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Question 1 / 19
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1
Identify which of the four provided alternatives (1, 2, 3, 4) correctly shows the pattern that would emerge when the transparent sheet (X) is folded along its dotted line.
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Solution: Step 1: Observe the initial transparent sheet marked (X), noting the shapes and their positions relative to the dotted fold line. Step 2: Mentally perform the fold operation along the dotted line, envisioning how the parts of the pattern will overlap. Step 3: Pay close attention to which parts of the pattern will coincide and how their combined appearance will look. Step 4: Compare your imagined folded pattern with the four given alternative patterns (1), (2), (3), and (4). Step 5: Select the alternative that accurately represents the final pattern after folding. In this case, option '1' is the correct answer.
2
Identify the box that is similar to the one formed by folding the given sheet of paper (X).
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Solution: Step 1: Determine the opposite face pairs from sheet (X). One specific patterned face is opposite the face bearing a circle. One pair of blank faces is opposite another blank face, and the remaining two blank faces are opposite each other. This implies no three blank faces can appear adjacent. Step 2: Analyze the given options: - Figure (1) cannot be formed as it lacks the specific patterned face. - Figure (2) cannot be formed as it shows three blank faces adjacent to each other, which is impossible. - Figure (3) cannot be formed because the specific patterned face and the face bearing the circle, which are opposite, are shown as adjacent. Step 3: Based on the eliminations, conclude that only the cube in figure (4) can be formed as it satisfies all conditions.
3
From the provided sheet (X), select the box that can be constructed.
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Solution: Step 1: Determine the opposite face pairs from sheet (X). The shaded face is opposite the face bearing a square. The face bearing a dot is opposite a blank face. The face with a circle (with a '+' sign inside it) is opposite another blank face. Step 2: Examine the given options. Cubes (2) and (4) show the shaded face adjacent to the face bearing a square. Step 3: This contradicts the fact that they are opposite faces, so cubes (2) and (4) cannot be formed. Step 4: Conclude that only cubes in figures (1) and (3) can be formed.
4
Which box is similar to the one formed by folding the provided sheet of paper (X)?
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Solution: Step 1: Identify the opposite face pairs from sheet (X). The face bearing the dot is opposite the shaded face. The face bearing a circle (with '+' sign inside) is opposite a blank face. The remaining two blank faces are opposite each other. Step 2: Examine the given options. - Cubes (2) and (4) cannot be formed because they show the shaded face adjacent to the face bearing a dot, but these are opposite faces. - Cube (3) cannot be formed because it shows three blank faces adjacent to each other, which implies an impossible arrangement given the opposite pairs of blank faces. Step 3: Therefore, cubes (2), (3), and (4) cannot be formed. Step 4: Conclude that only the cube shown in figure (1) can be formed.
5
Which box can be formed from the given sheet of paper (X)?
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Solution: Step 1: Identify the opposite faces when sheet (X) is folded into a cube. The face bearing a square lies opposite to the face bearing a circle. Step 2: Examine the given options. Cubes (1) and (2) show the faces with the square and the circle adjacent to each other. Step 3: This contradicts the fact that they are opposite faces, so cubes (1) and (2) cannot be formed. Step 4: Conclude that only the cubes in figures (3) and (4) can be formed.
6
Select the box that can be formed by folding the provided sheet of paper (X).
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Solution: Step 1: Identify the opposite faces from the sheet (X). One specific patterned face is opposite a blank face. The face with a circle is opposite the face with a dot. Step 2: Examine cubes (3) and (4). These cubes do not have faces or face combinations that can be formed by folding the sheet in figure (X). Step 3: Therefore, cubes (3) and (4) cannot be formed. Step 4: Conclude that only the cubes shown in figures (1) and (2) can be formed.
7
Which of the given boxes can be constructed from the provided sheet of paper (X)?
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Solution: Step 1: Determine the opposite faces when sheet (X) is folded into a cube. A face with a specific four-symbol pattern is opposite a blank face. A face with a square is opposite another blank face. The remaining two blank faces are opposite each other. Step 2: Observe the cube shown in figure (1). The face consisting of the four symbols in figure (1) is not the same as the pattern formed from sheet (X). Step 3: Therefore, the cube in figure (1) cannot be formed. Step 4: Conclude that cubes (2), (3), and (4) can be formed.
8
From the four given alternatives, determine the resulting pattern when the transparent sheet (X) is folded along the dotted line.
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Solution: Step 1: Carefully observe the initial pattern drawn on the transparent sheet (X). Step 2: Identify the dotted line, which serves as the axis for folding the sheet. Step 3: Mentally visualize the act of folding the transparent sheet precisely along this dotted line. Step 4: Imagine how the patterns from the section of the sheet being folded will superimpose and combine with the patterns on the stationary section. Step 5: Determine the final, combined pattern formed by these overlapping shapes after the fold. Step 6: Compare this mentally visualized pattern with the four provided alternatives and select the one that accurately depicts the outcome of the folded transparent sheet.
9
Which of the finished patterns can be created from the given piece of cardboard (X)?
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Solution: Step 1: Observe the pattern and the rectangular faces on the piece of cardboard (X). Step 2: Mentally fold the cardboard (X) to visualize the resulting 3D shape, specifically focusing on the visible patterns. Step 3: Compare the visual outcome of the folded shape with the given finished patterns (1, 2, 3, 4). Step 4: Conclude that only figure (1) correctly represents the pattern obtained by folding figure (X).
10
From the given options, identify the figure that most accurately represents the completely unfolded form of Figure (Z).
