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Edexcel GCSE Maths

Topic questions Pure mathematics Simplifying and manipulating expressions

Simplifying and manipulating expressions

113 questions · 435 marks · about 8 hours

Simplifying and manipulating expressions questions

Edexcel 1MA1 Simplifying and manipulating expressions 113 questions

Paper 1 June 2025 Higher tier, Question 7 6 marks

(a)
Question 7, shown as an image
[1]
Reveal mark scheme Mark scheme for question 7(a)
(b)
Question 7, shown as an image
[3]
Reveal mark scheme Mark scheme for question 7(b)
(c)

Solve 9 < 2y + 4 < 12

[2]
Reveal mark scheme Mark scheme for question 7(c)

Paper 1 June 2025 Higher tier, Question 17 5 marks

17g(x) = 1 โ€“ 3xh(x) = 2x2 โ€“ 1 Show that 3gh(x) + hg(x) = 0 has just one solution for x.

[5]
Reveal mark scheme Mark scheme for question 17

Paper 2 June 2025 Higher tier, Question 9 2 marks

9 3xโ€“1(4x โ€“ x3) = a + bxn for all the values of x that are not zero. Find the value of a, the value of b and the value of n.

[2]
Reveal mark scheme Mark scheme for question 9

Paper 2 June 2025 Higher tier, Question 13 3 marks

Show that (2 x + 3)(x โ€“ 1)(x + 2) can be written in the form ax3 + bx2 + cx + d where a, b, c and d are integers.

[3]
Reveal mark scheme Mark scheme for question 13

Paper 3 June 2025 Foundation tier, Question 21 5 marks

(a)

Simplify y10 รท y2

[1]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Simplify (e3)2

[1]
(c)

Expand x(3x2 + 5)

[1]
(d)

Expand and simplify (n + 5)(n โ€“ 2)

[2]
Reveal mark scheme Mark scheme for question 21(d)

Paper 3 June 2025 Foundation tier, Question 23 3 marks

23Ben is trying to make m the subject of p = fraction + 5 Here is his working.

Question 23, shown as an image

m = 3 p โ€“ 5 Benโ€™s answer is wrong.

(a)

What mistake has Ben made?

[1]
Reveal mark scheme Mark scheme for question 23(a)
(b)

Factorise fully 2x3y + 4xy2

[2]
Reveal mark scheme Mark scheme for question 23(b)

Paper 3 June 2025 Higher tier, Question 2 3 marks

Ben is trying to make m the subject of p = fraction + 5 Here is his working.

Question 2, shown as an image

m = 3 p โ€“ 5 Benโ€™s answer is wrong.

(a)

What mistake has Ben made?

[1]
Reveal mark scheme Mark scheme for question 2(a)
(b)

Factorise fully 2x3y + 4xy2

[2]
Reveal mark scheme Mark scheme for question 2(b)

Paper 3 June 2025 Higher tier, Question 11 4 marks

Question 11, shown as an image
(a)

Find the value of n.

[2]
Reveal mark scheme Mark scheme for question 11(a)
(b)

Write 64m12 fraction in the form amb where a and b are integers.

[2]
Reveal mark scheme Mark scheme for question 11(b)

Paper 1 November 2024 Foundation tier, Question 15 4 marks

(a)

Factorise 6 a + 15

[1]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Solve 4(3y + 1) = 28

[3]
Reveal mark scheme Mark scheme for question 15(b)

Paper 1 November 2024 Higher tier, Question 11 5 marks

Kate was asked to factorise x2 + 5x + 6 in the form (x + a)(x + b) Kate says, โ€œThe sum of a and b must be 6 and the product of a and b must be 5โ€

(a)

Explain what is wrong with Kateโ€™s statement.

[1]
Reveal mark scheme Mark scheme for question 11(a)
(b)

Factorise fully 2m2 โ€“ 2

[2]
Reveal mark scheme Mark scheme for question 11(b)
(c)

Factorise fully ax + bx โ€“ ay โ€“ by

[2]
Reveal mark scheme Mark scheme for question 11(c)

Paper 1 November 2024 Higher tier, Question 13 5 marks

Here are two cuboids.

Figure for question 13

All lengths are measured in centimetres. The volume of cuboid A is 142 cm3 greater than the volume of cuboid B. Work out the value of x.

