AQA 8300 Simplifying and manipulating expressions past paper questions

Paper 1: Non-calculator June 2025 Foundation tier, Question 26 4 marks

Also involves Area and perimeter

The area of the rectangle is 120 cm²

Work out the value of x.

x =

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Paper 1: Non-calculator June 2025 Higher tier, Question 10 4 marks

The area of the rectangle is 120 cm²

Work out the value of x.

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Paper 1: Non-calculator June 2025 Higher tier, Question 24 4 marks

$Question 24, shown as an image$

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Paper 2: Calculator June 2025 Foundation tier, Question 11 3 marks

Here are two expressions, A and B.

Show that A and B are equivalent.

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Paper 2: Calculator June 2025 Foundation tier, Question 24, also on the Higher paper 1 mark

Circle the expression which is a factor of 3 x + 15

3 x x + 12 x + 5 x + 15

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Paper 2: Calculator June 2025 Higher tier, Question 6, also on the Foundation paper 1 mark

Circle the expression which is a factor of 3 x + 15

3 x x + 12 x + 5 x + 15

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Paper 2: Calculator June 2025 Higher tier, Question 14 3 marks

a, b and c are positive integers.

a (9 x + 2) ≡ 45 x + 3 b + c

Work out one possible set of values for a, b and c.

$Question 14, shown as an image$

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Paper 3: Calculator June 2025 Higher tier, Question 20 3 marks

(a)

Factorise fully 3n² + 5n + 2

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(b)

A sequence has nth term 3n² + 5n + 2

Are any of the terms in the sequence a prime number? Tick a box.

Give a reason for your answer.

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Paper 1: Non-calculator November 2024 Foundation tier, Question 10 4 marks

(a)

Simplify fully 8 m + 4 – 2 m + 7

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(b)

$Question 10, shown as an image$

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Paper 1: Non-calculator November 2024 Higher tier, Question 19 5 marks

(a)

Expand and simplify fully (x + 2)(2 x + 3)(3 x + 4)

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(b)

Use your answer from part (a) to work out 102 × 203 × 304

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Paper 1: Non-calculator November 2024 Higher tier, Question 22 3 marks

Match each expression on the left to the correct expression on the right. One has been done for you.

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Paper 2: Calculator November 2024 Foundation tier, Question 3 4 marks

(a)

Solve 5 x = 30

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(b)

Solve – 2 + y = 10

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(c)

$Question 3, shown as an image$

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Paper 2: Calculator November 2024 Foundation tier, Question 12 5 marks

(a)

Work out the value of x² + 7x when x = –4

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(b)

Rearrange y = w – 1 to make w the subject.

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(c)

Simplify fully 4(a + 2) + a

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Paper 2: Calculator November 2024 Foundation tier, Question 25, also on the Higher paper 3 marks

Here are three terms.

$Question 25, shown as an image$

Alec multiplies two of these terms.

Work out the three possible fully simplified answers.

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Paper 2: Calculator November 2024 Higher tier, Question 11, also on the Foundation paper 3 marks

Also involves Indices

Here are three terms.

$Question 11, shown as an image$

Alec multiplies two of these terms.

Work out the three possible fully simplified answers.

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Paper 3: Calculator November 2024 Foundation tier, Question 2 1 mark

Simplify fully y maths symbol y y

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Paper 3: Calculator November 2024 Higher tier, Question 11 2 marks

Factorise fully 12t + 4t³

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Paper 3: Calculator November 2024 Higher tier, Question 20 2 marks

Factorise fully 3x² + 23x + 30

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Paper 2: Calculator June 2024 Foundation tier, Question 2 4 marks

(a)

Simplify fully x + 4 x

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(b)

Simplify fully 5 × 2 w

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(c)

Simplify fully 2 m ÷ m

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(d)

Simplify fully y × y × y

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Paper 2: Calculator June 2024 Higher tier, Question 19 5 marks

(a)

$Question 19, shown as an image$

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(b)

Factorise 8x² – 18x – 35

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Paper 3: Calculator June 2024 Foundation tier, Question 14 2 marks

Multiply out 3(2 x + 8)

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Paper 3: Calculator June 2024 Foundation tier, Question 15 3 marks

Complete these statements.

$Question 15, shown as an image$

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Paper 1: Non-calculator November 2023 Foundation tier, Question 6 4 marks

(a)

Simplify fully a + a + a + a

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(b)

Factorise 5 a + 10

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(c)

Multiply out 4(10 – x)

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Paper 1: Non-calculator November 2023 Foundation tier, Question 28, also on the Higher paper 2 marks

Factorise x² + 2x – 24

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Paper 1: Non-calculator November 2023 Higher tier, Question 4 1 mark

Simplify a + 3 a ÷ a

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Paper 1: Non-calculator November 2023 Higher tier, Question 11, also on the Foundation paper 2 marks

Factorise x² + 2x – 24

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Paper 1: Non-calculator November 2023 Higher tier, Question 13 3 marks

Here is an identity in x.

5(2 x + d) ≡ cx + 30

Work out the values of c and d.

$Question 13, shown as an image$

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Paper 1: Non-calculator November 2023 Higher tier, Question 26 4 marks

(a)

$Question 26, shown as an image$

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(b)

Write maths symbol 49m ^2.5 as a power of 7 in terms of m.

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Paper 2: Calculator November 2023 Higher tier, Question 1 1 mark

Expand 5x(x² + 3)

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Paper 2: Calculator November 2023 Higher tier, Question 22 1 mark

Factorise 25a² – b²

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Paper 2: Calculator November 2023 Higher tier, Question 24 3 marks

$Question 24, shown as an image$

You must show your working.

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Paper 3: Calculator November 2023 Foundation tier, Question 11 4 marks

(a)

Simplify fully 2 x + 9 y + 1 + 8 x – 5 y – 7

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(b)

Circle the expression that is equivalent to 0.5a²

$Question 11, shown as an image$

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Paper 3: Calculator November 2023 Higher tier, Question 18 3 marks

$Question 18, shown as an image$

Give your answer in the form ax² + bx + c where a, b and c are integers.

