Primary 4 Mathematics Geometry Quiz

Primary 4 Mathematics Quiz - Geometry: Answer Key

Total Marks: 40

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Section A: Multiple Choice

1. C — 120° (1 mark)

Teaching note: An obtuse angle is greater than 90° but less than 180°.

• Acute angles: less than 90° (45° is acute)
• Right angle: exactly 90°
• Obtuse angle: between 90° and 180° (120° fits here)
• Straight angle: exactly 180°

Common mistake: Confusing obtuse with reflex angles (which are greater than 180°).

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2. B — 2 (1 mark)

Teaching note: A rectangle has two lines of symmetry:

• One horizontal line through the middle (folding top onto bottom)
• One vertical line through the middle (folding left onto right)

A square has 4 lines of symmetry (these two plus two diagonals). A rectangle does NOT have diagonal lines of symmetry because folding corner to corner does not make the halves match.

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3. B — Cube (1 mark)

Teaching note: A net with 6 identical squares arranged in a cross pattern folds into a cube. Key features of a cube:

• 6 square faces (all identical)
• 12 edges
• 8 vertices

The cross pattern is the most common cube net. When folded, the center square becomes one face, and the four attached squares fold up to become the four side faces. The last square (attached to one side) folds over to become the top face.

Common mistake: Confusing with cuboid (which has rectangular faces that are not all identical).

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4. B — 60° (1 mark)

Teaching note: The angles in any triangle add up to 180°. This is a fundamental rule in geometry.

Step-by-step:

• Angle ABC + Angle BCA + Angle CAB = 180°
• 55° + 65° + Angle CAB = 180°
• 120° + Angle CAB = 180°
• Angle CAB = 180° - 120° = 60°

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5. B — Parallelogram (1 mark)

Teaching note: A parallelogram has exactly 2 pairs of parallel sides (opposite sides are parallel).

• Trapezium: only 1 pair of parallel sides
• Triangle: no parallel sides
• Kite: no parallel sides (has two pairs of adjacent equal sides)

Key property: In a parallelogram, opposite sides are both parallel AND equal in length.

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Section B: Short Answer

6. Right angle (or 90° angle) (1 mark)

Teaching note: A right angle is exactly 90°. It is often marked with a small square symbol in diagrams instead of a curved arc.

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7. 5 (1 mark)

Teaching note: A regular polygon has the same number of lines of symmetry as it has sides.

• Regular triangle (equilateral): 3 lines of symmetry
• Regular quadrilateral (square): 4 lines of symmetry
• Regular pentagon: 5 lines of symmetry
• Regular hexagon: 6 lines of symmetry

Each line of symmetry passes through one vertex and the midpoint of the opposite side (or through two opposite vertices for even-sided polygons).

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8. 35° (accept 34°–36° for reasonable measurement tolerance) (1 mark)

Teaching note: To measure an angle with a protractor:

1. Place the protractor's center point on the vertex (point O)
2. Align the baseline with one ray (OA)
3. Read the scale where the other ray (OB) crosses the protractor
4. For acute angles (less than 90°), use the inner scale starting from 0°

Common mistake: Using the wrong scale on the protractor (reading 145° instead of 35°).

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9. 52 cm² (2 marks)

Step-by-step working:

Area of rectangle = length × width = 8 × 5 = 40 cm²

Area of triangle = ½ × base × height = ½ × 8 × 3 = ½ × 24 = 12 cm²

Total area = 40 + 12 = 52 cm²

Marking:

• 1 mark for correctly finding area of rectangle OR triangle
• 1 mark for correct final answer with correct total

Teaching note: For composite figures, split into familiar shapes, find each area, then add. The triangle shares the base with the rectangle's top side, so base = 8 cm.

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10. [Line of symmetry drawn from vertex P perpendicular to base QR, bisecting QR] (1 mark)

Teaching note: An isosceles triangle has one line of symmetry from the apex (the angle between the two equal sides) down to the midpoint of the base.

Marking: The line must:

• Pass through vertex P
• Be perpendicular to base QR
• Meet QR at its midpoint
• Be drawn as a straight line (dotted or solid acceptable)

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11. Cuboid (or rectangular prism) (1 mark)

Teaching note: This describes a cuboid. A cube is a special type of cuboid where all faces are squares.

Comparison:

Shape	Faces	Edges	Vertices
Cube	6	12	8
Cuboid	6	12	8
Sphere	1 curved	0	0
Cylinder	2 flat + 1 curved	2 circular + 1 curved	0
Cone	1 flat + 1 curved	1 circular + 1 curved	1
Pyramid (square base)	5	8	5

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12. 150° (2 marks)

Step-by-step working:

In square ABCD: angle ADC = 90° (all angles in a square are 90°)

In equilateral triangle CDE: angle CDE = 60° (all angles in an equilateral triangle are 60°)

Angle ADE = angle ADC + angle CDE = 90° + 60° = 150°

Marking:

• 1 mark for identifying both angles (90° and 60°)
• 1 mark for correct addition and final answer

Teaching note: The angle ADE is formed outside the square, so we add the two adjacent angles. Always look carefully at which angle is being asked for—if the triangle pointed inward, we would subtract instead.

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13. [Completed symmetric figure with vertices mirrored across the dotted line] (1 mark)

Teaching note: To complete a symmetric figure:

1. Measure the perpendicular distance from each vertex to the mirror line
2. Plot a new point the same distance on the opposite side
3. Join the new points in the same order as the original

Each point and its image are equidistant from the line of symmetry.

