IGCSEFurther MathsEdexcelExam QuestionsLogarithms, Indices & SurdsSurds

Surds (Edexcel IGCSE Further Pure Maths): Exam Questions

Exam code: 4PM1

12 mins3 questions
1a
1 mark

Show that fraction numerator 3 over denominator square root of 0.9 end root end fraction equals square root of 10

How did you do?

1b
2 marks

Express fraction numerator 1 over denominator square root of 10 space minus space 3 end fraction in the form a square root of 10 space plus space b , where space a and b are integers.

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2
5 marks

Given that fraction numerator a plus 2 square root of 5 over denominator 3 minus square root of 5 end fraction equals fraction numerator 11 plus b square root of 5 over denominator 2 end fraction where a is an integer and b is prime,

find the value of a and the value of b
Show your working clearly.

How did you do?

3
4 marks
Right-angled triangle ABC; AB is 2+4√5 cm, BC is a+b√5 cm. The diagram notes it is not accurately drawn.

Figure 1 shows the triangle A B C

angle A B C equals 90 degree      A B equals left parenthesis 2 plus 4 square root of 5 right parenthesis text  cm end text      B C equals left parenthesis a plus b square root of 5 right parenthesis text  cm end text where and b are integers.

The area of triangle A B C equals open parentheses 34 plus 11 square root of 5 close parentheses space cm squared

Without using a calculator, find the value of a and the value of b

How did you do?