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Paper 3: Calculator November 2023 Higher tier, Question 22 2 marks

Also involves Rational expressions

Write $fraction$ – $fraction$ as a single fraction in its simplest form.

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Paper 1: Non-calculator June 2023 Foundation tier, Question 22, also on the Higher paper 2 marks

Expand and simplify fully 5(3 x + 4) – 2(x – 1)

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Paper 1: Non-calculator June 2023 Higher tier, Question 8, also on the Foundation paper 2 marks

Expand and simplify fully 5(3 x + 4) – 2(x – 1)

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Paper 1: Non-calculator June 2023 Higher tier, Question 27 3 marks

A journey has two stages.

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Paper 2: Calculator June 2023 Foundation tier, Question 2 4 marks

Match each expression on the left with the simplified expression on the right. One has been done for you.

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Paper 2: Calculator June 2023 Foundation tier, Question 14 1 mark

Factorise 12 a + 15 b

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Paper 2: Calculator June 2023 Higher tier, Question 15 2 marks

Expand (x² – 9xy)(2x + 5y)

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Paper 2: Calculator June 2023 Higher tier, Question 25 3 marks

Also involves Rational expressions · Algebraic argument and proof

$Question 25, shown as an image$

simplifies to $fraction$ where a and b are integers.

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Paper 3: Calculator June 2023 Foundation tier, Question 10 3 marks

(a)

Simplify fully p² × p

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(b)

Simplify fully 3 a + 5 c – a + 6 c

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Paper 3: Calculator June 2023 Foundation tier, Question 25 3 marks

(a)

Factorise x² + 8x + 15

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(b)

Write down the two solutions of (y + 2)(y – 4) = 0

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Paper 3: Calculator June 2023 Higher tier, Question 18 6 marks

f(x) = x² + 6x g(x) = 2 x + 4

(a)

Show that fg(x) = 4x² + 28x + 40

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(b)

Solve fg(x) = – 5

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Paper 3: Calculator June 2023 Higher tier, Question 19 3 marks

Two integers have a difference of 6 The integers are multiplied together. 9 is then added. Prove algebraically that the result is always a square number.

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Paper 1: Non-calculator November 2022 Foundation tier, Question 5 2 marks

Simplify fully 8 a + 5 b + 6 a – 2 b

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Paper 1: Non-calculator November 2022 Higher tier, Question 15 4 marks

Show that (3x + 4)(2x – 5) – 11x(x – 2) + 5(x² – 3x – 1) simplifies to an integer.

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Paper 1: Non-calculator November 2022 Higher tier, Question 20 3 marks

The only solution to x² + bx + c = 0 is x = –15 Work out the values of b and c.

$Question 20, shown as an image$

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Paper 2: Calculator November 2022 Foundation tier, Question 5 3 marks

(a)

Simplify fully d × d

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(b)

Simplify fully n ÷ n

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(c)

$Question 5, shown as an image$

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Paper 2: Calculator November 2022 Foundation tier, Question 22, also on the Higher paper 3 marks

Also involves Volume and surface area

(a)

Here is a cuboid. w, x and y are different whole numbers.

The total length of all the edges of the cuboid is 80 cm The volume is greater than 200 cm³ Work out one possible set of values for w, x and y.

$Question 22, shown as an image$

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(b)

Here is a solid cube.

Circle the expression for the total surface area in cm²

$Question 22, shown as an image$

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Paper 2: Calculator November 2022 Higher tier, Question 8, also on the Foundation paper 3 marks

Also involves Volume and surface area

(a)

Here is a cuboid. w, x and y are different whole numbers.

The total length of all the edges of the cuboid is 80 cm The volume is greater than 200 cm³ Work out one possible set of values for w, x and y.

$Question 8, shown as an image$

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(b)

Here is a solid cube.

Circle the expression for the total surface area in cm²

$Question 8, shown as an image$

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Paper 2: Calculator November 2022 Higher tier, Question 22 2 marks

Factorise fully x³ – 49x

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Paper 3: Calculator November 2022 Higher tier, Question 3 1 mark

Expand 6x²(x³ + 2) Circle your answer.

$Question 3, shown as an image$

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Paper 3: Calculator November 2022 Higher tier, Question 22 4 marks

Also involves Rational expressions

$Question 22, shown as an image$

Give your answer as a single fraction.

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Paper 1: Non-calculator June 2022 Foundation tier, Question 19 4 marks

(a)

$Question 19, shown as an image$

Give your answer as a whole number.

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(b)

Simplify 8 × 2⁶ × 2⁴ Give your answer as a power of 2

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Paper 1: Non-calculator June 2022 Higher tier, Question 19 3 marks

Also involves Sequences

The first three terms of a sequence are x y xy The sequence is continued by multiplying the previous two terms.

(a)

Circle the 5th term of the sequence.

$Question 19, shown as an image$

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(b)

The 8th term of the sequence is x⁸y¹³ The value of this term is negative. What does this mean about the values of x and y ? Tick one box for each row.

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Paper 1: Non-calculator June 2022 Higher tier, Question 24 6 marks

(a)

$Question 24, shown as an image$

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(b)

$Question 24, shown as an image$

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Paper 2: Calculator June 2022 Foundation tier, Question 17 4 marks

(a)

x is at least 7 Circle the correct inequality.

$Question 17, shown as an image$

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(b)

Multiply out 5 c (2 d + 1)

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(c)

Factorise 21 x + 28

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Paper 2: Calculator June 2022 Higher tier, Question 23 2 marks

Factorise 3x² – 16x – 12

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Paper 3: Calculator June 2022 Foundation tier, Question 4 1 mark

Simplify 4 × 2 c Circle your answer.

42 c 16 c 8 c 6 c

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Paper 3: Calculator June 2022 Foundation tier, Question 12 6 marks

(a)

Simplify fully 9 x + y – 6 x + y

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(b)

Here are two expressions.

