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Edexcel IGCSE Maths

Topic questions Pure mathematics Surds

Surds

18 questions · 80 marks · about 1.5 hours

Surds questions

Paper 1H June 2025 Higher tier, Question 15 4 marks

$Question 15, shown as an image$

(a)

Find the value of k

[1]

(b)

Show that $fraction$ can be written in the form c maths symbol $fraction$

where c and d are integers. Show each stage of your working clearly.

[3]

Reveal mark scheme

Mark scheme for question 15(b)

Paper 1H June 2024 Higher tier, Question 17 3 marks

$Question 17, shown as an image$

Show each stage of your working clearly.

[3]

Reveal mark scheme

Mark scheme for question 17

Paper 1H June 2024 (R) Higher tier, Question 17 4 marks

(a)

$Question 17, shown as an image$

Find the value of n

[1]

(b)

$Question 17, shown as an image$

Show your working clearly.

[3]

Reveal mark scheme

Mark scheme for question 17(b)

Paper 2H June 2023 Higher tier, Question 23 4 marks

Also involves Forming and solving equations

The diagram shows a cuboid with a square cross section.

Figure for question 23

$Question 23, shown as an image$

Without using a calculator, find the $fraction$ lue of x

$Question 23, shown as an image$

[4]

Reveal mark scheme

Mark scheme for question 23

Paper 2H January 2023 Higher tier, Question 17 4 marks

$Question 17, shown as an image$

where k is an integer and m is a prime number,

(a)

work out the value of k

[1]

(b)

$Question 17, shown as an image$

where a and b are integers. Show each stage of your working clearly.

[3]

Reveal mark scheme

Mark scheme for question 17(b)

Paper 1H June 2022 Higher tier, Question 16 3 marks

$Question 16, shown as an image$

[3]

Reveal mark scheme

Mark scheme for question 16

Paper 1H June 2022 (R) Higher tier, Question 21 4 marks

Also involves Simplifying and manipulating expressions

$Question 21, shown as an image$

Show each stage of your working clearly.

[4]

Reveal mark scheme

Mark scheme for question 21

Paper 2H January 2022 (R) Higher tier, Question 13 3 marks

$Question 13, shown as an image$

Find the value of y Show your working clearly.

[3]

Reveal mark scheme

Mark scheme for question 13

Paper 2H January 2022 Higher tier, Question 17 3 marks

$Question 17, shown as an image$

$Question 17, shown as an image$

[3]

Reveal mark scheme

Mark scheme for question 17

Paper 1H November 2021 Higher tier, Question 19 6 marks

Also involves Quadratic equations

ABCED is a five-sided shape.

Figure for question 19

$Question 19, shown as an image$

ABCD is a rectangle. CED is an equilateral triangle.

AB = xcm BC = ycm

The perimeter of ABCED is 100 cm. The area of ABCED is Rcm²

(a)

$Question 19, shown as an image$

[3]

Reveal mark scheme

Mark scheme for question 19(a)

(b)(i)

Find the value of x for which R has its maximum value.

$Question 19, shown as an image$

[2]

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Mark scheme for question 19(b)(i)

(b)(ii)

Explain why the maximum value of R is given by this value of x.

[1]

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Mark scheme for question 19(b)(ii)

Paper 1H January 2021 (R) Higher tier, Question 15 5 marks

(a)

$Question 15, shown as an image$

[2]

Reveal mark scheme

Mark scheme for question 15(a)

(b)

$Question 15, shown as an image$

$Question 15, shown as an image$

[3]

Reveal mark scheme

Mark scheme for question 15(b)

Paper 1H November 2020 Higher tier, Question 19 3 marks

$Question 19, shown as an image$

$Question 19, shown as an image$

[3]

Reveal mark scheme

Mark scheme for question 19

Paper 1H January 2020 (R) Higher tier, Question 13 4 marks

(a)

$Question 13, shown as an image$

[2]

Reveal mark scheme

Mark scheme for question 13(a)

(b)

Given that y is a prime number,

$Question 13, shown as an image$

[2]

Reveal mark scheme

Mark scheme for question 13(b)

Paper 1H January 2020 Higher tier, Question 17 6 marks

Also involves Simplifying and manipulating expressions

(a)

$Question 17, shown as an image$

Show each stage of your working.

[3]

Reveal mark scheme

Mark scheme for question 17(a)

(b)

$Question 17, shown as an image$

[3]

Reveal mark scheme

Mark scheme for question 17(b)

Paper 2H June 2019 Higher tier, Question 16 3 marks

Show that $fraction$ can be written in the form a + b $fraction$ 2, where a and b are integers.

Show each stage of your working clearly and give the value of a and the value of b.

[3]

Reveal mark scheme

Mark scheme for question 16

Paper 1H June 2018 (R) Higher tier, Question 14 8 marks

(a)

Simplify (2e² f³)³

[2]

Reveal mark scheme

Mark scheme for question 14(a)

(b)

Expand and simplify (3x maths symbol y)(x + 3y)

$Question 14, shown as an image$

[2]

Reveal mark scheme

Mark scheme for question 14(b)

(c)

Find the value of k.

[2]

Reveal mark scheme

Mark scheme for question 14(c)

(d)

$Question 14, shown as an image$

[2]

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Mark scheme for question 14(d)

Paper 1H June 2018 Higher tier, Question 14 7 marks

Also involves Linear equations

The function f is such that

(a)

Find f (–7)

[1]

Reveal mark scheme

Mark scheme for question 14(a)

(b)

Express the inverse function f^–1 in the form f^–1(x) =...

[2]

Reveal mark scheme

Mark scheme for question 14(b)

(c)

The function g is such that

Find fg (3)

[2]

Reveal mark scheme

Mark scheme for question 14(c)

(d)

Which values of x cannot be included in any domain of g?

[2]

Reveal mark scheme

Mark scheme for question 14(d)

Paper 2H June 2018 Higher tier, Question 21 6 marks

(a)

$Question 21, shown as an image$

Show your working clearly.

[2]

Reveal mark scheme

Mark scheme for question 21(a)

(b)

$Question 21, shown as an image$

where p and q are integers. Show your working clearly.

[2]

Reveal mark scheme

Mark scheme for question 21(b)

(c)

$Question 21, shown as an image$

Show your working clearly.

[2]

Reveal mark scheme

Mark scheme for question 21(c)

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