[5]
Reveal mark scheme Mark scheme for question 13

Paper 2 November 2024 Foundation tier, Question 11 3 marks

(a)

Simplify 2x ร— 3y

[1]
(b)

Simplify 3d โ€“ 4e + 2d + e

[2]
Reveal mark scheme Mark scheme for question 11(b)

Paper 2 November 2024 Foundation tier, Question 19 4 marks

(a)

Factorise fully 15w2 โ€“ 5w

[2]
Reveal mark scheme Mark scheme for question 19(a)
(b)

On the number line below, show the set of values of x for which โ€“2 maths symbol x โ‰ค 4

Question 19, shown as an image
[2]
Reveal mark scheme Mark scheme for question 19(b)

Paper 3 November 2024 Foundation tier, Question 25, also on the Higher paper 3 marks

Also involves Indices

(a)

Simplify fully 2x3y5 ร— 7x2y

[2]
Reveal mark scheme Mark scheme for question 25(a)
(b)

Simplify (m2)โ€“3

[1]
Reveal mark scheme Mark scheme for question 25(b)

Paper 3 November 2024 Higher tier, Question 9, also on the Foundation paper 3 marks

Also involves Indices

(a)

Simplify fully 2x3y5 ร— 7x2y

[2]
Reveal mark scheme Mark scheme for question 9(a)
(b)

Simplify (m2)โ€“3

[1]

Paper 1 June 2024 Higher tier, Question 14 3 marks

Expand and simplify (3 x โ€“ 1)(2 x + 3)(x โ€“ 5)

[3]
Reveal mark scheme Mark scheme for question 14

Paper 1 November 2023 Foundation tier, Question 27 3 marks

(a)

Expand and simplify (3 x + 2)(2 x โ€“ 5)

[2]
Reveal mark scheme Mark scheme for question 27(a)
(b)

Factorise x2 โ€“ 16

[1]
Reveal mark scheme Mark scheme for question 27(b)

Paper 1 November 2023 Higher tier, Question 17 4 marks

(a)

Factorise 6x2 โ€“ 5x โ€“ 4

[2]
Reveal mark scheme Mark scheme for question 17(a)
(b)

Hence, or otherwise, solve 6x2 โ€“ 5x โ€“ 4 < 0

[2]
Reveal mark scheme Mark scheme for question 17(b)

Paper 2 November 2023 Foundation tier, Question 22, also on the Higher paper 6 marks

(a)

Expand and simplify 3 (2 y โˆ’ 5) + 7 (y + 2)

[2]
Reveal mark scheme Mark scheme for question 22(a)
(b)

Factorise fully 6x2 + 15x

[2]
Reveal mark scheme Mark scheme for question 22(b)
(c)

Make g the subject of the formula f = 3g + 11

[2]
Reveal mark scheme Mark scheme for question 22(c)

Paper 2 November 2023 Higher tier, Question 1, also on the Foundation paper 6 marks

(a)

Expand and simplify 3(2y โˆ’ 5) + 7(y + 2)

[2]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Factorise fully 6x2 + 15x

[2]
Reveal mark scheme Mark scheme for question 1(b)
(c)

Make g the subject of the formula f = 3g + 11

[2]
Reveal mark scheme Mark scheme for question 1(c)

Paper 1 June 2023 Foundation tier, Question 13 4 marks

(a)
Question 13, shown as an image
[1]
Reveal mark scheme Mark scheme for question 13(a)
(b)

Simplify 19 + 5 b + 4 c โ€“ 7 b + c

[2]
Reveal mark scheme Mark scheme for question 13(b)
(c)

Factorise 8d โ€“ 6

[1]
Reveal mark scheme Mark scheme for question 13(c)

Paper 2 June 2023 Higher tier, Question 24 5 marks

24The diagram shows 8 identical regular octagons joined to enclose a shaded shape.

Figure for question 24

Each octagon has sides of length a. Find, in terms of a, an expression for the area of the shaded shape.

