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Secondary 1 Mathematics Statistics Probability Quiz
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Questions
Secondary 1 Mathematics Quiz - Statistics Probability
Name: ________________________
Class: ________________________
Date: ________________________
Score: ______ / 40
Duration: 50 minutes
Total Marks: 40
Instructions:
- Answer ALL questions.
- Show your working clearly in the spaces provided.
- Write your answers in the spaces provided.
- The number of marks for each question is shown in brackets [ ].
- You may use a calculator where appropriate.
- Give non-exact answers correct to 1 decimal place unless otherwise stated.
Section A: Data Handling and Interpretation (Questions 1–10)
Questions 1–5 are based on the table below.
The table shows the number of books read by 30 students in a class during the June holidays.
| Number of books | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Frequency | 3 | 5 | 8 | 7 | 4 | 3 |
1. How many students read more than 3 books? [2]
2. What is the modal number of books read? [1]
3. Calculate the mean number of books read by the students. Show your working. [3]
4. Find the median number of books read. Show your working. [2]
5. A student is chosen at random. What is the probability that the student read exactly 2 books? Give your answer as a fraction in its simplest form. [2]
Questions 6–8 are based on the bar chart below.
The bar chart shows the favourite sports of 40 students in a class.
| Sport | Basketball | Soccer | Swimming | Badminton | Volleyball |
|---|---|---|---|---|---|
| Number of students | 10 | 12 | 8 | 6 | 4 |
6. What fraction of the students chose Soccer as their favourite sport? Give your answer in its simplest form. [2]
7. Calculate the percentage of students who chose Swimming. [2]
8. Represent the data in a pie chart by finding the angle for the Basketball sector. Show your working. [3]
9. The mean of five numbers is 18. Four of the numbers are 12, 20, 15 and 25. Find the fifth number. [3]
10. The grouped frequency table below shows the masses (in kg) of 25 students.
| Mass (kg) | 30–34 | 35–39 | 40–44 | 45–49 | 50–54 |
|---|---|---|---|---|---|
| Frequency | 3 | 7 | 9 | 4 | 2 |
State the modal class. [1]
Section B: Probability (Questions 11–17)
11. A fair six-sided die is rolled once. Find the probability of obtaining: (a) a prime number [2]
(b) a number greater than 4 [1]
12. A bag contains 5 red marbles, 3 blue marbles and 2 green marbles. One marble is picked at random. Find the probability that the marble is: (a) red [1]
(b) blue or green [2]
(c) yellow [1]
13. A letter is chosen at random from the word PROBABILITY. Find the probability that the letter chosen is: (a) a vowel [2]
(b) the letter B [1]
14. In a class of 35 students, 14 are girls. A student is chosen at random. Find the probability that the student is a boy. Give your answer as a fraction in its simplest form. [2]
15. Two fair coins are tossed. List all the possible outcomes. Hence find the probability of getting two heads. [3]
16. A box contains 4 white cards, 6 black cards and 2 yellow cards. One card is drawn at random. Find the probability that the card is not white. Give your answer as a decimal. [3]
17. The probability that it rains on a particular day is 0.35. Find the probability that it does not rain on that day. [2]
Section C: Applied and Multi-Step Problems (Questions 18–20)
18. The pie chart below represents the favourite fruits of 60 students. The angle for the Apple sector is 90° and the angle for the Banana sector is 120°.
(a) Find the number of students who chose Apple. [2]
(b) Find the number of students who chose Banana. [2]
(c) The remaining students chose Cherry. Find the angle for the Cherry sector. [2]
19. The test scores of 10 students are shown below:
78, 85, 92, 67, 85, 73, 90, 85, 88, 76
(a) Find the mean score. [2]
(b) Find the median score. Show your working. [3]
(c) State the mode. [1]
(d) Which measure of central tendency (mean, median or mode) best represents this data set? Give a reason for your answer. [2]
20. A bag contains 3 red balls, 5 blue balls and x green balls. A ball is drawn at random from the bag. The probability of drawing a red ball is 1/4.
(a) Find the value of x. [3]
(b) Find the probability of drawing a green ball. [2]
End of Quiz
Answers
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