Primary 6 PSLE Mathematics Geometry Quiz

Primary 6 PSLE Mathematics Quiz - Geometry

Answer Key

Section A: Angles and Properties of Shapes

1. ∠ADC = 70°
[2 marks]
Working: In a parallelogram, consecutive angles are supplementary. ∠ABC + ∠ADC = 180°. 110° + ∠ADC = 180°. ∠ADC = 70°.
Common mistake: Students may incorrectly assume opposite angles are supplementary (they are equal, not supplementary).

2. ∠QPR = 84°
[2 marks]
Working: In an isosceles triangle, base angles are equal. ∠PQR = ∠PRQ = 48°. Sum of angles in triangle = 180°. ∠QPR = 180° − 48° − 48° = 84°.
Marking note: Award 1 mark for identifying base angles are equal, 1 mark for correct calculation.

3. ∠ABC = 116°
[2 marks]
Working: In a rhombus, consecutive angles are supplementary. ∠DAB + ∠ABC = 180°. 64° + ∠ABC = 180°. ∠ABC = 116°.
Note: A rhombus is a special parallelogram, so the same angle properties apply.

4. ∠B = 105°
[2 marks]
Working: In a trapezium with AB ∥ CD, consecutive interior angles between parallel lines are supplementary. ∠A + ∠D = 75° + 105° = 180° (confirms AB ∥ CD). ∠B + ∠C = 180°. Since ∠A = 75° and AB ∥ CD, ∠B = 180° − 75° = 105° (corresponding/co-interior reasoning). Alternatively, sum of interior angles of quadrilateral = 360°. ∠A + ∠B + ∠C + ∠D = 360°. 75° + ∠B + 75° + 105° = 360°. ∠B = 105°.
Marking note: Accept any valid reasoning.

5. ∠BEC = 70°
[2 marks]
Working: In parallelogram ABCD, ∠ABC = ∠ABE + ∠EBC = 30° + 40° = 70°. Since BE = BC, triangle BEC is isosceles with BE = BC. ∠BEC = ∠BCE. In triangle BEC, ∠EBC = 40°. ∠BEC + ∠BCE + ∠EBC = 180°. 2 × ∠BEC + 40° = 180°. 2 × ∠BEC = 140°. ∠BEC = 70°.
Marking note: Award 1 mark for identifying triangle BEC is isosceles, 1 mark for correct answer.

Section B: Area and Perimeter

6.
(a) Area = 216 cm²
[1 mark]
Working: Area = length × width = 18 × 12 = 216 cm².

(b) Perimeter = 60 cm
[1 mark]
Working: Perimeter = 2 × (length + width) = 2 × (18 + 12) = 2 × 30 = 60 cm.

7. Total area = 220 cm²
[2 marks]
Working: Area of square = 10 × 10 = 100 cm². Area of rectangle = 15 × 8 = 120 cm². Total area = 100 + 120 = 220 cm².
Marking note: Award 1 mark for each correct area calculation.

8. Area = 63 cm²
[2 marks]
Working: Area of triangle = ½ × base × height = ½ × 14 × 9 = 63 cm².
Common mistake: Forgetting to multiply by ½.

9. Perimeter = 58 cm
[2 marks]
Working: When joined along their lengths (12 cm), the larger rectangle has dimensions: length = 12 cm, width = 5 + 5 = 10 cm. Perimeter = 2 × (12 + 10) = 2 × 22 = 44 cm.
Correction: Re-reading the question — "joined along their lengths" means the 12 cm sides are joined. The resulting shape has length = 12 cm and width = 5 + 5 = 10 cm. Perimeter = 2 × (12 + 10) = 44 cm.
Answer: 44 cm
Marking note: Award 1 mark for correct dimensions of larger rectangle, 1 mark for correct perimeter.

10. Perimeter = 48 cm
[2 marks]
Working: Area of square = side² = 144 cm². Side = √144 = 12 cm. Perimeter = 4 × 12 = 48 cm.
Marking note: Award 1 mark for finding side length, 1 mark for correct perimeter.

Section C: Circles

11.
(a) Circumference = 44 cm
[2 marks]
Working: C = 2πr = 2 × ²²⁄₇ × 7 = 44 cm.