Question 24, shown as an image
[5]
Reveal mark scheme Mark scheme for question 24

Paper 3 June 2023 Foundation tier, Question 20, also on the Higher paper 4 marks

(a)

Simplify (m2)3

[1]
Reveal mark scheme Mark scheme for question 20(a)
(b)

Simplify x5ร—x8

[1]
(c)

Expand 4p(p2 + 3p)

[2]
Reveal mark scheme Mark scheme for question 20(c)

Paper 3 June 2023 Higher tier, Question 1, also on the Foundation paper 4 marks

(a)

Simplify (m2)3

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Simplify x5maths symbolx8

[1]
(c)

Expand 4p(p2 + 3p)

[2]
Reveal mark scheme Mark scheme for question 1(c)

Paper 3 June 2023 Higher tier, Question 12 3 marks

12Show that (x โ€“ 1)(x + 3)(x โ€“ 5) can be written in the form ax3 + bx2 + cx + d where a, b, c and d are integers.

[3]
Reveal mark scheme Mark scheme for question 12

Paper 3 June 2023 Higher tier, Question 15 3 marks

(a)

Factorise a2 โ€“ b2

[1]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Show that 240 โ€“ 1 is the product of two consecutive odd numbers.

[2]
Reveal mark scheme Mark scheme for question 15(b)

Paper 3 June 2023 Higher tier, Question 24 5 marks

There is a total of y counters in a box. There are x pink counters and 5 blue counters in the box. The rest of the counters are green. x:y = 1: 3 Freda takes at random two counters from the box. Find, in terms of x, an expression for the probability that Freda takes two counters of the same colour.

Question 24, shown as an image
[5]
Reveal mark scheme Mark scheme for question 24

Paper 1 November 2022 Foundation tier, Question 8 3 marks

(a)

Solve m โˆ’ 3 = 4

[1]
Reveal mark scheme Mark scheme for question 8(a)
(b)

Solve 3n + n = 24

[2]
Reveal mark scheme Mark scheme for question 8(b)

Paper 1 November 2022 Foundation tier, Question 26 5 marks

(a)
Question 26, shown as an image
[3]
Reveal mark scheme Mark scheme for question 26(a)
(b)

Factorise x2 + 10x + 9

[2]
Reveal mark scheme Mark scheme for question 26(b)

Paper 1 November 2022 Higher tier, Question 16 4 marks

(a)

Prove that (2m + 1)2 โˆ’ (2n โ€“ 1)2 = 4(m + n)(m โˆ’ n + 1)

[3]
Reveal mark scheme Mark scheme for question 16(a)
(b)

Sophia says that the result in part (a) shows that the difference of the squares of any two odd numbers must be a multiple of 4

Is Sophia correct? You must give reasons for your answer.

[1]

Paper 2 November 2022 Foundation tier, Question 14 7 marks

(a)

Simplify 4 c + 7 d + 3 c โˆ’ d

[2]
Reveal mark scheme Mark scheme for question 14(a)
(b)

Solve 5(2m โˆ’ 6) = 40

There are x sweets in a box. There are y sweets in a packet.

[3]
Reveal mark scheme Mark scheme for question 14(b)
(c)

Write an expression, in terms of x and y, for the total number of sweets in 3 boxes and 2 packets.

[2]
Reveal mark scheme Mark scheme for question 14(c)

Paper 3 November 2022 Higher tier, Question 10 1 mark

10Peter has to subtract (x2 โˆ’ 2x โˆ’ 4) from (x2 + 3x + 5) Here is his working

Question 10, shown as an image

= x + 1 Explain what is wrong with Peterโ€™s working.

[1]
Reveal mark scheme Mark scheme for question 10

Paper 3 November 2022 Higher tier, Question 14 5 marks

(a)

Simplify fully (3x5y6)4

[2]
Reveal mark scheme Mark scheme for question 14(a)
(b)

Expand and simplify (x + 2)(x โˆ’ 3)(x + 4)

[3]
Reveal mark scheme Mark scheme for question 14(b)

Paper 2 June 2022 Foundation tier, Question 21, also on the Higher paper 5 marks

(a)

Simplify (x3)5

[1]
(b)

Expand and simplify 4(x + 3) + 7(4 โˆ’ 2x)

[2]
Reveal mark scheme Mark scheme for question 21(b)
(c)

Factorise fully 15x3 + 3x2y

[2]
Reveal mark scheme Mark scheme for question 21(c)

Paper 2 June 2022 Higher tier, Question 1, also on the Foundation paper 5 marks

Also involves Indices

(a)