When a = 25 the expressions have the same value. Work out the value of b.

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(c)

12 $Question 12, shown as an image$

Circle your answer.

6 w + 8 3 w + 10 6 w + 5 3 w + 5

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Paper 3: Calculator June 2022 Higher tier, Question 13 1 mark

$Question 13, shown as an image$

Circle your answer.

$Question 13, shown as an image$

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Paper 3: Calculator June 2022 Higher tier, Question 19 5 marks

Also involves Area and perimeter

Here is the plan of the floor of an L-shaped room. All lengths are in metres.

(a)

The area of the floor is 75 m²

$Question 19, shown as an image$

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(b)

By factorising x² + x – 90 work out the value of x. You must show your working

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Paper 3: Calculator June 2022 Higher tier, Question 27 3 marks

Expand and simplify fully (x – 3)(x – 4)(x + 8)

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Paper 1: Non-calculator November 2021 Foundation tier, Question 2 1 mark

Circle the expression that is equal to x + x + x – x + x

x 2 x 3 x 4 x

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Paper 1: Non-calculator November 2021 Foundation tier, Question 22 3 marks

(a)

Lucy wants to simplify 6 a – (7 b – 2 a) She writes 4 a – 7 b Is she correct?

$Question 22, shown as an image$

Give a reason for your answer.

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(b)

Lucy also wants to simplify 3p² × 5p⁷ She says, “Add 3 and 5, then add 2 and 7”

$Question 22, shown as an image$

Tick a box for each part of her method.

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(c)

Lucy thinks of a number. 10 × the number = 10 ÷ the number Give a possible value of the number.

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Paper 1: Non-calculator November 2021 Foundation tier, Question 32 2 marks

Factorise x² + 7x + 10

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Paper 1: Non-calculator November 2021 Higher tier, Question 1 1 mark

Simplify maths symbol a⁵³ Circle your answer.

$Question 1, shown as an image$

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Paper 1: Non-calculator November 2021 Higher tier, Question 14 1 mark

$Question 14, shown as an image$

Circle your answer.

$Question 14, shown as an image$

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Paper 1: Non-calculator November 2021 Higher tier, Question 15 3 marks

Also involves Forming and solving equations

(x + a)(x + 3a) maths symbol x² + bx + 75 Work out the two possible values of b.

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Paper 2: Calculator November 2021 Foundation tier, Question 13 2 marks

Factorise fully 50 x + 100

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Paper 2: Calculator November 2021 Higher tier, Question 1 1 mark

Circle the factor of x² – 5x

x – 1 – 5 x x – 5 5 x

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Paper 2: Calculator November 2021 Higher tier, Question 21 4 marks

x is an integer. Prove that 35 + (3x + 1)² – 2x(4x – 3) is a square number.

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Paper 3: Calculator November 2021 Foundation tier, Question 17 2 marks

Multiply out 5 x (3 x – 2)

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Paper 3: Calculator November 2021 Foundation tier, Question 19 3 marks

Also involves Area and perimeter

Here are a triangle and a rectangle.

a and b are positive numbers. Which shape has the larger perimeter? You must work out expressions for both perimeters.

Tick a box.

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Paper 3: Calculator November 2021 Higher tier, Question 4 1 mark

Factorise x² – 64 Circle your answer.

(x + 8)² (x – 8)² (x + 8)(x – 8) x(x – 64)

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Paper 3: Calculator November 2021 Higher tier, Question 18 1 mark

Also involves Indices

Simplify w¹ × w⁰ Circle your answer.

$Question 18, shown as an image$

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Paper 3: Calculator November 2021 Higher tier, Question 25 3 marks

Expand and simplify fully (x – 3)(x + 2)(x + 5)

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Paper 1: Non-calculator November 2020 Foundation tier, Question 25 2 marks

Factorise fully 2 x 2 + 6 x

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Paper 1: Non-calculator November 2020 Higher tier, Question 13 3 marks

Also involves Quadratic equations

(a)

s and t are positive integers. (x + s)(x – t) is expanded and simplified. The answer is x 2 + kx – 40 where k is a positive integer. Work out the smallest possible value of k.

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(b)

Faisal tries to solve (x + 2)(x – 7) = 0 Here is his working. (x + 2) = 0 or (x – 7) = 0 x = 2 or x = 7 Give a reason why his answer is wrong.

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Paper 1: Non-calculator November 2020 Higher tier, Question 19 1 mark

Also involves Fractions

Circle the expression that is equivalent to $fraction$ + $fraction$

$Question 19, shown as an image$

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Paper 1: Non-calculator November 2020 Higher tier, Question 28 2 marks

Factorise fully 144 – 4 x 2

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Paper 2: Calculator November 2020 Higher tier, Question 19 3 marks

a and b are positive values.

$Question 19, shown as an image$

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Paper 2: Calculator November 2020 Higher tier, Question 25 2 marks

Factorise 3 x 2 + 11 x – 20

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Paper 3: Calculator November 2020 Foundation tier, Question 27 1 mark

Circle the expression that is equivalent to (x – 1) 2

x 2 – 1 x 2 + 1 x 2 – 2 x – 1 x 2 – 2 x + 1

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Paper 3: Calculator November 2020 Foundation tier, Question 30, also on the Higher paper 2 marks

Expand and simplify fully 4(2 c + 3) – (5 c – 1)

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Paper 3: Calculator November 2020 Higher tier, Question 10, also on the Foundation paper 2 marks

Expand and simplify fully 4(2 c + 3) – (5 c – 1)

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Paper 1: Non-calculator November 2019 Foundation tier, Question 26 2 marks

$Question 26, shown as an image$

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Paper 1: Non-calculator November 2019 Foundation tier, Question 27 3 marks

Also involves Indices · Powers and roots

Write 27 × maths symbol 3²⁷ as a single power of 3

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Paper 1: Non-calculator November 2019 Higher tier, Question 4 1 mark

Circle the expression equivalent to (2 x) 4

$Question 4, shown as an image$

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Paper 1: Non-calculator November 2019 Higher tier, Question 23 5 marks

(a)

Factorise 5x² + 6x – 8

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(b)

23 $Question 23, shown as an image$

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Paper 2: Calculator November 2019 Foundation tier, Question 1 1 mark

Simplify 8 a – 3 a + a Circle your answer.

