Primary 6 PSLE Mathematics Data Analysis Quiz

Primary 6 PSLE Mathematics Quiz - Data Analysis (Answer Key)

Total Marks: 50

Section A: Multiple Choice Questions (10 marks)

1. Answer: (2) 2.0 [2 marks]

Working: Total books = (0 × 5) + (1 × 12) + (2 × 10) + (3 × 8) + (4 × 5) = 0 + 12 + 20 + 24 + 20 = 76

Total students = 5 + 12 + 10 + 8 + 5 = 40

Average = 76 ÷ 40 = 1.9 = 2.0 (to 1 decimal place)

Marking notes:

• 1 mark for correct total books (76)
• 1 mark for correct average (2.0)
• Common mistake: Forgetting to multiply frequency by value

2. Answer: (1) 0 to 2 minutes [2 marks]

Working: Temperature drops:

• 0 to 2 min: 90 - 75 = 15°C
• 2 to 4 min: 75 - 62 = 13°C
• 4 to 6 min: 62 - 52 = 10°C
• 6 to 8 min: 52 - 45 = 7°C

Greatest drop = 15°C (0 to 2 minutes)

Marking notes:

• 1 mark for calculating all drops correctly
• 1 mark for identifying the correct interval
• Key concept: Read values from graph, calculate differences

3. Answer: (2) 60 [2 marks]

Working: MRT sector angle = 60° Total students = 360 Number of students by MRT = (60/360) × 360 = 60

Marking notes:

• 1 mark for correct fraction (60/360 = 1/6)
• 1 mark for correct answer (60)
• Key concept: Pie chart angle ÷ 360° × total = quantity

4. Answer: (2) 80 [2 marks]

Working: Highest visitors = Thursday = 180 Lowest visitors = Wednesday = 100 Difference = 180 - 100 = 80

Marking notes:

• 1 mark for identifying highest and lowest correctly
• 1 mark for correct difference
• Common mistake: Reading wrong bars

5. Answer: (2) 4.0 kg [2 marks]

Working: Total mass of 5 parcels = 2.8 × 5 = 14.0 kg Total mass of 6 parcels = 3.0 × 6 = 18.0 kg Mass of parcel F = 18.0 - 14.0 = 4.0 kg

Marking notes:

• 1 mark for finding total mass of 5 parcels (14.0 kg)
• 1 mark for finding mass of parcel F (4.0 kg)
• Key concept: Average × number = total

Section B: Short Answer Questions (20 marks)

6. Answer: 1 [2 marks]

Working: The mode is the value with the highest frequency. Frequency of 0 goals = 4 Frequency of 1 goal = 6 ← highest Frequency of 2 goals = 5 Frequency of 3 goals = 3 Frequency of 4 goals = 2

Mode = 1 goal

Marking notes:

• 1 mark for identifying highest frequency (6)
• 1 mark for correct mode (1)
• Key concept: Mode = most frequent value

7. Answer: 56.67 km/h (or 56 2/3 km/h) [2 marks]

Working: Distance at 2nd hour = 110 km Distance at 5th hour = 280 km Distance travelled = 280 - 110 = 170 km Time taken = 5 - 2 = 3 hours Average speed = 170 ÷ 3 = 56 2/3 ≈ 56.67 km/h

Marking notes:

• 1 mark for correct distance (170 km) and time (3 h)
• 1 mark for correct average speed
• Accept 56.67 km/h or 56 2/3 km/h
• Key concept: Average speed = distance ÷ time

8. Answer: 24 [2 marks]

Working: Banana angle = 108°, Orange angle = 72° Difference in angle = 108° - 72° = 36° Total children = 240 Difference in children = (36/360) × 240 = 24

Marking notes:

• 1 mark for angle difference (36°) or individual quantities
• 1 mark for correct answer (24)
• Alternative: Banana = (108/360)×240 = 72, Orange = (72/360)×240 = 48, Difference = 24

9. Answer: 3 [2 marks]

Working: Total pupils = 3 + 5 + 8 + 4 + 2 = 22 Median position = (22 + 1) ÷ 2 = 11th and 12th values (average of both) Cumulative frequency: 1 book: 3 pupils (positions 1-3) 2 books: 5 pupils (positions 4-8) 3 books: 8 pupils (positions 9-16) ← contains 11th and 12th Median = 3 books

Marking notes:

• 1 mark for correct total (22) and median position (11th/12th)
• 1 mark for correct median (3)
• Key concept: For even number of data, median = average of two middle values

10. Answer: 25.8% [2 marks]

Working: Total rainfall = 120 + 80 + 150 + 200 + 250 + 180 = 980 mm May rainfall = 250 mm Percentage = (250 ÷ 980) × 100% = 25.51...% ≈ 25.5% (to 1 d.p.)

