Primary 4 Mathematics Geometry Quiz

Primary 4 Mathematics Quiz - Geometry (Answer Key)

Total Marks: 40

Section A: Multiple Choice Questions (10 × 1 mark = 10 marks)

1. C (1 mark)
Explanation: An acute angle is an angle less than 90°. Among the options, only 45° is less than 90°.

• 90° is a right angle
• 120° is an obtuse angle (between 90° and 180°)
• 180° is a straight angle

2. B (1 mark)
Explanation: A straight angle measures 180°. A right angle measures 90°.
180° ÷ 90° = 2 right angles.

3. C (1 mark)
Explanation: An obtuse angle is an angle between 90° and 180°. 135° lies between 90° and 180°, so it is an obtuse angle.

4. C (1 mark)
Explanation: A rectangle has exactly 2 lines of symmetry (vertical and horizontal through the centre).

• Equilateral triangle: 3 lines of symmetry
• Square: 4 lines of symmetry
• Circle: Infinite lines of symmetry

5. C (1 mark)
Explanation: The capital letter H has 2 lines of symmetry: one vertical (through the middle of the crossbar) and one horizontal (through the middle of the crossbar).

6. A (1 mark)
Explanation: A valid cube net must have 6 squares that can fold to form a closed cube. Option A (cross shape) and Option C (T-shape) are both valid cube nets. However, only Option A is listed as a choice. Option B has 4 squares in a row with 2 attached on the same side — this creates overlapping faces when folded. Option D has an arrangement that cannot form a closed cube.

7. B (1 mark)
Explanation: ∠AOB = 90° (right angle). ∠AOC = 30°.
∠COB = ∠AOB − ∠AOC = 90° − 30° = 60°.

8. C (1 mark)
Explanation: A rectangle (that is not a square) has exactly 2 lines of symmetry: one vertical and one horizontal through the centre. The dimensions (12 cm × 8 cm) confirm it is not a square.

9. B (1 mark)
Explanation: A regular hexagon can tessellate because its interior angle is 120°, and 360° ÷ 120° = 3, so three hexagons meet perfectly at a point.

• Regular pentagon: interior angle 108°, 360° ÷ 108° = 3.33... (not whole number)
• Regular heptagon: interior angle ≈ 128.6°, does not divide 360° evenly
• Circle: cannot tessellate (gaps remain)

10. A (1 mark)
Explanation: The protractor shows one ray at 0° and the other at 75°. The angle measured is 75°.

Section B: Short Answer Questions (10 × 2 marks = 20 marks)

11. 120° (2 marks)
Working:

• Ray YX is at 10° on the protractor.
• Ray YZ is at 130° on the protractor.
• ∠XYZ = 130° − 10° = 120°.

Marking: 1 mark for correct reading of both rays, 1 mark for correct subtraction and answer with degree symbol.

Common mistake: Reading the wrong scale on the protractor (using 180° − 130° = 50° and 180° − 10° = 170°). Always read from the same scale (usually the inner scale starting from 0° on the baseline ray).

12. (2 marks)
Expected drawing:

• Place protractor centre at point P, baseline along PQ.
• Mark a point at 110° on the protractor (using inner scale).
• Remove protractor and draw ray PR through the marked point.
• Label the angle ∠RPQ.

Marking: 1 mark for accurate angle (110° ± 2°), 1 mark for correct labelling (∠RPQ or ∠QPR with vertex at P).

Teaching note: An angle of 110° is an obtuse angle (between 90° and 180°). The ray should open upward from the horizontal line PQ.

13. 115° (2 marks)
Working:

• AB is a straight line, so ∠AOB = 180° (angles on a straight line).
• ∠AOC = 65° (given).
• ∠COB = ∠AOB − ∠AOC = 180° − 65° = 115°.
• ∠x = 115°.

Marking: 1 mark for stating "angles on a straight line = 180°" or equivalent reasoning, 1 mark for correct answer.

Key concept: Angles on a straight line add up to 180°.

14. (2 marks)
Expected completion: Reflect the given half-shape across the vertical dotted line of symmetry. Each grid square on the right must have a matching square on the left at the same distance from the line.

