Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Simultaneous Equations — exam questions

11 original Incandio exam-style questions on Simultaneous Equations, 32 marks, about 40 minutes of writing. Each one carries the command word, the tariff and the specification statement it assesses, exactly as a paper presents them. This is an original Incandio practice question, written to reflect the structure and demands of the qualification. It is not an official Pearson Edexcel past-paper question.

This is the practice set for Simultaneous Equations — the module that teaches it. Read the module first if the idea is new; come here when you want to find out whether you can turn it into marks. Completely free, no account needed to read.

What these questions ask of you

6 command words run through this set, and on Pearson Edexcel International GCSE Mathematics A each one means something precise. Answering the wrong command is the commonest way a candidate who understands the module still loses the mark.

Write down (1–2 marks)
a value that needs no working — read off, recalled or stated
Solve (1–4 marks)
the value(s) of the unknown that satisfy the equation
Explain why (1–2 marks)
one short justification — mathematics almost never asks for extended explanation
Show that (2–5 marks)
every step of a derivation to a value that is already printed in the question Misread as: stating the printed answer again instead of deriving it
Find (1–5 marks)
a value or expression obtained by a method the learner chooses
Work out (1–5 marks)
a calculated result, with the working that produced it

Assessed on Paper 1 and Paper 2.

Where these sit in the specification

Pearson Edexcel International GCSE Mathematics A (4MA1) — statement 2.6. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and it reproduces none of Pearson's wording.

The 11 questions

Answer them on paper, then open the module's exam practice to have them marked. The mark scheme, the accepted and rejected answers and the annotated model answer are in Incandio and are not printed here — an answer beside its question is not practice.

  1. (1)Write down

    Two straight lines cross at the point (3, 5). Write down the solution of the pair of simultaneous equations that the lines represent.

    Specification 2.6 · about 1 min

    (Total for Question 1 = 1 mark)

  2. (2)Solve

    Solve the simultaneous equations x + y = 12 and x − y = 4.

    Specification 2.6 · about 2 min

    (Total for Question 2 = 2 marks)

  3. (3)Solve

    Solve the simultaneous equations 2x + 3y = 19 and 4x − 3y = 11.

    Specification 2.6 · about 4 min

    (Total for Question 3 = 3 marks)

  4. (1)Explain why

    Explain why there is no pair of values that satisfies both 2x + 3y = 8 and 4x + 6y = 20.

    Specification 2.6 · about 1 min

    (Total for Question 4 = 1 mark)

  5. (3)Solve

    Solve the simultaneous equations y = 2x − 1 and 3x + y = 14.

    Specification 2.6 · about 4 min

    (Total for Question 5 = 3 marks)

  6. (3)Show that

    Show that the equations 4x − y = 7 and 8x − 2y = 14 are satisfied by infinitely many pairs of values.

    Specification 2.6 · about 4 min

    (Total for Question 6 = 3 marks)

  7. (3)Find

    Find the coordinates of the point where the lines 2x + y = 11 and x − 2y = 3 cross.

    Specification 2.6 · about 4 min

    (Total for Question 7 = 3 marks)

  8. (3)Solve

    Solve the simultaneous equations 5x + 2y = 24 and 3x + 5y = 22.

    Specification 2.6 · about 4 min

    (Total for Question 8 = 3 marks)

  9. (4)Solve

    Solve the simultaneous equations y = x + 3 and x² + y² = 29.

    Specification 2.6 · about 5 min

    (Total for Question 9 = 4 marks)

  10. (4)Work out

    Three pens and two rulers cost £5.60. Five pens and four rulers cost £10.00. Work out the cost of one pen.

    cost of one pen = ............................

    Specification 2.6 · about 5 min

    (Total for Question 10 = 4 marks)

  11. (5)Work out

    Four adult tickets and three child tickets cost £71. Two adult tickets and five child tickets cost £57. Work out the cost of one adult ticket and the cost of one child ticket.

    adult and child ticket prices = ............................ £

    Specification 2.6 · about 6 min

    (Total for Question 11 = 5 marks)

Have them marked, then defend the answer

Practice tells you the mark; teaching it back tells you whether you understand it. On Incandio a topic counts as mastered only once you have taught it and defended it.

  1. Mark these questions — 11 questions, marked on Incandio against the authored scheme, with the mistake you actually made named.
  2. Teach it — explain Simultaneous Equations to Ember, an AI pupil who does not have it yet and asks the awkward question.
  3. Defend it — argue it against Carl Friedrich Gauss over three rounds, marked against descriptors you can read first.

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