4 a 6 a 5 + a 8 a – 3 a 2

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Paper 2: Calculator November 2019 Foundation tier, Question 17 3 marks

Match each expression in Column P with the equivalent expression in Column Q. One has been done for you.

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Paper 2: Calculator November 2019 Higher tier, Question 1 1 mark

Expand 4 x 2 (3 x + 5) Circle your answer.

$Question 1, shown as an image$

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Paper 3: Calculator November 2019 Foundation tier, Question 9 2 marks

(a)

Rearrange m = p + 2 to make p the subject.

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(b)

Simplify 5 x 2 – x 2

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Paper 3: Calculator November 2019 Foundation tier, Question 19 3 marks

Also involves Algebraic notation and vocabulary · Properties of triangles and quadrilaterals

S and T are rectangles. S has dimensions (x + 2) and x. Some of these rectangles make the larger rectangle shown.

Work out an expression for the perimeter of T. Give your answer in its simplest form.

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Paper 3: Calculator November 2019 Higher tier, Question 3 1 mark

(2 x – 4)(3 x + 5) is expanded and simplified. Circle the term which is part of the answer.

2 x – 2 x 22 x – 22 x

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Paper 1: Non-calculator June 2019 Foundation tier, Question 19 4 marks

Also involves Simultaneous equations

You are given that 4 a – 2 b = 10

(a)

Write down the value of 2 a – b

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(b)

Write down the value of 2 b – 4 a

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(c)

You are given that 4 a – 2 b = 10 and a + c = 3 Write an expression in a, b and c that is equal to 23 Give your answer in its simplest form. You must show your working.

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Paper 1: Non-calculator June 2019 Foundation tier, Question 28 2 marks

Multiply out and simplify (x + 5)(x – 1)

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Paper 1: Non-calculator June 2019 Higher tier, Question 16 3 marks

$Question 16, shown as an image$

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Paper 1: Non-calculator June 2019 Higher tier, Question 18 3 marks

Here is an identity.

$Question 18, shown as an image$

(a)

Use the identity to work out the value of 193² – 7² You must show your working.

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(b)

Factorise 100a² – 81b²

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Paper 2: Calculator June 2019 Higher tier, Question 26 3 marks

(x + 5)(x + 2)(x + a) maths symbol x³ + bx² + cx – 30 Work out the values of the integers a, b and c.

$Question 26, shown as an image$

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Paper 3: Calculator June 2019 Foundation tier, Question 19 5 marks

(a)

Simplify fully 3a² + 7a + 3 – a² + 8a – 4

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(b)

Factorise fully 24y² – 20y

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Paper 3: Calculator June 2019 Higher tier, Question 15 3 marks

$Question 15, shown as an image$

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Paper 1: Non-calculator November 2018 Foundation tier, Question 23 4 marks

Two consecutive whole numbers are n and n + 1

(a)

Simplify n – (n + 1)

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(b)

Multiply out n (n + 1)

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(c)

The two numbers are added. Show that the answer must be an odd number.

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Paper 1: Non-calculator November 2018 Higher tier, Question 3 1 mark

Simplify 16a² ÷ a + 3a × 2 Circle your answer.

22 a 8 a 38 a 2 a

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Paper 1: Non-calculator November 2018 Higher tier, Question 22 4 marks

$Question 22, shown as an image$

You must show your working.

x =

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Paper 1: Non-calculator November 2018 Higher tier, Question 25 3 marks

Also involves Quadratic graphs

A quadratic curve intersects the axes at (–3, 0), (3, 0) and (0, 18)

Work out the equation of the curve.

[3]

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Paper 2: Calculator November 2018 Foundation tier, Question 3 1 mark

Simplify 8 x – 3 + 6 x Circle your answer.

2 x – 3 11 x 5 + 6 x 14 x – 3

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Paper 2: Calculator November 2018 Foundation tier, Question 20, also on the Higher paper 4 marks

Work out the values of a and b in the identity

$Question 20, shown as an image$

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Paper 2: Calculator November 2018 Higher tier, Question 7, also on the Foundation paper 4 marks

Work out the values of a and b in the identity

$Question 7, shown as an image$

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Paper 2: Calculator November 2018 Higher tier, Question 22 3 marks

Also involves Algebraic division

$Question 22, shown as an image$

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Paper 3: Calculator November 2018 Higher tier, Question 17 1 mark

Also involves Indices · Surds

Circle the expression for w²

$Question 17, shown as an image$

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Paper 1: Non-calculator June 2018 Foundation tier, Question 3 1 mark

Simplify 3 × a × 3 × a Circle your answer.

$Question 3, shown as an image$

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Paper 1: Non-calculator June 2018 Higher tier, Question 3 1 mark

Circle the expression that is equivalent to 3 a – a × 4 a + 2 a

$Question 3, shown as an image$

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Paper 2: Calculator June 2018 Foundation tier, Question 7 4 marks

e is 3 more than d. f is 5 less than d.

(a)

Write an expression for e in terms of d.

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(b)

Write an expression for f in terms of d.

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(c)

Work out e – f Simplify your answer.

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Paper 2: Calculator June 2018 Foundation tier, Question 19 1 mark

Multiply out x (x – 4) Circle your answer.

$Question 19, shown as an image$

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Paper 2: Calculator June 2018 Higher tier, Question 13 3 marks

Also involves Rational expressions

Show that, for x ≠ –1 13 $fraction$ simplifies to the form ax + b where a and b are integers.