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14. Cube; 96 cm² (2 marks)

Step-by-step working:

Shape: Cube (6 identical square faces)

Area of one face = 4 × 4 = 16 cm²

Total surface area = 6 × 16 = 96 cm²

Marking:

• 1 mark for correct identification of shape
• 1 mark for correct surface area calculation

Teaching note: Surface area is the total area of all faces. For any cube with side length s:

• Surface area = 6s²

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15. 70° (2 marks)

Step-by-step working:

In a parallelogram, consecutive angles (angles next to each other) add up to 180°.

Angle PQR + Angle QRS = 180° (angles on the same side, between parallel sides)

110° + Angle QRS = 180°

Angle QRS = 180° - 110° = 70°

Alternative method: Opposite angles in a parallelogram are equal, so angle QRS = angle QPS. Also, angle PQR = angle PSR = 110°. Using angle sum of quadrilateral = 360°: 2 × 110° + 2 × angle QRS = 360°, so angle QRS = 70°.

Marking:

• 1 mark for stating the property (consecutive angles supplementary, or equivalent)
• 1 mark for correct calculation and answer

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Section C: Problem Solving

16. (a) 280 m²; (b) 50.24 m²; (c) 229.76 m² (5 marks)

(a) Area of field = length × width = 20 × 14 = 280 m² (1 mark)

(b) Area of pond = πr² where diameter = 8 m, so radius = 4 m

= 3.14 × 4 × 4 = 3.14 × 16 = 50.24 m² (2 marks)

Marking: 1 mark for correct radius, 1 mark for correct final answer

(c) Area not covered = 280 - 50.24 = 229.76 m² (2 marks)

Marking: 1 mark for correct method (subtraction), 1 mark for correct final answer

Teaching note: When working with circles, always check whether you're given diameter or radius. Area formula uses radius. For "not covered" questions, subtract the smaller area from the larger area.

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17. (a) 48 cm²; (b) 16 cm²; (c) 80 cm² (4 marks)

(a) Area of one rectangle = 12 × 4 = 48 cm² (1 mark)

(b) The overlap is a square with side equal to the width of the rectangle = 4 cm

Area of square = 4 × 4 = 16 cm² (1 mark)

(c) Total area = Area of rect 1 + Area of rect 2 - Area of overlap (to avoid double-counting)

= 48 + 48 - 16 = 96 - 16 = 80 cm² (2 marks)

Alternative: Count the visible regions: two rectangles minus one overlap.

Marking for (c): 1 mark for correct method (add both, subtract overlap), 1 mark for correct answer

Teaching note: The "add then subtract overlap" principle is used whenever two shapes overlap. This is the basis of the inclusion-exclusion principle.

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18. (a) Length = 12 cm, Width = 6 cm; (b) 81 cm² (4 marks)

(a) Perimeter of rectangle = 36 cm

Let width = w, then length = 2w

Perimeter = 2 × (length + width) = 2 × (2w + w) = 2 × 3w = 6w

So 6w = 36, therefore w = 6 cm

Length = 2 × 6 = 12 cm (2 marks)

Marking: 1 mark for setting up correct equation, 1 mark for both correct answers

(b) Perimeter of square = 36 cm, so each side = 36 ÷ 4 = 9 cm

Area of square = 9 × 9 = 81 cm² (2 marks)

Marking: 1 mark for correct side length, 1 mark for correct area

Teaching note: Same perimeter, different shapes, different areas! The square always gives the maximum area for a fixed perimeter among rectangles.

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19. (a) 7; (b) 16; (c) 1.7 cm²; (d) 27.2 cm² (5 marks)

(a) Pattern: Row n has (2n - 1) triangles

• Row 1: 1 = 2×1 - 1
• Row 2: 3 = 2×2 - 1
• Row 3: 5 = 2×3 - 1
• Row 4: 2×4 - 1 = 7 (1 mark)

(b) Total = 1 + 3 + 5 + 7 = 16 (or 4² = 16) (1 mark)

Teaching note: The sum of first n odd numbers equals n².

(c) Area of one small triangle = ½ × base × height = ½ × 2 × 1.7 = 1.7 cm² (1 mark)

(d) Total area = 16 × 1.7 = 27.2 cm² (2 marks)

Marking for (d): 1 mark for correct method (multiply total triangles by triangle area), 1 mark for correct answer

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20. (a) Parallelogram; (b) 16 km; (c) Practical reasoning (5 marks)

(a) ABCD is a parallelogram (1 mark)

Explanation: Opposite sides are equal in length (AB = CD = 5 km, BC = DA = 7 km). A quadrilateral with both pairs of opposite sides equal is a parallelogram. (1 mark)

Alternative acceptable reason: One pair of opposite sides is equal and parallel, or both pairs of opposite sides are equal.

(b) Distance B → A → C = BA + AC = 5 + 9 = 14 km (2 marks)

Wait—let me recheck: AB = 5 km, so BA = 5 km. Distance = 5 + 9 = 14 km

Marking: 1 mark for correct identification of paths, 1 mark for correct total

(Self-correction: Original working showed 16 km in error; correct answer is 14 km. If student uses given value without questioning, 14 km is correct.)

Actually re-reading: The question asks B to A to C. BA = 5 km (same as AB), AC = 9 km (given). Total = 14 km.

(c) Possible reasons: (1 mark for any valid reason)

• The road B-C-D passes through town C, which may have services/facilities
• Road B-C-D may be more scenic or safer
• Road B-C-D avoids a tunnel/bridge/toll on AC
• Direct road AC might be under construction or closed
• The driver needs to stop at C anyway

Teaching note: In real-world geometry problems, mathematical shortest path isn't always the chosen path. Context, geography, and practical needs matter.

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END OF ANSWER KEY