Simplify (x3)5

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Expand and simplify 4(x + 3) + 7(4 โˆ’ 2x)

[2]
Reveal mark scheme Mark scheme for question 1(b)
(c)

Factorise fully 15x3 + 3x2y

[2]
Reveal mark scheme Mark scheme for question 1(c)

Paper 3 June 2022 Foundation tier, Question 17 4 marks

(a)

Expand 3(4 โˆ’ 2 x)

[1]
(b)
Question 17, shown as an image
[2]
Reveal mark scheme Mark scheme for question 17(b)
(c)

Factorise 4p + 6

[1]
Reveal mark scheme Mark scheme for question 17(c)

Paper 3 June 2022 Foundation tier, Question 28, also on the Higher paper 3 marks

The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm.

Figure for question 28

The area of trapezium QUVR is Acm2 Show that A = 2x2 + 20x

[3]
Reveal mark scheme Mark scheme for question 28

Paper 3 June 2022 Higher tier, Question 7, also on the Foundation paper 3 marks

The diagram shows rectangle STUV. TQU and SRV are straight lines. All measurements are in cm.

Figure for question 7

The area of trapezium QUVR is Acm2 Show that A = 2x2 + 20x

[3]
Reveal mark scheme Mark scheme for question 7

Paper 3 June 2022 Higher tier, Question 14 5 marks

(a)

Factorise fully 4p2 โˆ’ 36

[2]
Reveal mark scheme Mark scheme for question 14(a)
(b)

Show that (m + 4)(2m โˆ’ 5)(3m + 1) can be written in the form am3 + bm2 + cm + d where a, b, c and d are integers.

[3]
Reveal mark scheme Mark scheme for question 14(b)

Paper 1 November 2021 Foundation tier, Question 15 4 marks

(a)

Expand 2(a + d)

[1]
(b)

Factorise 6y2 โ€“ 5y

[1]
(c)

Solve 4x โ€“ 7 = 37

[2]
Reveal mark scheme Mark scheme for question 15(c)

Paper 1 November 2021 Higher tier, Question 14 3 marks

Here is a shape with all its measurements in centimetres.

Question 14, shown as an image
Figure for question 14

The area of the shape is Acm2 Show that A = 2x2 + 24x + 46

[3]
Reveal mark scheme Mark scheme for question 14

Paper 3 November 2021 Foundation tier, Question 6 3 marks

(a)

Simplify amaths symbolbmaths symbol4

[1]
(b)

Simplify 4x + 3 โ€“ x + 5

[2]
Reveal mark scheme Mark scheme for question 6(b)

Paper 3 November 2021 Foundation tier, Question 17 7 marks

(a)

Expand y (y + 5)

[1]
(b)

Factorise 4a โ€“ 6

[1]
(c)

Solve 2(5x โ€“ 4) = 21

[3]
Reveal mark scheme Mark scheme for question 17(c)
(d)

Simplify 4e2f maths symbol5ef3

[2]
Reveal mark scheme Mark scheme for question 17(d)

Paper 1 November 2020 Foundation tier, Question 19 4 marks

(a)

Expand x (x โ€“ 4)

[1]
Reveal mark scheme Mark scheme for question 19(a)
(b)

Factorise 15y โ€“ 10

[1]
(c)

Solve 7(f โ€“ 5) = 28

[2]
Reveal mark scheme Mark scheme for question 19(c)

Paper 1 November 2020 Foundation tier, Question 30 3 marks

(a)

Make q the subject of p = 6 q + 7

[2]
Reveal mark scheme Mark scheme for question 30(a)
(b)

Simplify (mโ€“2)โ€“3

[1]
Reveal mark scheme Mark scheme for question 30(b)

Paper 1 November 2020 Higher tier, Question 11 6 marks

(a)
Question 11, shown as an image
[2]
Reveal mark scheme Mark scheme for question 11(a)
(b)
Question 11, shown as an image
[2]
Reveal mark scheme Mark scheme for question 11(b)
(c)
Question 11, shown as an image
[2]
Reveal mark scheme Mark scheme for question 11(c)

Paper 2 November 2020 Higher tier, Question 10 4 marks

Also involves Indices

(a)
Question 10, shown as an image
[1]
Reveal mark scheme Mark scheme for question 10(a)
(b)
Question 10, shown as an image
[1]
Reveal mark scheme Mark scheme for question 10(b)
(c)

Simplify (3n4w2)3

[2]
Reveal mark scheme Mark scheme for question 10(c)

Paper 2 November 2020 Higher tier, Question 14 4 marks

Here are two squares, A and B.

