Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Number 10
19 practice questions
Practice questions
1–10 of 10 · Normal
Question 1
2 marks · Normal
Answer and see the solution →Write down one rational number and one irrational number between 3 and 4.
Question 2
3 marks · Normal
Answer and see the solution →Simplify . Give your answer as a surd in its simplest form.
Question 3
3 marks · Normal
Answer and see the solution →Explain why cannot be written as a rational number, but can. Use your knowledge of surds and rational numbers.
Question 4
4 marks · Normal
Answer and see the solution →Consider the numbers:
- A
- 0.333...
- B
- C
- D
- 2.505505550...
(a)[2 marks]Write each number (A, B, C, D) as either rational or irrational.
(b)[1 mark]State the value of B.
(c)[1 mark]Explain why D is irrational.
Question 5
4 marks · Normal
Answer and see the solution →Complete the table below by writing each surd in its simplest form.
Surd Simplest form Question 6
2 marks · Normal
Answer and see the solution →Expand and simplify . Express your answer in the form , where and are integers.
Question 7
3 marks · Normal
Answer and see the solution →Rationalise the denominator and simplify: .
Question 8
2 marks · Normal
Answer and see the solution →Simplify the surd and write your answer in the form , where and are integers and is as small as possible.
Question 9
3 marks · Normal
Answer and see the solution →The expressions and . (a) Simplify as far as possible. [1] (b) Write down in the form , where is an integer. [2]
(a)[1 mark]Simplify as far as possible.
(b)[2 marks]Write in the form , where is an integer.
Question 10
3 marks · Normal
Answer and see the solution →Is the number rational or irrational? Explain how you know, using what you know about rational and irrational numbers.