Marking: 1 mark for correct reflection of main shape, 1 mark for correct reflection of the notch/detail. Deduct ½ mark per grid square error (max 2 marks).

Teaching note: For line symmetry, every point on one side has a matching point on the other side at the same perpendicular distance from the line of symmetry.

15. (2 marks)
Expected completion: Reflect the quarter-shape across the vertical dotted line to the top-left quadrant, then reflect both top quadrants across the horizontal dotted line to the bottom two quadrants. The final shape has 4-fold rotational symmetry (or 2 lines of symmetry).

Marking: 1 mark for correct vertical reflection, 1 mark for correct horizontal reflection (or 2 marks for fully correct completed shape).

16. Net A and Net C (2 marks)
Explanation: A cuboid net must have 6 rectangular faces (3 pairs of identical rectangles).

• Net A: 6 rectangles arranged in a valid cross pattern — can fold into a cuboid. ✓
• Net B: Only 5 rectangles — missing one face. ✗
• Net C: 6 rectangles in a T-shape arrangement — valid cuboid net. ✓
• Net D: Only 4 rectangles — missing two faces. ✗

Marking: 1 mark for each correct net identified (A and C). No marks if incorrect nets are also ticked.

17. Faces: 6, Edges: 12, Vertices: 8 (2 marks)
Explanation: A cube is a 3D solid with:

• 6 square faces (top, bottom, front, back, left, right)
• 12 edges (4 on top, 4 on bottom, 4 vertical)
• 8 vertices (4 on top, 4 on bottom)

Marking: 1 mark for all three correct, ½ mark each if 1–2 correct (round down to nearest ½ mark).

Teaching note: Euler's formula for polyhedra: Faces + Vertices = Edges + 2 → 6 + 8 = 12 + 2 ✓

18. 120° (2 marks)
Working:

• PQRS is a rectangle, so all interior angles are 90°.
• ∠SPT = 25° (given), so ∠TPR = 90° − 25° = 65°.
• ∠QRT = 35° (given), so ∠TRS = 90° − 35° = 55°.
• In triangle PTR: ∠TPR + ∠TRS + ∠PTR = 180° (angle sum of triangle).
• 65° + 55° + ∠PTR = 180°
• 120° + ∠PTR = 180°
• ∠PTR = 60°

Wait — correction: The angles at P and R in triangle PTR are ∠TPR and ∠PRT, not ∠TRS. Let's re-read the diagram carefully.

Point T is inside rectangle PQRS.
∠SPT = 25° → ∠TPR = 90° − 25° = 65° (since ∠SPR = 90°).
∠QRT = 35° → ∠PRT = 90° − 35° = 55° (since ∠QRP = 90°).
In ΔPTR: ∠TPR + ∠PRT + ∠PTR = 180°
65° + 55° + ∠PTR = 180°
120° + ∠PTR = 180°
∠PTR = 60°

Correct Answer: 60° (2 marks)

Marking: 1 mark for finding ∠TPR = 65° and ∠PRT = 55°, 1 mark for correct triangle angle sum and final answer.

Common mistake: Using ∠TRS (55°) instead of ∠PRT, or forgetting that rectangle corners are 90°.

19. (2 marks)
Expected shading: Shade the 4th and 5th triangles (counting from left) — the mirror images of the 3rd and 2nd triangles respectively, across the vertical dotted line between the 3rd and 4th triangles.

Marking: 1 mark for each correctly shaded triangle in the symmetric position.

Teaching note: The line of symmetry acts like a mirror. The pattern on the right must be the mirror image of the pattern on the left.

20. 4 holes (2 marks)
Explanation:

• First fold (vertical): 2 layers
• Second fold (horizontal): 4 layers total
• One hole punched through all 4 layers
• When unfolded: 4 holes (one in each quadrant)

Marking: 1 mark for understanding 2 folds = 4 layers, 1 mark for correct answer "4 holes".

Teaching note: Each fold doubles the number of layers. Number of holes = 2^(number of folds) = 2² = 4.

End of Answer Key