Figure for question 14

The length of each side of square B is 4 cm greater than the length of each side of square A. The area of square B is 70 cm2 greater than the area of square A. Find the area of square B. Give your answer correct to 3 significant figures. You must show all your working.

[4]
Reveal mark scheme Mark scheme for question 14

Paper 3 November 2020 Foundation tier, Question 14 4 marks

(a)

Simplify 3 x + 5 y + 2 x โˆ’ 4 y

[2]
Reveal mark scheme Mark scheme for question 14(a)
(b)

Solve 5p + 7 = 22

[2]
Reveal mark scheme Mark scheme for question 14(b)

Paper 3 November 2020 Foundation tier, Question 23, also on the Higher paper 5 marks

(a)

Simplify n3 ร— n5

[1]
Reveal mark scheme Mark scheme for question 23(a)
(b)
Question 23, shown as an image
[2]
Reveal mark scheme Mark scheme for question 23(b)
(c)
Question 23, shown as an image
[2]
Reveal mark scheme Mark scheme for question 23(c)

Paper 3 November 2020 Higher tier, Question 1, also on the Foundation paper 5 marks

(a)

Simplify n3 ร— n5

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)
Question 1, shown as an image
[2]
Reveal mark scheme Mark scheme for question 1(b)
(c)
Question 1, shown as an image
[2]
Reveal mark scheme Mark scheme for question 1(c)

Paper 3 November 2020 Higher tier, Question 12 6 marks

(a)

Express fraction fraction as a single fraction in its simplest form.

[3]
Reveal mark scheme Mark scheme for question 12(a)
(b)

Expand and simplify (x โˆ’ 3)(2x + 3)(4x + 5)

[3]
Reveal mark scheme Mark scheme for question 12(b)

Paper 3 November 2020 Higher tier, Question 21 5 marks

5 c + d = c + 4 d

(a)

Find the ratio c: d

6xยฒ = 7xy + 20yยฒ where x หƒ 0 and y หƒ 0

[2]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Find the ratio x: y

[3]
Reveal mark scheme Mark scheme for question 21(b)

Paper 1 November 2019 Foundation tier, Question 26, also on the Higher paper 3 marks

Also involves Indices

(a)

Simplify (p2)5

[1]
Reveal mark scheme Mark scheme for question 26(a)
(b)

Simplify 12x7y3 รท 6x3y

[2]
Reveal mark scheme Mark scheme for question 26(b)

Paper 1 November 2019 Higher tier, Question 7, also on the Foundation paper 3 marks

Also involves Indices

(a)

Simplify (p2)5

[1]
Reveal mark scheme Mark scheme for question 7(a)
(b)

Simplify 12x7y3 รท 6x3y

[2]
Reveal mark scheme Mark scheme for question 7(b)

Paper 1 November 2019 Higher tier, Question 13 3 marks

(a)
Question 13, shown as an image
[2]
Reveal mark scheme Mark scheme for question 13(a)
(b)

Factorise (x + y)2 + 3(x + y)

[1]
Reveal mark scheme Mark scheme for question 13(b)

Paper 3 November 2019 Foundation tier, Question 22, also on the Higher paper 4 marks

(a)

Expand and simplify (x + 5)(x โ€“ 9)

[2]
Reveal mark scheme Mark scheme for question 22(a)
(b)

Factorise fully 9x2 + 6x

[2]
Reveal mark scheme Mark scheme for question 22(b)

Paper 3 November 2019 Higher tier, Question 1, also on the Foundation paper 4 marks

(a)

Expand and simplify (x + 5)(x โ€“ 9)

[2]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Factorise fully 9x2 + 6x

[2]
Reveal mark scheme Mark scheme for question 1(b)

Paper 3 November 2019 Higher tier, Question 15 3 marks

Prove algebraically that the sum of the squares of any two consecutive even numbers is always a multiple of 4

[3]
Reveal mark scheme Mark scheme for question 15

Paper 1 June 2019 Higher tier, Question 21 7 marks

The functions f and g are such that

Question 21, shown as an image
(a)

Find fโ€“1(x)

Question 21, shown as an image
[2]
Reveal mark scheme Mark scheme for question 21(a)
(b)

Given that fg(x) = 2gf(x),

show that 15x2 โ€“ 12x โ€“ 1 = 0

[5]
Reveal mark scheme Mark scheme for question 21(b)

Paper 3 June 2019 Higher tier, Question 18 6 marks

(a)

Show that (2x + 1)(x maths symbol 3)(3x + 7) can be written in the form ax3 + bx2 + cx maths symbol d where a, b, c and d are integers.

