fourth square in the top row shows the grey paper after the third fold. The folded portion of the paper now consists of four layers of paper (three layers on top of one layer). The fourth square also shows holes that have been punched through the folded paper.

Two holes are punched through the folded portion of paper, and the folded portion of paper has four layers of paper, so when the folded portion is unfolded, there will be eight holes (two holes per layer).

To find where the holes will be when the paper is unfolded, you need to work backwards by unfolding the last fold, and continue unfolding all folds until you have unfolded the first fold.

The third square on the top row shows the direction of the third fold operation (i.e. a fold from the centre to the left side). To unfold the paper (or undo the fold), you need to unfold in the opposite direction (i.e. from the left side to the centre) as shown in diagram (i) below. Diagram (ii) below shows the result of unfolding the third fold. A white line which is the crease or fold line (i.e. the line about which the paper has been folded and about which the paper needs to be unfolded) has been added to make the unfolding process clearer. Note that when you unfold a folded portion of paper, any holes on the folded paper are reflected in the fold line (i.e. the white line shown in diagram (ii)). Then removing the white line from diagram (ii), we get diagram (iii) which is the result of unfolding the third fold.

The second square on the top row shows the direction of the second fold operation (i.e. a fold from three quarters of the way across from the left side to one quarter of the way across from the left side). To unfold the paper (or undo the fold), you need to unfold in the opposite direction (i.e. from one quarter of the way across from the left side to three quarters of the way across from the left side) as shown in diagram (i) below. Diagram (ii) below shows the result of unfolding the second fold. A white line which is the crease or fold line (i.e. the line about which the paper has been folded and about which the paper needs to be unfolded) has been added to make the unfolding process clearer. Note that when you unfold a folded portion of paper, any holes on the folded paper are reflected in the fold line (i.e. the white line shown in diagram (ii)). Then removing the white line from diagram (ii), we get diagram (iii) which is the result of unfolding the second fold.

Next, you need to unfold (or undo) the first fold, which was a fold from the right side of the paper across towards the centre as shown in the first square on the top row of the question. To unfold the paper (or undo the fold), you need to unfold in the opposite direction (i.e. from the centre to the right side) as shown in diagram (i) below. Diagram (ii) below shows the result of unfolding the first fold. A white line which is the crease or fold line (i.e. the line about which the paper has been folded and about which the paper needs to be unfolded) has been added to make the unfolding process clearer. Note that when you unfold a folded portion of paper, any holes on the folded paper are reflected in the fold line (i.e. the white line shown in diagram (ii)). Then removing the white line from diagram (ii), we get diagram (iii) which is the result of unfolding the first fold.

Therefore the answer to the question is C.

This question is about folding paper and punching holes in it. You must decide how the paper would look when it is unfolded. Choose which of the five squares beneath the folded squares shows how the paper would look when it is unfolded.

• a

• b

• c

• d

• e

Answer explanation

The first square in the top row shows a grey piece of paper at the start (before it is folded). There are small marks that show where the middle of each side is. The white line shows the crease along which the paper will be folded. The arrow shows the direction that the paper will be folded i.e. from left to centre.

The second square in the top row shows the grey paper after the fold. The second square also shows the direction of the second fold i.e. from bottom to centre.

The third square in the top row shows the grey paper after the second fold. The third square also shows holes that have been punched through the paper.

To find where the holes will be when the paper is unfolded, you need to work backwards by unfolding the last fold, and continue unfolding all folds until you have unfolded the first fold.

The second square on the top row shows the direction of the second fold operation (i.e. a fold from bottom to centre). To unfold the paper (or undo the fold), you need to unfold in the opposite direction (i.e. from centre to bottom) as shown in diagram (i) below. Diagram (ii) below shows the result of unfolding the second fold. A white line which is the crease or fold line (i.e. the line about which the paper has been folded and about which the paper needs to be unfolded) has been added to make the unfolding process clearer. Note that when you unfold a folded portion of paper, any holes on the folded paper are reflected in the fold line (i.e. the white line shown in diagram (ii)). In this case, there are no holes on the folded portion of paper that is being unfolded, therefore there is nothing to reflect. Then removing the white line from diagram (ii), we get diagram (iii) which is the result of unfolding the second fold.

Next, you need to unfold (or undo) the first fold, which was a fold from left to centre as shown in the first square on the top row of the question. To unfold the paper (or undo the fold), you need to unfold in the opposite direction (i.e. from centre to left) as shown in diagram (i) below. Diagram (ii) below shows the result of unfolding the first fold. A white line which is the crease or fold line (i.e. the line about which the paper has been folded and about which the paper needs to be unfolded) has been added to make the unfolding process clearer. Note that when you unfold a folded portion of paper, any holes on the folded paper are reflected in the fold line (i.e. the white line shown in diagram (ii)). Then removing the white line from diagram (ii), we get diagram (iii) which is the result of unfolding the first fold.

Therefore the answer to the question is B.

This question is about folding paper and punching holes in it. You must decide how the paper would look when it is unfolded. Choose which of the five squares beneath the folded squares shows how the paper would look when it is unfolded.

