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Maths Gcse Aqa Foundation

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  2. Statistical-Diagrams Aqa Foundation
    6 主题
  3. Averages-Ranges-And-Data Aqa Foundation
    7 主题
  4. Tree-Diagrams-And-Combined-Probability Aqa Foundation
    2 主题
  5. Simple-Probability-Diagrams Aqa Foundation
    4 主题
  6. Transformations Aqa Foundation
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  7. Vectors Aqa Foundation
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  8. Pythagoras-And-Trigonometry Aqa Foundation
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  9. Congruence-Similarity-And-Geometrical-Proof Aqa Foundation
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  10. Volume-And-Surface-Area Aqa Foundation
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  11. Circles-Arcs-And-Sectors Aqa Foundation
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  12. Area-And-Perimeter Aqa Foundation
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  13. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Foundation
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  14. 2D-And-3D-Shapes Aqa Foundation
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  15. Angles-In-Polygons-And-Parallel-Lines Aqa Foundation
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  16. Symmetry-And-Shapes Aqa Foundation
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  18. Standard-And-Compound-Units Aqa Foundation
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  19. Direct-And-Inverse-Proportion Aqa Foundation
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  20. Ratio-Problem-Solving Aqa Foundation
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  21. Sequences Aqa Foundation
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  23. Real-Life-Graphs Aqa Foundation
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  24. Graphs-Of-Functions Aqa Foundation
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  25. Linear-Graphs Aqa Foundation
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  26. Coordinate-Geometry Aqa Foundation
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  27. Functions Aqa Foundation
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  28. Forming-And-Solving-Equations Aqa Foundation
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  32. Algebraic-Reasoning Aqa Foundation
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  34. Introduction Aqa Foundation
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Exam code:8300

Problem-solving with areas

What is problem-solving?

  • Problem-solving, usually has two key features:

    • A question is given as a real-life scenario

      • eg. Mary is painting a bedroom in her house…

    • There is usually more than one topic of maths you will need in order to answer the question

      • eg. Area and percentages

What are common problems that involve area?

  • Area is a commonly used topic of ‘real-world’ maths

    • For example, laying a carpet, painting a house or designing a sports field all involve area

  • Typically, the ‘real-world’ scenarios also have a cost

    • A lot of area problems also involve calculations with money

How do I solve problems that involve area?

  • There is often a lot of text in a problem-solving question, which can make it seem harder than it is

    • Avoid focusing only on what the question asks you, think about what you can do with the information given

      • This may lead you to think of something else you can do

      • Eventually you may be able to see your way to answering the original question

    • Think about the context of the question, what makes sense?

  • Look out for key information in the text:

    • Real-life context

      • A question involving the size of a field, will mean be talking about its area 

    • Key words

      • Types of measure: area, length, cost, … 

      • Conditions: minimum, maximum, greatest, …

    • Units

      • You may see compound units, e.g. $/m2 , these may help you to identify calculations that you need to do

  • Annotate diagrams with information that you can work out

    • Remember to do this in pencil in case you need to erase it!

  • Problem solving questions could appear on either a non-calculator paper or a calculator paper

Examiner Tips and Tricks

  • Even if you never get to a final answer always try to do some maths with the information from the question

    • You are likely to score some extra marks from your working!

Worked Example

John wants a new carpet for the lounge in his house. 

A sketch of his lounge is given below.

Compound shape made up of two rectangles

He gets quote from two local companies, Company A and Company B.

The amount they charge for laying a carpet is given below. 

  • Company A: Fixed price of $5.50 per square metre

  • Company B: $6 per square metre for the first ten square metres, then $4 per square metre for anything over that.

Which company should John choose in order to keep the cost of laying the carpet to a minimum?

Although this question doesn’t specifically tell you you need to find the area, it is implied as the costs both use ‘square metre’ 

The shape of the lounge is a compound shape consisting of two rectangles
Split the area into these two rectangles and find the missing distances by subtracting the smaller length (2.4 m) from the longer one (6 m)

6 – 2.4 = 3.6 

Lounge-Floor-Area, downloadable IGCSE & GCSE Maths revision notes

 Find the area of the lounge by adding the two areas together

<img alt=”table row cell Total space Area space end cell equals cell space Area space straight A space plus space Area space straight B end cell row blank equals cell space open parentheses 3.2 cross times 3.6 close parentheses plus open parentheses 2.4 cross times 1.8 close parentheses end cell row blank equals cell space 11.52 plus 4.32 end cell row blank equals cell space 15.84 space straight m to the power of 2 space end exponent end cell end table” data-mathml='<math ><semantics><mtable columnspacing=”0px” columnalign=”right center left”><mtr><mtd><mi >Total</mi><mo >&#160;</mo><mi >Area</mi><mo >&#160;</mo></mtd><mtd><mo >=</mo></mtd><mtd><mo >&#160;</mo><mi >Area</mi><mo >&#160;</mo><mi mathvariant=”normal” >A</mi><mo >&#160;</mo><mo >+</mo><mo >&#160;</mo><mi >Area</mi><mo >&#160;</mo><mi mathvariant=”normal” >B</mi></mtd></mtr><mtr><mtd></mtd><mtd><mo >=</mo></mtd><mtd><mo >&#160;</mo><mfenced 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