[3]
Reveal mark scheme Mark scheme for question 18(a)
(b)
Question 18, shown as an image
[3]
Reveal mark scheme Mark scheme for question 18(b)

Paper 2 November 2018 Foundation tier, Question 7 2 marks

(a)

Simplify 3mmaths symbolmmaths symbolm + 3m

[1]
Reveal mark scheme Mark scheme for question 7(a)
(b)

Simplify 2 maths symbol n maths symbol p maths symbol 4

[1]
Reveal mark scheme Mark scheme for question 7(b)

Paper 2 November 2018 Foundation tier, Question 19 4 marks

(a)

Solve 3(x โ€“ 4) = 12

[2]
Reveal mark scheme Mark scheme for question 19(a)
(b)

Factorise fully 9b โ€“ 3b2

[2]
Reveal mark scheme Mark scheme for question 19(b)

Paper 2 November 2018 Foundation tier, Question 26 4 marks

(a)

Expand and simplify (5 x + 2)(2 x โ€“ 3)

[2]
Reveal mark scheme Mark scheme for question 26(a)
(b)

Factorise x2 + 4x + 3

[2]
Reveal mark scheme Mark scheme for question 26(b)

Paper 2 November 2018 Higher tier, Question 12 6 marks

(a)

Write fraction maths symbol fraction in the form fraction where a, b, c and d are integers.

[3]
Reveal mark scheme Mark scheme for question 12(a)
(b)

Express fraction + fraction โˆ’ fraction as a single fraction in its simplest form.

[3]
Reveal mark scheme Mark scheme for question 12(b)

Paper 3 November 2018 Foundation tier, Question 17 5 marks

Also involves Symmetry

The diagram shows a pentagon. The pentagon has one line of symmetry.

Figure for question 17

AE = 4 x AB = 2 x + 1 BC = x + 2

All these measurements are given in centimetres.

The perimeter of the pentagon is 18 cm.

(a)

Show that 10 x + 6 = 18

[3]
Reveal mark scheme Mark scheme for question 17(a)
(b)

Find the value of x.

[2]
Reveal mark scheme Mark scheme for question 17(b)

Paper 3 November 2018 Higher tier, Question 9 8 marks

(a)

Expand and simplify (x โ€“ 2)(2 x + 3)(x + 1)

Question 9, shown as an image
[3]
Reveal mark scheme Mark scheme for question 9(a)
(b)

Find the value of n.

[2]
Reveal mark scheme Mark scheme for question 9(b)
(c)

Solve 5x2 โ€“ 4x โ€“ 3 = 0 Give your solutions correct to 3 significant figures.

[3]
Reveal mark scheme Mark scheme for question 9(c)

Paper 1 June 2018 Foundation tier, Question 6 2 marks

(a)

Simplify 3 maths symbol 4t

[1]
Reveal mark scheme Mark scheme for question 6(a)
(b)

Simplify 8a โ€“ 3a + 2a

[1]
Reveal mark scheme Mark scheme for question 6(b)

Paper 1 June 2018 Foundation tier, Question 16 6 marks

P = 4 x + 3 y

xmaths symbol y = โ€“ 2

(a)

Work out the value of P.

