Secondary 1 Mathematics Statistics Probability Quiz

Secondary 1 Mathematics Quiz - Statistics Probability

Answer Key

Section A: Data Handling and Interpretation

1. [2]

• Students who read more than 3 books = students who read 4 or 5 books
• = 4 + 3 = 7 students
• ✓ [1] for correct values identified; ✓ [1] for correct final answer

2. [1]

• The mode is the value with the highest frequency.
• Highest frequency = 8, which corresponds to 2 books.
• ✓ [1] for answer: 2

3. [3]

• Mean = (Sum of all values) / (Total frequency)
• Sum = (0 × 3) + (1 × 5) + (2 × 8) + (3 × 7) + (4 × 4) + (5 × 3)
• Sum = 0 + 5 + 16 + 21 + 16 + 15 = 73
• Mean = 73 ÷ 30 = 2.43 (or 2.4 to 1 d.p.)
• ✓ [1] for correct multiplication/frequency products; ✓ [1] for correct sum; ✓ [1] for correct division and answer
• Common mistake: Forgetting to multiply each value by its frequency.

4. [2]

• Total frequency = 30 (even), so median = average of 15th and 16th values.
• Cumulative frequency: 0→3, 1→8, 2→16, 3→23, 4→27, 5→30
• 15th value falls in the "2" group (cumulative reaches 16 at value 2)
• 16th value also falls in the "2" group
• Median = (2 + 2) / 2 = 2
• ✓ [1] for correct cumulative frequency or identification of middle position; ✓ [1] for correct answer

5. [2]

• Number of students who read exactly 2 books = 8
• Total students = 30
• P(2 books) = 8/30 = 4/15
• ✓ [1] for correct fraction 8/30; ✓ [1] for simplification to 4/15
• Common mistake: Not simplifying the fraction.

6. [2]

• Students who chose Soccer = 12
• Total students = 40
• Fraction = 12/40 = 3/10
• ✓ [1] for correct fraction 12/40; ✓ [1] for simplification to 3/10

7. [2]

• Students who chose Swimming = 8
• Percentage = (8/40) × 100 = 20%
• ✓ [1] for correct fraction; ✓ [1] for correct percentage

8. [3]

• Students who chose Basketball = 10
• Total = 40
• Angle = (10/40) × 360° = 90°
• ✓ [1] for correct fraction 10/40; ✓ [1] for multiplying by 360°; ✓ [1] for correct answer 90°

9. [3]

• Mean of five numbers = 18
• Sum of five numbers = 18 × 5 = 90
• Sum of four known numbers = 12 + 20 + 15 + 25 = 72
• Fifth number = 90 − 72 = 18
• ✓ [1] for finding total sum (18 × 5 = 90); ✓ [1] for sum of four numbers; ✓ [1] for correct answer 18

10. [1]

• Modal class = class with the highest frequency
• Highest frequency = 9, which corresponds to 40–44
• ✓ [1] for answer: 40–44

Section B: Probability

11. [3 total] (a) [2]

• Sample space on a die: {1, 2, 3, 4, 5, 6}
• Prime numbers: {2, 3, 5} → 3 outcomes
• P(prime) = 3/6 = 1/2
• ✓ [1] for identifying prime numbers correctly; ✓ [1] for correct probability

(b) [1]

• Numbers greater than 4: {5, 6} → 2 outcomes
• P(> 4) = 2/6 = 1/3
• ✓ [1] for correct answer

12. [4 total] (a) [1]

• Total marbles = 5 + 3 + 2 = 10
• P(red) = 5/10 = 1/2
• ✓ [1] for correct answer

(b) [2]

• P(blue or green) = (3 + 2) / 10 = 5/10 = 1/2
• ✓ [1] for adding blue and green; ✓ [1] for correct simplified answer

(c) [1]

• There are no yellow marbles in the bag.
• P(yellow) = 0
• ✓ [1] for answer: 0

13. [3 total] (a) [2]

• Word: P-R-O-B-A-B-I-L-I-T-Y (11 letters)
• Vowels: O, A, I, I → 4 vowels
• P(vowel) = 4/11
• ✓ [1] for correct count of vowels; ✓ [1] for correct probability

(b) [1]

• Letter B appears 2 times out of 11 letters.
• P(B) = 2/11
• ✓ [1] for correct answer

14. [2]

• Number of boys = 35 − 14 = 21
• P(boy) = 21/35 = 3/5
• ✓ [1] for finding number of boys; ✓ [1] for simplified fraction

15. [3]

• Possible outcomes when tossing two coins: {HH, HT, TH, TT}
• Total outcomes = 4
• Favourable outcome (two heads) = {HH} → 1 outcome
• P(two heads) = 1/4
• ✓ [1] for listing all outcomes correctly; ✓ [1] for identifying total outcomes; ✓ [1] for correct probability

16. [3]

• Total cards = 4 + 6 + 2 = 12
• Cards that are not white = 6 + 2 = 8
• P(not white) = 8/12 = 2/3 = 0.667 (or 0.7 to 1 d.p., or accept 2/3)
• ✓ [1] for finding total; ✓ [1] for finding non-white cards; ✓ [1] for correct decimal answer
• Note: Accept 0.667, 0.67, or 0.7 depending on rounding instruction.

17. [2]

• P(rain) + P(no rain) = 1
• P(no rain) = 1 − 0.35 = 0.65
• ✓ [1] for using complement rule; ✓ [1] for correct answer

Section C: Applied and Multi-Step Problems

18. [6 total] (a) [2]

• Number choosing Apple = (90/360) × 60 = 15 students
• ✓ [1] for correct fraction; ✓ [1] for correct answer

(b) [2]

• Number choosing Banana = (120/360) × 60 = 20 students
• ✓ [1] for correct fraction; ✓ [1] for correct answer

(c) [2]

• Angle for Cherry = 360° − 90° − 120° = 150°
• ✓ [1] for subtracting from 360°; ✓ [1] for correct answer

19. [8 total] (a) [2]

• Sum = 78 + 85 + 92 + 67 + 85 + 73 + 90 + 85 + 88 + 76 = 819
• Mean = 819 ÷ 10 = 81.9
• ✓ [1] for correct sum; ✓ [1] for correct mean

(b) [3]

• Arrange in order: 67, 73, 76, 78, 85, 85, 85, 88, 90, 92
• n = 10 (even), so median = average of 5th and 6th values
• 5th value = 85, 6th value = 85
• Median = (85 + 85) / 2 = 85
• ✓ [1] for correct ordering; ✓ [1] for identifying 5th and 6th values; ✓ [1] for correct median

(c) [1]

• Mode = 85 (appears 3 times, most frequent)
• ✓ [1] for correct answer

(d) [2]

• Accept any of mean, median, or mode with a valid reason.
• Sample answer: The median best represents the data because the data has no extreme outliers and the median is not affected by extreme values. (Or: The mode of 85 is close to the mean and median, and it is the most common score.)
• ✓ [1] for stating a measure; ✓ [1] for a valid reason

20. [5 total] (a) [3]

• Total balls = 3 + 5 + x = 8 + x
• P(red) = 3 / (8 + x) = 1/4
• Cross multiply: 3 × 4 = 1 × (8 + x)
• 12 = 8 + x
• x = 4
• ✓ [1] for setting up equation; ✓ [1] for cross multiplication; ✓ [1] for correct answer

(b) [2]

• Total balls = 3 + 5 + 4 = 12
• Green balls = 4
• P(green) = 4/12 = 1/3
• ✓ [1] for correct total; ✓ [1] for correct probability

Total: 40 marks