Correction: 250/980 = 0.2551... = 25.5% (to 1 d.p.)

Marking notes:

• 1 mark for correct total (980 mm)
• 1 mark for correct percentage to 1 d.p. (25.5%)
• Common mistake: Rounding error or wrong total

11. Answer: 1.28 m [2 marks]

Working: Total height of 6 girls = 1.42 × 6 = 8.52 m Total height of 7 girls = 1.40 × 7 = 9.80 m Height of new girl = 9.80 - 8.52 = 1.28 m

Marking notes:

• 1 mark for total height of 6 girls (8.52 m) or 7 girls (9.80 m)
• 1 mark for correct answer (1.28 m)
• Key concept: New total - old total = new value

12. Answer: 6.1 hours [2 marks]

Working: Use midpoints of intervals: 0-2: midpoint = 1, 3-5: midpoint = 4, 6-8: midpoint = 7, 9-11: midpoint = 10, 12-14: midpoint = 13

Estimated total hours = (1×4) + (4×8) + (7×10) + (10×5) + (13×3) = 4 + 32 + 70 + 50 + 39 = 183

Estimated mean = 183 ÷ 30 = 6.1 hours

Marking notes:

• 1 mark for correct midpoints and multiplication
• 1 mark for correct estimated mean (6.1)
• Key concept: Grouped data mean = Σ(fx) ÷ Σf

13. Answer: 4 to 6 hours [2 marks]

Working: Temperature increases: 0-2 h: 23 - 22 = 1°C 2-4 h: 25 - 23 = 2°C 4-6 h: 27 - 25 = 2°C 6-8 h: 28 - 27 = 1°C 8-10 h: 27 - 28 = -1°C (decrease) 10-12 h: 25 - 27 = -2°C (decrease)

Greatest increase = 2°C (both 2-4 h and 4-6 h) But 4-6 h is the later interval with same increase. Accept either 2-4 or 4-6.

Marking notes:

• 1 mark for calculating all increases correctly
• 1 mark for correct interval (2-4 or 4-6)
• Key concept: Read values, calculate differences, compare

14. Answer: 90 [2 marks]

Working: Dog angle = 100°, Cat angle = 80° Total angle for Dog and Cat = 180° Total families = 180 Number of families = (180/360) × 180 = 90

Marking notes:

• 1 mark for combined angle (180°) or individual quantities
• 1 mark for correct answer (90)
• Key concept: Half the circle = half the total

15. Answer: 70% [2 marks]

Working: Total students = 1 + 2 + 3 + 2 + 1 + 1 = 10 Students who passed (score ≥ 75): 3 + 2 + 1 + 1 = 7 Percentage = (7 ÷ 10) × 100% = 70%

Marking notes:

• 1 mark for correct total (10) and passed (7)
• 1 mark for correct percentage (70%)
• Key concept: Passing includes the passing mark itself (≥ 75)

Section C: Long Answer Questions (20 marks)

16. (a) [2 marks]

Line graph requirements:

• Axes labelled correctly (Days, Number of books)
• Scale on y-axis appropriate (0 to 200, intervals of 20)
• Points plotted correctly: Mon(120), Tue(150), Wed(100), Thu(180), Fri(140)
• Points joined with straight line segments
• Title: "Books Borrowed from Library"

Marking:

• 1 mark for correct plotting of all 5 points
• 1 mark for correct line joining and labels/title

(b) Answer: Thursday to Friday [1 mark]

Working: Changes: Mon-Tue: +30 Tue-Wed: -50 Wed-Thu: +80 ← greatest increase Thu-Fri: -40

(c) Answer: 138 [1 mark]

Working: Total = 120 + 150 + 100 + 180 + 140 = 690 Average = 690 ÷ 5 = 138

17. (a) Answer: $1440 [1 mark]

Working: Food angle = 108° Amount = (108/360) × $4800 =$1440

(b) Answer: 1/4 [1 mark]

Working: Savings angle = 90° Fraction = 90/360 = 1/4

(c) Answer: $240 [2 marks]

