PAss Functional Skills

Simultaneous equations

Simultaneous equations for A Level Art and Design OCR Higher: what it means, how to set the working out, and the questions it is asked in.
  • A Level
  • OCR
  • Art and Design
  • Higher
  • Spec G10 · G20 · G9
  • 14 min read
  • 8 revision boxes

Introduction

2 boxes
4 min read

What is simultaneous equations?

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Transcript

A short spoken summary of simultaneous equations and where it is used.

A spoken walk-through of simultaneous equations before you read the notes.
Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing simultaneous equations laid out step by step

The same idea drawn out, so the method is visible.
4 rows

The simultaneous equations reference table

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
49=7\sqrt{49} = 7
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 3 column 1
Row 3 column 2
×10\times 10 moves every digit one column left

Learning

4 boxes
4 steps

How to work with simultaneous equations

Read the units in the question before you start; a converted unit is the most common slip.
The layout below is the one the mark scheme expects.

Diagram showing simultaneous equations laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ≈160\approx 160.
  1. Read the question and write down what is being asked for.
  2. Set out the working for simultaneous equations in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Simultaneous equations

The specification wording is precise here, and the mark scheme follows that wording exactly.

  • Rule 1

    How simultaneous equations behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How simultaneous equations behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}
4 steps

How to work with simultaneous equations

Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing simultaneous equations laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.
  1. Read the question and write down what is being asked for.
  2. Set out the working for simultaneous equations in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: ×10\times 10 moves every digit one column left
3 rules

Key facts: Simultaneous equations

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.

  • Rule 1

    How simultaneous equations behaves in the 1st of the cases the specification names.
    ×10\times 10 moves every digit one column left

  • Rule 2

    How simultaneous equations behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How simultaneous equations behaves in the 3rd of the cases the specification names.
    49=7\sqrt{49} = 7

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Examples

2 boxes
1 marks · worked

Worked example: simultaneous equations

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: ×10\times 10 moves every digit one column left.
3 marks · worked

Practice question 8: ×10\times 10 moves every digit one column left

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: 34×25\frac{3}{4} \times \frac{2}{5}.

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Common questions

How many marks is simultaneous equations usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the A Level Art and Design OCR Higher paper?
Yes — it sits in the Vectors strand.