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Maths Gcse Aqa Higher

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  1. Scatter-Graphs-And-Correlation Aqa Higher
    2 主题
  2. Cumulative-Frequency-And-Box-Plots Aqa Higher
    4 主题
  3. Histograms Aqa Higher
    3 主题
  4. Statistical-Diagrams Aqa Higher
    5 主题
  5. Averages-Ranges-And-Data Aqa Higher
    7 主题
  6. Combined-And-Conditional-Probability Aqa Higher
    3 主题
  7. Tree-Diagrams Aqa Higher
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  8. Simple-Probability-Diagrams Aqa Higher
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  9. Transformations Aqa Higher
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  10. Vectors Aqa Higher
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  11. 3D-Pythagoras-And-Trigonometry Aqa Higher
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  12. Sine-Cosine-Rule-And-Area-Of-Triangles Aqa Higher
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  13. Pythagoras-And-Trigonometry Aqa Higher
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  14. Area-And-Volume-Of-Similar-Shapes Aqa Higher
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  15. Congruence-Similarity-And-Geometrical-Proof Aqa Higher
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  16. Volume-And-Surface-Area Aqa Higher
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  17. Circles-Arcs-And-Sectors Aqa Higher
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  18. Area-And-Perimeter Aqa Higher
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  19. Circle-Theorems Aqa Higher
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  20. Bearings-Scale-Drawing-Constructions-And-Loci Aqa Higher
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  21. Angles-In-Polygons-And-Parallel-Lines Aqa Higher
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  22. Symmetry-And-Shapes Aqa Higher
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  23. Exchange-Rates-And-Best-Buys Aqa Higher
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  24. Standard-And-Compound-Units Aqa Higher
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  25. Direct-And-Inverse-Proportion Aqa Higher
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  26. Problem-Solving-With-Ratios Aqa Higher
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  27. Ratios Aqa Higher
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  28. Sequences Aqa Higher
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  29. Transformations-Of-Graphs Aqa Higher
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  30. Graphing-Inequalities Aqa Higher
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  31. Solving-Inequalities Aqa Higher
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  32. Real-Life-Graphs Aqa Higher
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  33. Estimating-Gradients-And-Areas-Under-Graphs Aqa Higher
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  34. Equation-Of-A-Circle Aqa Higher
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  35. Functions Aqa Higher
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  36. Forming-And-Solving-Equations Aqa Higher
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  37. Graphs-Of-Functions Aqa Higher
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  38. Linear-Graphs Aqa Higher
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  39. Coordinate-Geometry Aqa Higher
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  40. Iteration Aqa Higher
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  41. Simultaneous-Equations Aqa Higher
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  42. Quadratic-Equations Aqa Higher
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  43. Linear-Equations Aqa Higher
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  44. Algebraic-Proof Aqa Higher
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  45. Rearranging-Formulas Aqa Higher
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  46. Algebraic-Fractions Aqa Higher
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  47. Completing-The-Square Aqa Higher
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  48. Factorising Aqa Higher
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  49. Expanding-Brackets Aqa Higher
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  50. Algebraic-Roots-And-Indices Aqa Higher
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  51. Using-A-Calculator Aqa Higher
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  52. Surds Aqa Higher
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  53. Rounding-Estimation-And-Bounds Aqa Higher
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  54. Fractions-Decimals-And-Percentages Aqa Higher
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  55. Introduction Aqa Higher
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  56. Simple-And-Compound-Interest-Growth-And-Decay Aqa Higher
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  57. Percentages Aqa Higher
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  58. Fractions Aqa Higher
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  59. Powers-Roots-And-Standard-Form Aqa Higher
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  60. Prime-Factors-Hcf-And-Lcm Aqa Higher
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  61. Number-Operations Aqa Higher
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Exam code:8300

Area & Circumference

Why are circles different to other 2D shapes?

  • Circles are a shape that is made up of all the points on a 2D plane that are equidistant from a single point

    • Equidistant means the same distance

  • The circumference of a circle is its perimeter

  • π (pi) is the number (3.14159 …) that links a circle’s diameter to its circumference

  • You may be asked to give an area answer to a certain number of decimal places or significant figures

    • Alternatively you may be asked to give the exact value – or “give your answer in terms of π” – so this topic could crop up on the non-calculator paper!Diameter (d) is twice the radius (r)

How do I work with circles?

  • You must know the formulae for the area and circumference of a circle

  • There are two versions for the circumference and it is important not to get the radius and diameter confused

  • Remember that d = 2r

    But you may prefer to remember the formulae by having different letters involved

Circumference-Formulae, IGCSE & GCSE Maths revision notes

  • Working with circle formulae is just like working with any other formula:

    • WRITE DOWN – what you know (what you want to know)

    • Pick correct FORMULA

    • SUBSTITUTE and SOLVE

Examiner Tips and Tricks

  • If you’re under pressure and can’t remember which formula is which, remember that area is always measured in square units (cm2, m2 etc.) so the formula with r2 in it is the one for area

  • The circumference is just a length, so its units will be the same as for length (cm, m, etc)

Worked Example

Find the area and perimeter of the semicircle shown in the diagram.

Give your answers in terms of pi.

Semicircle-d=16, IGCSE & GCSE Maths revision notes

 

The area of a semicircle is half the area of the full circle with the same diameter, so begin by finding the area of the full circle.

Find the radius by dividing the diameter by 2.

r space equals space 16 over 2 space equals space 8 space cm

Substitute this into the formula for the area of a circle A space equals space πr squared.
Leave your answer in terms of <img alt=”straight pi” data-mathml='<math ><semantics><mi mathvariant=”normal”>π</mi><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ data-type=”commentary” height=”19″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2219%22%20width%3D%2213%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%20mathcolor%3D%22%23000%22%20mathvariant%3D%22normal%22%3E%26%23x3C0%3B%3C%2Fmi%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math1437d7d1d97917cd627a34a6a0f’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAt2hlYWQQC2qxAAACRAAAADZoaGVhCGsXSAAAAnwAAAAkaG10eE2rRkcAAAKgAAAACGxvY2EAHTwYAAACqAAAAAxtYXhwBT0FPgAAArQAAAAgbmFtZaBxlY4AAALUAAABn3Bvc3QB9wD6AAAEdAAAACBwcmVwa1uragAABJQAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAA

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