[3]

Reveal mark scheme

Paper 2: Calculator June 2018 Higher tier, Question 28 6 marks

f(x) = 5 – x and g(x) = 3 x + 7

(a)

Simplify f(2 x) + g(x – 1)

[3]

Reveal mark scheme

(b)

Solve g^–1(x) = 2x

x =

[3]

Reveal mark scheme

Paper 3: Calculator June 2018 Foundation tier, Question 17 1 mark

Simplify 7 x – (3 x – 2 x) Circle your answer.

7 x – 1 2 x 6 x 8 x

[1]

Reveal mark scheme

Paper 3: Calculator June 2018 Higher tier, Question 18 3 marks

Also involves Algebraic argument and proof

Show that, for x ≠ 0

$Question 18, shown as an image$

can be written in the form $fraction$ where a, b and c are integers.

[3]

Reveal mark scheme

Paper 1: Non-calculator November 2017 Foundation tier, Question 26, also on the Higher paper 4 marks

Three identical isosceles triangles are joined to make this trapezium. Each triangle has base b cm and perpendicular height h cm

(a)

Work out an expression, in terms of b and h, for the area of the trapezium. Give your answer in its simplest form.

[2]

Reveal mark scheme

(b)

This diagram shows the same trapezium.

b: s = 2: 3 Work out an expression, in terms of b, for the perimeter of the trapezium.

[2]

Reveal mark scheme

Paper 1: Non-calculator November 2017 Foundation tier, Question 31, also on the Higher paper 3 marks

(a)

Factorise x² – 100

[1]

Reveal mark scheme

(b)

Solve 7x + 6 maths symbol 1 + 2x

[2]

Reveal mark scheme

Paper 1: Non-calculator November 2017 Higher tier, Question 3 1 mark

Also involves Indices

3 maths symbol ₅ ² Circle the expression that is equivalent to 4a

$Question 3, shown as an image$

[1]

Reveal mark scheme

Paper 1: Non-calculator November 2017 Higher tier, Question 5, also on the Foundation paper 3 marks

(a)

Factorise x² – 100

[1]

Reveal mark scheme

(b)

Solve 7x + 6 maths symbol 1 + 2x

[2]

Reveal mark scheme

Paper 1: Non-calculator November 2017 Higher tier, Question 10, also on the Foundation paper 4 marks

Also involves Properties of triangles and quadrilaterals

Three identical isosceles triangles are joined to make this trapezium. Each triangle has base b cm and perpendicular height h cm

(a)

Work out an expression, in terms of b and h, for the area of the trapezium. Give your answer in its simplest form.

[2]

Reveal mark scheme

(b)

This diagram shows the same trapezium.

b: s = 2: 3 Work out an expression, in terms of b, for the perimeter of the trapezium.

[2]

Reveal mark scheme

Paper 2: Calculator November 2017 Foundation tier, Question 5 3 marks

(a)

Simplify y × y

[1]

Reveal mark scheme

(b)

Simplify 5 a + 2 – a + 9

[2]

Reveal mark scheme

Paper 2: Calculator November 2017 Higher tier, Question 11 1 mark

Also involves Rational expressions

Circle the expression that is equivalent to $fraction$

$Question 11, shown as an image$

[1]

Reveal mark scheme

Paper 2: Calculator November 2017 Higher tier, Question 16 4 marks

(a)

Factorise fully 9y³ – 6y

[2]

Reveal mark scheme

(b)

Factorise 3x² – 22x + 7

[2]

Reveal mark scheme

Paper 3: Calculator November 2017 Foundation tier, Question 12 3 marks

a – b = 5

(a)

Work out the value of 2(a – b)

[1]

Reveal mark scheme

(b)

Work out the value of 7 a – 7 b

[1]

Reveal mark scheme

(c)

Work out the value of b – a

[1]

Reveal mark scheme

Paper 3: Calculator November 2017 Foundation tier, Question 28, also on the Higher paper 2 marks

Multiply out and simplify (x maths symbol 8)²

[2]

Reveal mark scheme

Paper 3: Calculator November 2017 Higher tier, Question 5, also on the Foundation paper 2 marks

Multiply out and simplify (x maths symbol 8)²

[2]

Reveal mark scheme

Paper 3: Calculator November 2017 Higher tier, Question 18 4 marks

Expand and simplify (3x² + 2)(2x + 5) – 6x(x² – 3)

[4]

Reveal mark scheme

Paper 1: Non-calculator June 2017 Foundation tier, Question 17 1 mark

Also involves Indices

Circle the expression which does not simplify to y³

$Question 17, shown as an image$

[1]

Reveal mark scheme

Paper 1: Non-calculator June 2017 Higher tier, Question 26 4 marks

Expand and simplify (x maths symbol 4)(2x + 3y)²

[4]

Reveal mark scheme

Paper 3: Calculator June 2017 Foundation tier, Question 5 5 marks

(a)

Simplify a × a × a + b + b

[2]

Reveal mark scheme

(b)

Simplify 5(x + 3) – x + 2

[3]

Reveal mark scheme

Paper 3: Calculator June 2017 Foundation tier, Question 26 1 mark

Circle the expression equivalent to x² – 4x – 12

(x – 4)(x – 8) (x + 3)(x – 4) (x – 12)(x + 1) (x + 2)(x – 6)

[1]

Reveal mark scheme

Simplifying and manipulating expressions

Simplifying and manipulating expressions questions

AQA 8300 Simplifying and manipulating expressions 137 questions

Paper 1: Non-calculator June 2025 Foundation tier, Question 26 Foundation Paper 1: Non-calculator · June 2025 · Question 26 4 marks

Paper 1: Non-calculator June 2025 Higher tier, Question 10 Higher Paper 1: Non-calculator · June 2025 · Question 10 4 marks

Paper 1: Non-calculator June 2025 Higher tier, Question 24 Higher Paper 1: Non-calculator · June 2025 · Question 24 4 marks