[2]
Reveal mark scheme Mark scheme for question 16(a)
(b)

Expand 4 e (e + 2)

[2]
Reveal mark scheme Mark scheme for question 16(b)
(c)

Solve 3(m โ€“ 4) = 21

[2]
Reveal mark scheme Mark scheme for question 16(c)

Paper 1 June 2018 Higher tier, Question 15 4 marks

(a)

Factorise a2 โˆ’ b2

[1]
Reveal mark scheme Mark scheme for question 15(a)
(b)

Hence, or otherwise, simplify fully (x2 + 4)2 โ€“ (x2 โ€“ 2)2

[3]
Reveal mark scheme Mark scheme for question 15(b)

Paper 2 June 2018 Foundation tier, Question 20, also on the Higher paper 5 marks

(a)

Simplify m3maths symbol m4

[1]
Reveal mark scheme Mark scheme for question 20(a)
(b)

Simplify (5np3)3

[2]
Reveal mark scheme Mark scheme for question 20(b)
(c)
Question 20, shown as an image
[2]
Reveal mark scheme Mark scheme for question 20(c)

Paper 2 June 2018 Higher tier, Question 1, also on the Foundation paper 5 marks

(a)

Simplify m3maths symbol m4

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Simplify (5np3)3

[2]
Reveal mark scheme Mark scheme for question 1(b)
(c)
Question 1, shown as an image
[2]
Reveal mark scheme Mark scheme for question 1(c)

Paper 3 June 2018 Foundation tier, Question 20, also on the Higher paper 2 marks

Expand and simplify 5(p + 3) โ€“ 2(1 โ€“ 2 p)

[2]
Reveal mark scheme Mark scheme for question 20

Paper 3 June 2018 Higher tier, Question 2, also on the Foundation paper 2 marks

Expand and simplify 5(p + 3) โ€“ 2(1 โ€“ 2 p)

[2]
Reveal mark scheme Mark scheme for question 2

Paper 1 November 2017 Foundation tier, Question 6 3 marks

Here are five straight rods.

Question 6, shown as an image
Figure for question 6

All measurements are in centimetres.

The total length of the five rods is L cm.

Find a formula for L in terms of a. Write your formula as simply as possible.

[3]
Reveal mark scheme Mark scheme for question 6

Paper 1 November 2017 Higher tier, Question 23 5 marks

Here is a rectangle and a right-angled triangle.

Figure for question 23

All measurements are in centimetres. The area of the rectangle is greater than the area of the triangle.

Find the set of possible values of x.

[5]
Reveal mark scheme Mark scheme for question 23

Paper 2 November 2017 Foundation tier, Question 3 3 marks

(a)

Simplify 3 fmaths symbolg

[1]
Reveal mark scheme Mark scheme for question 3(a)
(b)

Simplify t ร— t

[1]
Reveal mark scheme Mark scheme for question 3(b)
(c)
Question 3, shown as an image
[1]
Reveal mark scheme Mark scheme for question 3(c)

Paper 2 November 2017 Foundation tier, Question 21 4 marks

Figure for question 21
(a)

Find the value of x.

[1]
Reveal mark scheme Mark scheme for question 21(a)
(b)

(72)ymaths symbol10

Find the value of y.

[1]
Reveal mark scheme Mark scheme for question 21(b)
(c)

100a ร— 1000b can be written in the form 10w

Show that wmaths symbola + 3b

[2]
Reveal mark scheme Mark scheme for question 21(c)

Paper 2 November 2017 Foundation tier, Question 24 5 marks

(a)

Solve 2x2maths symbol

[2]
Reveal mark scheme Mark scheme for question 24(a)
(b)

Expand and simplify (2 x + 1)(3 x โˆ’ 2)

[2]
Reveal mark scheme Mark scheme for question 24(b)
(c)

Factorise x2 + 6x + 9

[1]
Reveal mark scheme Mark scheme for question 24(c)

Paper 3 November 2017 Foundation tier, Question 17 3 marks

(a)

Factorise 4 m + 12

[1]
Reveal mark scheme Mark scheme for question 17(a)
(b)

expression equation formula identity

inequality term factor multiple

Choose two words from the box above to make this statement correct.

5y is a........ in the........ 3x + 5y

[2]
Reveal mark scheme Mark scheme for question 17(b)

Paper 1 June 2017 Foundation tier, Question 24 3 marks

Figure for question 24

The area of square ABCD is 10 cm2.

Show that x2 + 6x = 1

[3]
Reveal mark scheme Mark scheme for question 24

Paper 2 June 2017 Higher tier, Question 19 4 marks

2 โˆ’ fraction โˆ’ fraction can be written as a single fraction in the form fraction where a and b are integers.

Work out the value of a and the value of b.

[4]
Reveal mark scheme Mark scheme for question 19

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