Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Number 10
19 practice questions
Practice questions
11–19 of 19
Question 11
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 12
4 marks · Normal
Answer and see the solution →Complete the table below by writing each surd in its simplest form.
Surd Simplest form Question 13
2 marks · Normal
Answer and see the solution →Expand and simplify . Express your answer in the form , where and are integers.
Question 14
3 marks · Normal
Answer and see the solution →Rationalise the denominator and simplify: .
Question 15
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 16
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 17
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.
Question 18
2 marks · Hard
Answer and see the solution →The length of one side of a square is cm. Express the area of the square in the form cm², where and are integers and is as small as possible.
Question 19
4 marks · Hard
Answer and see the solution →State for each of the following numbers whether it is rational or irrational. If rational, write it as a fraction in the form , where and are integers. Show full reasoning.
(a)[1 mark](the decimal repeats with 25)
(b)[1 mark](c)[1 mark](d)[1 mark]