Paper 2: Calculator June 2025 Foundation tier, Question 11 Foundation Paper 2: Calculator · June 2025 · Question 11 3 marks

Paper 2: Calculator June 2025 Foundation tier, Question 24, also on the Higher paper Foundation Paper 2: Calculator · June 2025 · Question 24 Also on Higher 1 mark

Paper 2: Calculator June 2025 Higher tier, Question 6, also on the Foundation paper Higher Paper 2: Calculator · June 2025 · Question 6 Also on Foundation 1 mark

Paper 2: Calculator June 2025 Higher tier, Question 14 Higher Paper 2: Calculator · June 2025 · Question 14 3 marks

Paper 3: Calculator June 2025 Higher tier, Question 20 Higher Paper 3: Calculator · June 2025 · Question 20 3 marks

Paper 1: Non-calculator November 2024 Foundation tier, Question 10 Foundation Paper 1: Non-calculator · November 2024 · Question 10 4 marks

Paper 1: Non-calculator November 2024 Higher tier, Question 19 Higher Paper 1: Non-calculator · November 2024 · Question 19 5 marks

Paper 1: Non-calculator November 2024 Higher tier, Question 22 Higher Paper 1: Non-calculator · November 2024 · Question 22 3 marks

Paper 2: Calculator November 2024 Foundation tier, Question 3 Foundation Paper 2: Calculator · November 2024 · Question 3 4 marks

Paper 2: Calculator November 2024 Foundation tier, Question 12 Foundation Paper 2: Calculator · November 2024 · Question 12 5 marks

Paper 2: Calculator November 2024 Foundation tier, Question 25, also on the Higher paper Foundation Paper 2: Calculator · November 2024 · Question 25 Also on Higher 3 marks

Paper 2: Calculator November 2024 Higher tier, Question 11, also on the Foundation paper Higher Paper 2: Calculator · November 2024 · Question 11 Also on Foundation 3 marks

Paper 3: Calculator November 2024 Foundation tier, Question 2 Foundation Paper 3: Calculator · November 2024 · Question 2 1 mark

Paper 3: Calculator November 2024 Higher tier, Question 11 Higher Paper 3: Calculator · November 2024 · Question 11 2 marks

Paper 3: Calculator November 2024 Higher tier, Question 20 Higher Paper 3: Calculator · November 2024 · Question 20 2 marks

Paper 2: Calculator June 2024 Foundation tier, Question 2 Foundation Paper 2: Calculator · June 2024 · Question 2 4 marks

Paper 2: Calculator June 2024 Higher tier, Question 19 Higher Paper 2: Calculator · June 2024 · Question 19 5 marks

Paper 3: Calculator June 2024 Foundation tier, Question 14 Foundation Paper 3: Calculator · June 2024 · Question 14 2 marks

Paper 3: Calculator June 2024 Foundation tier, Question 15 Foundation Paper 3: Calculator · June 2024 · Question 15 3 marks

Paper 1: Non-calculator November 2023 Foundation tier, Question 6 Foundation Paper 1: Non-calculator · November 2023 · Question 6 4 marks

Paper 1: Non-calculator November 2023 Foundation tier, Question 28, also on the Higher paper Foundation Paper 1: Non-calculator · November 2023 · Question 28 Also on Higher 2 marks

Paper 1: Non-calculator November 2023 Higher tier, Question 4 Higher Paper 1: Non-calculator · November 2023 · Question 4 1 mark

Paper 1: Non-calculator November 2023 Higher tier, Question 11, also on the Foundation paper Higher Paper 1: Non-calculator · November 2023 · Question 11 Also on Foundation 2 marks

Paper 1: Non-calculator November 2023 Higher tier, Question 13 Higher Paper 1: Non-calculator · November 2023 · Question 13 3 marks

Paper 1: Non-calculator November 2023 Higher tier, Question 26 Higher Paper 1: Non-calculator · November 2023 · Question 26 4 marks

Paper 2: Calculator November 2023 Higher tier, Question 1 Higher Paper 2: Calculator · November 2023 · Question 1 1 mark

Paper 2: Calculator November 2023 Higher tier, Question 22 Higher Paper 2: Calculator · November 2023 · Question 22 1 mark

Paper 2: Calculator November 2023 Higher tier, Question 24 Higher Paper 2: Calculator · November 2023 · Question 24 3 marks

Paper 3: Calculator November 2023 Foundation tier, Question 11 Foundation Paper 3: Calculator · November 2023 · Question 11 4 marks

Paper 3: Calculator November 2023 Higher tier, Question 18 Higher Paper 3: Calculator · November 2023 · Question 18 3 marks

Paper 3: Calculator November 2023 Higher tier, Question 22 Higher Paper 3: Calculator · November 2023 · Question 22 2 marks

Paper 1: Non-calculator June 2023 Foundation tier, Question 22, also on the Higher paper Foundation Paper 1: Non-calculator · June 2023 · Question 22 Also on Higher 2 marks

Paper 1: Non-calculator June 2023 Higher tier, Question 8, also on the Foundation paper Higher Paper 1: Non-calculator · June 2023 · Question 8 Also on Foundation 2 marks

Paper 1: Non-calculator June 2023 Higher tier, Question 27 Higher Paper 1: Non-calculator · June 2023 · Question 27 3 marks

Paper 2: Calculator June 2023 Foundation tier, Question 2 Foundation Paper 2: Calculator · June 2023 · Question 2 4 marks

Paper 2: Calculator June 2023 Foundation tier, Question 14 Foundation Paper 2: Calculator · June 2023 · Question 14 1 mark

Paper 2: Calculator June 2023 Higher tier, Question 15 Higher Paper 2: Calculator · June 2023 · Question 15 2 marks

Paper 2: Calculator June 2023 Higher tier, Question 25 Higher Paper 2: Calculator · June 2023 · Question 25 3 marks

Paper 3: Calculator June 2023 Foundation tier, Question 10 Foundation Paper 3: Calculator · June 2023 · Question 10 3 marks