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Solution: Step 1: Carefully observe Figure (Z) to understand the sequence and manner in which the paper was folded, noting the creases and the final cut/puncture marks. Step 2: Mentally unfold the paper step-by-step, reversing the folding sequence. Step 3: For each fold, visualize how the cut/punch marks would reflect symmetrically across the fold line. Step 4: Continue this process until the paper is fully unfolded to its original shape (e.g., square or rectangle). Step 5: Compare the visualized unfolded pattern with the provided option figures (1, 2, 3, 4). Step 6: Select the option that precisely matches the completely unfolded figure.
11
Choose the box that corresponds to the cube formed by folding the provided sheet of paper (X).
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Solution: Step 1: Determine the opposite face pairs from sheet (X). The shaded face is opposite one blank face. The face bearing a circle is opposite another blank face. The face bearing a shaded square is opposite the third blank face. Step 2: Based on these opposite pairs, observe that cubes (1), (2), and (4) can be formed as their visible faces are consistent with the net and its rotations. Step 3: The cube shown in figure (3) has faces that could appear adjacent, but the specific rotation or arrangement shown cannot be formed by folding the sheet in figure (X). Step 4: Therefore, cubes (1), (2), and (4) can be formed.
12
Choose the box that can be formed by folding the provided sheet of paper (X).
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Solution: Step 1: Determine the opposite face pairs when sheet (X) is folded into a cuboid. The two rectangular shaded faces are opposite each other. The two rectangular white faces are opposite each other. The two square faces (one shaded and one white) are opposite each other. Step 2: Examine the given options. Cuboids (2) and (4) show the two shaded rectangular faces adjacent to each other. Step 3: This contradicts the fact that they are opposite faces, so cuboids (2) and (4) cannot be formed. Step 4: Conclude that only the cuboids in figures (1) and (3) can be formed.
13
Choose the box that is similar to the box formed from the given sheet of paper (X).
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Solution: Step 1: Determine the opposite face pairs from sheet (X). The face with a dot is opposite a blank face. The face with a '+' sign is opposite another blank face. The face with a circle is opposite the third blank face. Step 2: Given these pairs, each of the three patterned faces is opposite a blank face. This means any combination of these three patterned faces or two patterned faces and one blank, or one patterned and two blank faces can be adjacent. Step 3: All four cubes shown in figures (1), (2), (3), and (4) present valid arrangements of faces that are consistent with the identified opposite pairs and can be formed by rotating the cube. Step 4: Therefore, all four options can be formed.
14
Select the option that represents the complete unfolded shape of the figure labeled (Z).
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Solution: Step 1: Carefully observe the folded paper in Figure (Z), noting the sequence of folds and the cuts made. Step 2: Mentally unfold the paper step-by-step in reverse order of folding. Step 3: For each fold, mirror the cuts and shapes across the fold line. Step 4: Continue this process until the paper is fully unfolded. Step 5: Compare the final unfolded pattern with the given options to find the best match.
15
Determine which box is similar to the one created by folding the given sheet of paper (X).
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Solution: Step 1: Identify the opposite faces on the unfolded sheet (X). The completely shaded face lies opposite the half-shaded face. Step 2: Check the given cube options. Cubes (1) and (3) show the completely shaded face adjacent to the half-shaded face, which is impossible as they are opposite. Step 3: Figure (4) does not show at least one shaded face, which is inconsistent with the net in (X). Step 4: Therefore, cubes (1), (3), and (4) cannot be formed. Step 5: Conclude that only the cube in figure (2) can be formed.
16
Identify which of the provided boxes can be formed by folding the given sheet of paper (X).
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Solution: Step 1: Analyze the unfolded sheet (X) to determine the pairs of faces that will lie opposite each other when folded into a cube. Step 2: From the net, determine that the face with a dot is opposite to one of the shaded faces. Step 3: Examine each option. Cube (2) shows both shaded faces adjacent to the face bearing the dot, which contradicts the opposite face rule. Step 4: Therefore, cube (2) cannot be formed. Step 5: Conclude that the cubes shown in figures (1), (3), and (4) can be formed.
17
When the given figure is folded to create a cube, how many dots will be on the face opposite the face with five dots?
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Solution: Step 1: Identify the standard cube net configuration similar to Form III. Step 2: Apply the rule for identifying opposite faces in this configuration: Alternate faces are opposite. Step 3: Based on the figure, the face bearing three dots will lie opposite the face bearing five dots. Step 4: Therefore, the face opposite to five dots has three dots.
18
Identify the figure that most accurately represents the completely unfolded form of Figure (Z).
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Solution: Step 1: Analyze the sequence of folds shown in Figure (Z) and the cuts or punches made. Step 2: Begin by mentally unfolding the paper in the reverse order of the folds, starting from the last fold. Step 3: For each unfolding step, apply the principle of symmetry. Any cut or mark made when folded will create a symmetrical pattern when unfolded across the fold line. Step 4: Continue this process until the paper is completely unfolded. Step 5: Carefully compare the resulting unfolded pattern with the given answer options. Step 6: Select the option that most closely resembles the fully unfolded form. In this instance, option 3 is the correct representation.
19
Choose the box that can be constructed from the given sheet of paper (X).
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Solution: Step 1: Determine the opposite face pairs from sheet (X). The 'plus-shaped' pattern and the 'cross-shaped' pattern are opposite each other. The 'x' sign is opposite the black circle. The white circle is opposite the square (having a dot inside it). Step 2: Examine the given options. Cubes (2) and (4) consist of faces or arrangements of faces that are not possible to form when the sheet in figure (X) is folded. Step 3: Therefore, cubes (2) and (4) cannot be formed. Step 4: Conclude that only the cubes in figures (1) and (3) are formed, as they present valid combinations of adjacent faces consistent with the opposite pairs.
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