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Natural numbers, integers, rational and irrational numbers

WJEC GCSE Maths

Topic questions Number Natural numbers, integers, rational & irrational numbers

Natural numbers, integers, rational & irrational numbers

9 questions · 35 marks · about 45 minutes

Natural numbers, integers, rational and irrational numbers questions

TopicNatural numbers, integers, rational & irrational numbers

Unit 1: Non-calculator June 2025 Higher tier, Question 19 5 marks

Figure for question 19

Figure for question 19

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Mark scheme for question 19

Unit 1: Non-calculator June 2024 Higher tier, Question 15 3 marks

(a)

Circle the correct answer in each of the following questions:

(a)(i)

$Question 15, shown as an image$

$Question 15, shown as an image$

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Mark scheme for question 15(a)(i)

(a)(ii)

$Question 15, shown as an image$

$Question 15, shown as an image$

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Mark scheme for question 15(a)(ii)

$Question 15, shown as an image$

$Question 15, shown as an image$

$Question 15, shown as an image$

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Mark scheme for question 15(b)

Unit 1: Non-calculator November 2023 Higher tier, Question 16 7 marks

(a)

Circle the correct answer for each of the following statements.

(a)(i)

$Question 16, shown as an image$

$Question 16, shown as an image$

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Mark scheme for question 16(a)(i)

(a)(ii)

$Question 16, shown as an image$

$Question 16, shown as an image$

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(b)

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(c)

Figure for question 16

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(d)

Give an example of an irrational number that lies between 6 and 7.

My example of an irrational number is_........

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Mark scheme for question 16(d)

Unit 1: Non-calculator June 2023 Higher tier, Question 17 5 marks

(a)

$Question 17, shown as an image$

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(b)

(b)(i)

Figure for question 17

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(b)(ii)

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(b)(iii)

Write down an integer value of x that is greater than 5, for which $fraction$ and $fraction$

are both rational.

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Mark scheme for question 17(b)(iii)

Unit 2: Calculator-allowed November 2022 Higher tier, Question 15 1 mark

Write down an irrational number whose value is between 9 and 10.

Write your answer in the box below.

Figure for question 15

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Mark scheme for question 15

Unit 1: Non-calculator June 2022 Higher tier, Question 15 5 marks

Figure for question 15

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Mark scheme for question 15

Unit 1: Non-calculator November 2020 Higher tier, Question 18 2 marks

A circle has radius r cm, where r is an integer.

The side of a square is of length xcm.

If the circle and square have the same area, explain why x cannot be an integer.

You should consider algebraic expressions in your answer.

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Mark scheme for question 18

Unit 1: Non-calculator November 2019 Higher tier, Question 15 5 marks

Figure for question 15

Figure for question 15

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Mark scheme for question 15

Unit 2: Calculator-allowed June 2017 Higher tier, Question 19 2 marks

(a)

Give one example to show that the square of an irrational number is not always rational.

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Mark scheme for question 19(a)

(b)

Find two different irrational numbers to make the answer to the calculation below rational.

Complete the calculation by filling in the three boxes.

Figure for question 19

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Mark scheme for question 19(b)

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