Paper 3: Calculator June 2023 Foundation tier, Question 25 Foundation Paper 3: Calculator · June 2023 · Question 25 3 marks

Paper 3: Calculator June 2023 Higher tier, Question 18 Higher Paper 3: Calculator · June 2023 · Question 18 6 marks

Paper 3: Calculator June 2023 Higher tier, Question 19 Higher Paper 3: Calculator · June 2023 · Question 19 3 marks

Paper 1: Non-calculator November 2022 Foundation tier, Question 5 Foundation Paper 1: Non-calculator · November 2022 · Question 5 2 marks

Paper 1: Non-calculator November 2022 Higher tier, Question 15 Higher Paper 1: Non-calculator · November 2022 · Question 15 4 marks

Paper 1: Non-calculator November 2022 Higher tier, Question 20 Higher Paper 1: Non-calculator · November 2022 · Question 20 3 marks

Paper 2: Calculator November 2022 Foundation tier, Question 5 Foundation Paper 2: Calculator · November 2022 · Question 5 3 marks

Paper 2: Calculator November 2022 Foundation tier, Question 22, also on the Higher paper Foundation Paper 2: Calculator · November 2022 · Question 22 Also on Higher 3 marks

Paper 2: Calculator November 2022 Higher tier, Question 8, also on the Foundation paper Higher Paper 2: Calculator · November 2022 · Question 8 Also on Foundation 3 marks

Paper 2: Calculator November 2022 Higher tier, Question 22 Higher Paper 2: Calculator · November 2022 · Question 22 2 marks

Paper 3: Calculator November 2022 Higher tier, Question 3 Higher Paper 3: Calculator · November 2022 · Question 3 1 mark

Paper 3: Calculator November 2022 Higher tier, Question 22 Higher Paper 3: Calculator · November 2022 · Question 22 4 marks

Paper 1: Non-calculator June 2022 Foundation tier, Question 19 Foundation Paper 1: Non-calculator · June 2022 · Question 19 4 marks

Paper 1: Non-calculator June 2022 Higher tier, Question 19 Higher Paper 1: Non-calculator · June 2022 · Question 19 3 marks

Paper 1: Non-calculator June 2022 Higher tier, Question 24 Higher Paper 1: Non-calculator · June 2022 · Question 24 6 marks

Paper 2: Calculator June 2022 Foundation tier, Question 17 Foundation Paper 2: Calculator · June 2022 · Question 17 4 marks

Paper 2: Calculator June 2022 Higher tier, Question 23 Higher Paper 2: Calculator · June 2022 · Question 23 2 marks

Paper 3: Calculator June 2022 Foundation tier, Question 4 Foundation Paper 3: Calculator · June 2022 · Question 4 1 mark

Paper 3: Calculator June 2022 Foundation tier, Question 12 Foundation Paper 3: Calculator · June 2022 · Question 12 6 marks

Paper 3: Calculator June 2022 Higher tier, Question 13 Higher Paper 3: Calculator · June 2022 · Question 13 1 mark

Paper 3: Calculator June 2022 Higher tier, Question 19 Higher Paper 3: Calculator · June 2022 · Question 19 5 marks

Paper 3: Calculator June 2022 Higher tier, Question 27 Higher Paper 3: Calculator · June 2022 · Question 27 3 marks

Paper 1: Non-calculator November 2021 Foundation tier, Question 2 Foundation Paper 1: Non-calculator · November 2021 · Question 2 1 mark

Paper 1: Non-calculator November 2021 Foundation tier, Question 22 Foundation Paper 1: Non-calculator · November 2021 · Question 22 3 marks

Paper 1: Non-calculator November 2021 Foundation tier, Question 32 Foundation Paper 1: Non-calculator · November 2021 · Question 32 2 marks

Paper 1: Non-calculator November 2021 Higher tier, Question 1 Higher Paper 1: Non-calculator · November 2021 · Question 1 1 mark

Paper 1: Non-calculator November 2021 Higher tier, Question 14 Higher Paper 1: Non-calculator · November 2021 · Question 14 1 mark

Paper 1: Non-calculator November 2021 Higher tier, Question 15 Higher Paper 1: Non-calculator · November 2021 · Question 15 3 marks

Paper 2: Calculator November 2021 Foundation tier, Question 13 Foundation Paper 2: Calculator · November 2021 · Question 13 2 marks

Paper 2: Calculator November 2021 Higher tier, Question 1 Higher Paper 2: Calculator · November 2021 · Question 1 1 mark

Paper 2: Calculator November 2021 Higher tier, Question 21 Higher Paper 2: Calculator · November 2021 · Question 21 4 marks

Paper 3: Calculator November 2021 Foundation tier, Question 17 Foundation Paper 3: Calculator · November 2021 · Question 17 2 marks

Paper 3: Calculator November 2021 Foundation tier, Question 19 Foundation Paper 3: Calculator · November 2021 · Question 19 3 marks

Paper 3: Calculator November 2021 Higher tier, Question 4 Higher Paper 3: Calculator · November 2021 · Question 4 1 mark

Paper 3: Calculator November 2021 Higher tier, Question 18 Higher Paper 3: Calculator · November 2021 · Question 18 1 mark

Paper 1: Non-calculator June 2025 Foundation tier, Question 26 4 marks

Paper 1: Non-calculator June 2025 Higher tier, Question 10 4 marks

Paper 1: Non-calculator June 2025 Higher tier, Question 24 4 marks

Paper 2: Calculator June 2025 Foundation tier, Question 11 3 marks

Paper 2: Calculator June 2025 Foundation tier, Question 24, also on the Higher paper 1 mark

Paper 2: Calculator June 2025 Higher tier, Question 6, also on the Foundation paper 1 mark