(b) Area = 154 cm²
[2 marks]
Working: A = πr² = ²²⁄₇ × 7 × 7 = 154 cm².
Marking note: Award 1 mark for correct formula, 1 mark for correct answer.

12. Circumference = 62.8 cm
[2 marks]
Working: Diameter = 20 cm, so radius = 10 cm. C = πd = 3.14 × 20 = 62.8 cm.
Note: Using π = 3.14 as specified.
Marking note: Award 1 mark for using correct value of π, 1 mark for correct answer.

13. Perimeter = 36 cm
[2 marks]
Working: Perimeter of semicircle = curved part + diameter. Curved part = ½ × πd = ½ × ²²⁄₇ × 14 = 22 cm. Perimeter = 22 + 14 = 36 cm.
Common mistake: Forgetting to include the diameter in the perimeter.

14. Radius = 14 m
[2 marks]
Working: C = 2πr. 88 = 2 × ²²⁄₇ × r. 88 = ⁴⁴⁄₇ × r. r = 88 × ⁷⁄₄₄ = 2 × 7 = 14 m.
Marking note: Award 1 mark for correct equation setup, 1 mark for correct answer.

15. Perimeter = 144 m
[2 marks]
Working: The perimeter consists of the two lengths of the rectangle and the circumference of one full circle (two semicircles make one circle). Diameter of semicircles = width of rectangle = 14 m. Circumference of circle = πd = ²²⁄₇ × 14 = 44 m. Perimeter = 50 + 50 + 44 = 144 m.
Common mistake: Using only one semicircle's curved length instead of both.

Section D: Volume and Composite Figures

16.
(a) Volume = 216 cm³
[1 mark]
Working: Volume = edge³ = 6³ = 216 cm³.

(b) Surface area = 216 cm²
[1 mark]
Working: Surface area = 6 × edge² = 6 × 36 = 216 cm².

17. Volume = 200 cm³
[2 marks]
Working: Volume = length × width × height = 10 × 5 × 4 = 200 cm³.
Marking note: Award 1 mark for correct formula, 1 mark for correct answer.

18.
(a) Volume of water = 1600 cm³
[1 mark]
Working: Volume = base area × height = 200 × 8 = 1600 cm³.

(b) Additional water needed = 1400 cm³
[2 marks]
Working: Total volume of tank = 200 × 15 = 3000 cm³. Additional water = 3000 − 1600 = 1400 cm³.
Marking note: Award 1 mark for total volume, 1 mark for correct subtraction.

19. Total volume = 282 cm³
[2 marks]
Working: Volume of Cuboid A = 8 × 6 × 4 = 192 cm³. Volume of Cuboid B = 6 × 6 × 3 = 108 cm³. Overlap volume = 6 × 3 × 3 = 54 cm³ (the overlapping region is 6 cm × 3 cm × 3 cm, where the 3 cm is the height of Cuboid B that overlaps with Cuboid A's 4 cm height). Total volume = 192 + 108 − 54 = 246 cm³.
Revised calculation: The overlap is the shared region. Cuboid A is 8×6×4. Cuboid B is 6×6×3. They join along a 6×3 face (the overlap). The overlap volume = 6 × 3 × 3 = 54 cm³. Total = 192 + 108 − 54 = 246 cm³.
Answer: 246 cm³
Marking note: Award 1 mark for individual volumes, 1 mark for subtracting overlap.

20.
(a) Volume of water = 1600 cm³
[2 marks]
Working: Total volume = 25 × 16 × 10 = 4000 cm³. Water fills ²⁄₅ of height, so water height = ²⁄₅ × 10 = 4 cm. Volume of water = 25 × 16 × 4 = 1600 cm³.
Marking note: Award 1 mark for finding water height, 1 mark for correct volume.

(b) Height = 8 cm
[2 marks]
Working: Volume of water = 1600 cm³. Base area of second container = 200 cm². Height = Volume ÷ Base area = 1600 ÷ 200 = 8 cm.
Marking note: Award 1 mark for correct formula, 1 mark for correct answer.

Summary of Marks

End of Answer Key