Find the reciprocal of .

\begin{solution} Goal: We need to find the reciprocal of the mixed number . Step 1: First, convert the mixed number into an improper fraction. Step 2: The reciprocal of a number is 1 divided by that number. For a fraction, this is found by inverting the fraction (swapping the numerator and the denominator). The reciprocal of is . \textbf{M1} This can also be expressed as a decimal: Conclusion: The reciprocal of is . \end{solution} Mark Scheme: - or 0.8 (1.0 M)

From this list, write down an irrational number.

An irrational number is a number that cannot be expressed as a simple fraction , where and are integers. An irrational number has a decimal representation that is non-terminating and non-repeating.We examine each number in the given list: is a fraction, so it is a rational number. is a terminating decimal, which can be written as the fraction or . It is a rational number. is equal to , which can be written as the fraction . It is a rational number. is an integer, which can be written as the fraction . It is a rational number. is the square root of 7, which is not a perfect square. Its decimal value is non-terminating and non-repeating, so it cannot be written as a simple fraction. Thus, is an irrational number.Therefore, the irrational number from the list is .

From this list, write downan irrational number.

Goal: Identify the irrational number from the list .We will examine each number in the list to determine if it is rational or irrational. An irrational number is a number that cannot be written as a simple fraction where and are integers. is a rational number because it is a fraction. is a rational number because it is an integer (). is equal to , which is an integer and therefore rational. is a rational number because it is an integer (). is a rational number because it can be written as the fraction . is the square root of a number that is not a perfect square. This means it cannot be written as a simple fraction and is therefore an irrational number.Conclusion: The irrational number from the list is .

3. Write down the number in this list that is irrational.

Marking Scheme Analysis: Question: 3 Answer: Marks: 1 mark is awarded for correctly identifying the irrational number. There are no method marks. Step-by-step Solution: Understand the definition of an irrational number. An irrational number is a number that cannot be expressed as a simple fraction , where 'p' and 'q' are integers and q ≠ 0. When written as a decimal, an irrational number is non-terminating and non-repeating. Examine the list of numbers provided in the question. Although the list is not shown in the marking scheme, the task is to check each number to determine if it is rational or irrational. Identify the irrational number. The marking scheme indicates that the correct answer is . This is because the square root of any integer that is not a perfect square is an irrational number. Since 3 is not a perfect square, is irrational. Its decimal representation is approximately 1.7320508..., which continues infinitely without repeating. Conclusion. The only irrational number in the list is . According to the mark scheme, writing this down earns 1 mark.

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IGCSE (CAMBRIDGE)|9th and 10th|Extended Maths (0580)

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