Paper 2: Calculator June 2025 Higher tier, Question 14 3 marks

Paper 3: Calculator June 2025 Higher tier, Question 20 3 marks

Paper 1: Non-calculator November 2024 Foundation tier, Question 10 4 marks

Paper 1: Non-calculator November 2024 Higher tier, Question 19 5 marks

Paper 1: Non-calculator November 2024 Higher tier, Question 22 3 marks

Paper 2: Calculator November 2024 Foundation tier, Question 3 4 marks

Paper 2: Calculator November 2024 Foundation tier, Question 12 5 marks

Paper 2: Calculator November 2024 Foundation tier, Question 25, also on the Higher paper 3 marks

Paper 2: Calculator November 2024 Higher tier, Question 11, also on the Foundation paper 3 marks

Paper 3: Calculator November 2024 Foundation tier, Question 2 1 mark

Paper 3: Calculator November 2024 Higher tier, Question 11 2 marks

Paper 3: Calculator November 2024 Higher tier, Question 20 2 marks

Paper 2: Calculator June 2024 Foundation tier, Question 2 4 marks

Paper 2: Calculator June 2024 Higher tier, Question 19 5 marks

Paper 3: Calculator June 2024 Foundation tier, Question 14 2 marks

Paper 3: Calculator June 2024 Foundation tier, Question 15 3 marks

Paper 1: Non-calculator November 2023 Foundation tier, Question 6 4 marks

Paper 1: Non-calculator November 2023 Foundation tier, Question 28, also on the Higher paper 2 marks

Paper 1: Non-calculator November 2023 Higher tier, Question 4 1 mark

Paper 1: Non-calculator November 2023 Higher tier, Question 11, also on the Foundation paper 2 marks

Paper 1: Non-calculator November 2023 Higher tier, Question 13 3 marks

Paper 1: Non-calculator November 2023 Higher tier, Question 26 4 marks

Paper 2: Calculator November 2023 Higher tier, Question 1 1 mark

Paper 2: Calculator November 2023 Higher tier, Question 22 1 mark

Paper 2: Calculator November 2023 Higher tier, Question 24 3 marks

Paper 3: Calculator November 2023 Foundation tier, Question 11 4 marks

Paper 3: Calculator November 2023 Higher tier, Question 18 3 marks

Paper 3: Calculator November 2023 Higher tier, Question 22 2 marks

Paper 1: Non-calculator June 2023 Foundation tier, Question 22, also on the Higher paper 2 marks

Paper 1: Non-calculator June 2023 Higher tier, Question 8, also on the Foundation paper 2 marks

Paper 1: Non-calculator June 2023 Higher tier, Question 27 3 marks

Paper 2: Calculator June 2023 Foundation tier, Question 2 4 marks

Paper 2: Calculator June 2023 Foundation tier, Question 14 1 mark

Paper 2: Calculator June 2023 Higher tier, Question 15 2 marks

Paper 2: Calculator June 2023 Higher tier, Question 25 3 marks

Paper 3: Calculator June 2023 Foundation tier, Question 10 3 marks

Paper 3: Calculator June 2023 Foundation tier, Question 25 3 marks

Paper 3: Calculator June 2023 Higher tier, Question 18 6 marks

Paper 3: Calculator June 2023 Higher tier, Question 19 3 marks

Paper 1: Non-calculator November 2022 Foundation tier, Question 5 2 marks

Paper 1: Non-calculator November 2022 Higher tier, Question 15 4 marks

Paper 1: Non-calculator November 2022 Higher tier, Question 20 3 marks

Paper 2: Calculator November 2022 Foundation tier, Question 5 3 marks

Paper 2: Calculator November 2022 Foundation tier, Question 22, also on the Higher paper 3 marks

Paper 2: Calculator November 2022 Higher tier, Question 8, also on the Foundation paper 3 marks

Paper 2: Calculator November 2022 Higher tier, Question 22 2 marks

Paper 3: Calculator November 2022 Higher tier, Question 3 1 mark

Paper 3: Calculator November 2022 Higher tier, Question 22 4 marks

Paper 1: Non-calculator June 2022 Foundation tier, Question 19 4 marks

Paper 1: Non-calculator June 2022 Higher tier, Question 19 3 marks

Paper 1: Non-calculator June 2022 Higher tier, Question 24 6 marks

Paper 2: Calculator June 2022 Foundation tier, Question 17 4 marks

Paper 2: Calculator June 2022 Higher tier, Question 23 2 marks

Paper 3: Calculator June 2022 Foundation tier, Question 4 1 mark

Paper 3: Calculator June 2022 Foundation tier, Question 12 6 marks

Paper 3: Calculator June 2022 Higher tier, Question 13 1 mark

Paper 3: Calculator June 2022 Higher tier, Question 19 5 marks

Paper 3: Calculator June 2022 Higher tier, Question 27 3 marks

Paper 1: Non-calculator November 2021 Foundation tier, Question 2 1 mark

Paper 1: Non-calculator November 2021 Foundation tier, Question 22 3 marks

Paper 1: Non-calculator November 2021 Foundation tier, Question 32 2 marks

Paper 1: Non-calculator November 2021 Higher tier, Question 1 1 mark

Paper 1: Non-calculator November 2021 Higher tier, Question 14 1 mark

Paper 1: Non-calculator November 2021 Higher tier, Question 15 3 marks

Paper 2: Calculator November 2021 Foundation tier, Question 13 2 marks

Paper 2: Calculator November 2021 Higher tier, Question 1 1 mark

Paper 2: Calculator November 2021 Higher tier, Question 21 4 marks

Paper 3: Calculator November 2021 Foundation tier, Question 17 2 marks

Paper 3: Calculator November 2021 Foundation tier, Question 19 3 marks

Paper 3: Calculator November 2021 Higher tier, Question 4 1 mark

Paper 3: Calculator November 2021 Higher tier, Question 18 1 mark

Paper 3: Calculator November 2021 Higher tier, Question 25 3 marks

Paper 1: Non-calculator November 2020 Foundation tier, Question 25 2 marks

Paper 1: Non-calculator November 2020 Higher tier, Question 13 3 marks