• a

• b

• c

• d

• e

Answer explanation

The first square in the top row shows a grey piece of paper at the start (before it is folded). There are small marks that show where the middle of each side is. The white line shows the crease along which the paper will be folded. The arrow shows the direction that the paper will be folded i.e. from top right to bottom left.

The second square in the top row shows the grey paper after the fold. The folded portion of the paper consists of two layers of paper (one on top of the other) because a single layer of paper has been folded on top of an underlying layer. The second square also shows the direction of the second fold i.e. from bottom right to top left.

The third square in the top row shows the grey paper after the second fold. The folded portion of the paper now consists of four layers of paper (two layers on top of another two layers). The third square also shows holes that have been punched through the folded paper.

Two holes are punched through the folded portion of paper, and the folded portion of paper has four layers of paper, so when the folded portion is unfolded, there will be eight holes (two holes per layer). This means that we can rule out any answer which does not have eight holes i.e. we can rule out the answers A and C.

To find where the holes will be when the paper is unfolded, you need to work backwards by unfolding the last fold, and continue unfolding all folds until you have unfolded the first fold.

The second square on the top row shows the direction of the second fold operation (i.e. a fold from bottom right to top left). To unfold the paper (or undo the fold), you need to unfold in the opposite direction (i.e. from top left to bottom right) as shown in diagram (i) below. Diagram (ii) below shows the result of unfolding the second fold. A white line which is the crease or fold line (i.e. the line about which the paper has been folded and about which the paper needs to be unfolded) has been added to make the unfolding process clearer. Note that when you unfold a folded portion of paper, any holes on the folded paper are reflected in the fold line (i.e. the white line shown in diagram (ii)). Then removing the white line from diagram (ii), we get diagram (iii) which is the result of unfolding the second fold.

Next, you need to unfold (or undo) the first fold, which was a fold from top right to bottom left as shown in the first square on the top row of the question. To unfold the paper (or undo the fold), you need to unfold in the opposite direction (i.e. from bottom left to top right) as shown in diagram (i) below. Diagram (ii) below shows the result of unfolding the first fold. A white line which is the crease or fold line (i.e. the line about which the paper has been folded and about which the paper needs to be unfolded) has been added to make the unfolding process clearer. Note that when you unfold a folded portion of paper, any holes on the folded paper are reflected in the fold line (i.e. the white line shown in diagram (ii)). Then removing the white line from diagram (ii), we get diagram (iii) which is the result of unfolding the first fold.

Therefore the answer to the question is E.

This question is about counting the number of blocks in a pile. Each block in the pile is the same size and shape. Some blocks are hidden from view but must be there to hold the visible blocks up. Choose the answer that shows the total number of blocks in the pile.

• a

• b

• c

• d

• e

Answer explanation

Define a single-storey block as being made up of 1 block (with no blocks stacked on top of it).

Define a two-storey block as being made up of 2 blocks (i.e. 2 single blocks stacked on top of each other).

This pile is made up of:

4 single-storey blocks which is a total of 4 blocks, and
4 two-storey blocks which is a total of 4 x 2 = 8 blocks.

Therefore the total number of blocks in the pile is 4 + 8 = 12.

This question is about counting the number of blocks in a pile. Each block in the pile is the same size and shape. Some blocks are hidden from view but must be there to hold the visible blocks up. Choose the answer that shows the total number of blocks in the pile.

• a

• b

• c

• d

• e

Answer explanation

Define a single-storey block as being made up of 1 block (with no blocks stacked on top of it).

Define a two-storey block as being made up of 2 blocks (i.e. 2 single blocks stacked on top of each other).

Define a three-storey block as being made up of 3 blocks (i.e. 3 single blocks stacked on top of each other).

This pile is made up of:

3 single-storey blocks which is a total of 3 blocks,
2 two-storey blocks which is a total of 2 x 2 = 4 blocks, and
3 three-storey blocks which is a total of 3 x 3 = 9 blocks.

Therefore the total number of blocks in the pile is 3 + 4 + 9 = 16.

This question is about counting the number of blocks in a pile. Each block in the pile is the same size and shape. Some blocks are hidden from view but must be there to hold the visible blocks up. Choose the answer that shows the total number of blocks in the pile.

• a

• b

• c

• d

• e

Answer explanation

Define a single-storey block as being made up of 1 block (with no blocks stacked on top of it).

Define a two-storey block as being made up of 2 blocks (i.e. 2 single blocks stacked on top of each other).

Define a three-storey block as being made up of 3 blocks (i.e. 3 single blocks stacked on top of each other).

This pile is made up of:

5 single-storey blocks which is a total of 5 blocks,
5 two-storey blocks which is a total of 5 x 2 = 10 blocks, and
2 three-storey blocks which is a total of 2 x 3 = 6 blocks.

Therefore the total number of blocks in the pile is 5 + 10 + 6 = 21.

One of the five shapes on the right matches the shape on the left i.e. it is the same as the shape on the left, but it has been spun round. The other four shapes on the right do not match the shape on the left because they have been picked up and turned over, as well as possibly spun round. Choose the answer that shows the matching shape.

• a

• b

• c

• d

• e