Instructions

  • English Section B – Comprehension
  • Duration: 45 minutes + 5 minutes reading time
  • Instructions:
    • Do not open this booklet until instructed.
    • Write your name, school, and candidate number at the top of the page.
    • Comprehension questions are included in this booklet.
    • The comprehension passage is on a separate green sheet.
    • Read through both the passage and all questions before writing anything.
    • Spend at least 5 minutes reading and thinking about the material.
    • Write your answers in the spaces provided after each question.
    • If you need more space for an answer, use the section at the end of the booklet, ensuring to number your answers carefully.
    • Base your answers solely on the provided passage.
  • Total Marks: 50 marks

Mathematics is often seen as a challenging subject, but it has a unique way of revealing the beauty of the world around us. From the way leaves grow on trees to the patterns in a snowflake, mathematics is everywhere! In this passage, we will explore various mathematical concepts and how they relate to our everyday lives.

Imagine you are walking through a park and you see a beautiful fountain. Did you know that the shape of the fountain can be described using geometry? Geometry is the branch of mathematics that deals with shapes and sizes. For example, a fountain might be circular, which means it is shaped like a round coin. The formula for finding the area of a circle is given by A = \pi r^2

, where r
is the radius of the circle.

Next, think about the trees in the park. Many trees have leaves that grow in a pattern. This pattern can often be described using sequences in mathematics. A sequence is a list of numbers that follow a certain rule. For example, the Fibonacci sequence is a famous sequence where each number is the sum of the two previous numbers (0, 1, 1, 2, 3, 5, 8, …). This sequence is not only interesting in mathematics but also appears in nature, such as in the arrangement of leaves on a stem.

Now, let’s talk about estimation. Estimation is when you make an educated guess about a number. For example, if you see a jar full of marbles, instead of counting each marble, you can estimate the total by looking at the size of the jar and how full it seems. This skill can be very useful in real-life situations, such as shopping, where you might want to quickly calculate the total cost of items.

Statistics is another important area of mathematics. It involves collecting and analysing data to understand patterns and trends. For instance, if you wanted to know how many students in your class prefer cats over dogs, you could conduct a survey. After collecting the data, you might find that 60% of your classmates prefer cats. This information can help you understand the preferences of your peers better.

Lastly, let’s not forget about problem-solving. Mathematics teaches you how to think critically and solve problems effectively. For instance, if you have 12 apples and you want to share them equally among 4 friends, you can use division. Dividing 12 by 4 gives you 3, meaning each friend gets 3 apples. This type of thinking is not just useful in maths; it can help you in many aspects of life.

Now that we have explored these interesting aspects of mathematics, let’s test your understanding with some questions!

Questions:

  1. What is geometry, and how is it related to the fountain in the park?
  2. Describe the formula for calculating the area of a circle.
  3. What is a sequence in mathematics, and can you give an example?
  4. How does the Fibonacci sequence appear in nature?
  5. What is estimation, and why is it useful in everyday situations?
  6. How might you estimate the number of marbles in a jar?
  7. What is the purpose of statistics in mathematics?
  8. How can conducting a survey help you understand your classmates’ preferences?
  9. What does it mean if 60% of students prefer cats over dogs?
  10. Explain the importance of problem-solving in mathematics.
  11. How do you divide 12 apples among 4 friends, and what does this illustrate?
  12. Why is it helpful to have a good understanding of shapes and sizes?
  13. Can you think of a real-life scenario where estimation would be crucial?
  14. How does the study of patterns in mathematics apply to everyday life?
  15. What skills do you think are enhanced by learning mathematics?
  16. How can mathematics help in making informed decisions?
  17. In what ways do you think mathematics is present in art and architecture?
  18. Why is it important to learn about data analysis in today’s world?
  19. How can understanding sequences help in predicting future events?
  20. What role does critical thinking play in solving mathematical problems?

Answers:

  1. Geometry is the branch of mathematics that deals with shapes and sizes. It relates to the fountain because its shape can be described and measured using geometric principles.
  2. The formula for calculating the area of a circle is A = \pi r^2
    , where r
    is the radius of the circle.
  3. A sequence in mathematics is a list of numbers that follow a certain rule, such as the Fibonacci sequence, where each number is the sum of the two previous numbers.
  4. The Fibonacci sequence appears in nature in various forms, such as in the arrangement of leaves on a stem or the pattern of seeds in a sunflower.
  5. Estimation is making an educated guess about a number, which is useful in everyday situations for quickly calculating totals without precise counting.
  6. You might estimate the number of marbles in a jar by observing the size of the jar and how full it looks instead of counting each marble.
  7. The purpose of statistics is to collect and analyse data to understand patterns and trends in a population or dataset.
  8. Conducting a survey helps you gather information on your classmates’ preferences, allowing for a better understanding of their likes and dislikes.
  9. If 60% of students prefer cats over dogs, it means that out of every 10 students, approximately 6 prefer cats.
  10. Problem-solving is important in mathematics as it teaches critical thinking and how to approach challenges logically.
  11. To divide 12 apples among 4 friends, you divide 12 by 4, which gives each friend 3 apples. This illustrates the concept of division.
  12. Understanding shapes and sizes helps in many areas, such as construction, art, and even cooking, where measurements are crucial.
  13. A real-life scenario where estimation is crucial could be estimating expenses while budgeting for a trip.
  14. Studying patterns in mathematics applies to everyday life by helping us identify trends, make predictions, and understand relationships between different elements.
  15. Learning mathematics enhances skills such as critical thinking, problem-solving, and analytical reasoning.
  16. Mathematics helps in making informed decisions by providing tools for analysing data and evaluating options logically.
  17. Mathematics is present in art and architecture through geometric shapes, symmetry, and proportions.
  18. Learning about data analysis is important today to interpret information accurately and make data-driven decisions in various fields.
  19. Understanding sequences helps predict future events by recognising trends and patterns that might repeat or evolve.
  20. Critical thinking plays a significant role in solving mathematical problems as it encourages logical reasoning and creativity in finding solutions.