Working: Current savings = (90/360) × $4800 =$1200 20% increase = 0.20 × $1200 =$240 OR New savings = $1200 × 1.2 =$1440, Increase = $1440 -$1200 = $240

Marking notes:

• 1 mark for current savings ($1200)
• 1 mark for increase ($240)

18. (a) Answer: 2021 [1 mark]

Working: Increases: 2019-2020: 150 - 200 = -50 (decrease) 2020-2021: 300 - 150 = +150 ← greatest 2021-2022: 350 - 300 = +50 2022-2023: 400 - 350 = +50

(b) Answer: 100% [2 marks]

Working: 2020 participants = 150 2021 participants = 300 Increase = 150 Percentage increase = (150 ÷ 150) × 100% = 100%

Marking notes:

• 1 mark for correct increase (150)
• 1 mark for correct percentage (100%)

(c) Answer: 450 [1 mark]

Working: Trend 2021-2023: +50 per year (300 → 350 → 400) 2024 estimate = 400 + 50 = 450

19. (a) Answer: 2.0-2.4 kg [1 mark]

Working: Total parcels = 20 Median position = (20 + 1) ÷ 2 = 10.5th → average of 10th and 11th values Cumulative frequency: 1.0-1.4: 3 (positions 1-3) 1.5-1.9: 5 (positions 4-8) 2.0-2.4: 6 (positions 9-14) ← contains 10th and 11th Median interval = 2.0-2.4 kg

(b) Answer: 2.075 kg [2 marks]

Working: Use midpoints: 1.0-1.4: midpoint = 1.2 1.5-1.9: midpoint = 1.7 2.0-2.4: midpoint = 2.2 2.5-2.9: midpoint = 2.7 3.0-3.4: midpoint = 3.2

Estimated total mass = (1.2×3) + (1.7×5) + (2.2×6) + (2.7×4) + (3.2×2) = 3.6 + 8.5 + 13.2 + 10.8 + 6.4 = 42.5 kg

Estimated mean = 42.5 ÷ 20 = 2.125 kg

Correction: Let me recalculate: 1.2×3 = 3.6 1.7×5 = 8.5 2.2×6 = 13.2 2.7×4 = 10.8 3.2×2 = 6.4 Sum = 42.5 Mean = 42.5/20 = 2.125 kg

Marking notes:

• 1 mark for correct midpoints and Σfx (42.5)
• 1 mark for correct mean (2.125 kg)

(c) Answer: 3/10 [1 mark]

Working: Parcels with mass ≥ 2.5 kg: intervals 2.5-2.9 (4) and 3.0-3.4 (2) = 6 parcels Total parcels = 20 Probability = 6/20 = 3/10

20. (a) Answer: 10 cm/h [1 mark]

Working: Water level rises from 10 cm to 50 cm in 4 hours (0 to 4 hours) Rise = 50 - 10 = 40 cm Rate = 40 cm ÷ 4 h = 10 cm/h

(b) Answer: 7.5 cm/h [1 mark]

Working: Water level falls from 50 cm to 20 cm in 4 hours (4 to 8 hours) Fall = 50 - 20 = 30 cm Rate = 30 cm ÷ 4 h = 7.5 cm/h

(c) Answer: 3 hours and 7 hours [2 marks]

Working: First time (rising): Water level = 40 cm From 10 cm at 10 cm/h: Time = (40 - 10) ÷ 10 = 3 hours

Second time (falling): Water level = 40 cm From 50 cm at 7.5 cm/h: Time from 4h = (50 - 40) ÷ 7.5 = 10 ÷ 7.5 = 4/3 h = 1 h 20 min Time = 4 + 1 1/3 = 5 1/3 hours = 5 hours 20 minutes

Wait, let me recheck the graph values: At 6 hours, water level = 35 cm (given) At 4 hours, water level = 50 cm Rate = (50-35)/2 = 7.5 cm/h ✓

From 50 cm to 40 cm = 10 cm drop Time = 10 ÷ 7.5 = 4/3 hours = 1 hour 20 minutes So time = 4 + 1 1/3 = 5 1/3 hours

But the question asks "At what time was the water level exactly 40 cm?" - there are two times.

Marking notes:

• 1 mark for first time (3 hours)
• 1 mark for second time (5 1/3 hours or 5 hours 20 minutes)
• Accept 5.33 hours or 5 h 20 min

End of Answer Key