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

Deciding the quadratic method

When should I solve by factorisation?

  • Use factorisation when the question asks to solve by factorisation

    • For example

      • part (a) Factorise 6x2 + 7x – 3

      • part (b) Solve 6x2 + 7x – 3 = 0

  • Use factorisation when solving two-term quadratic equations

    • For example, solve x2 – 4x = 0

      • Take out a common factor of x to get x(x – 4) = 0

      • So x = 0 and x = 4

    • For example, solve x2 – 9 = 0

      • Use the difference of two squares to factorise it as (x + 3)(x – 3) = 0

      • So x = -3 and x = 3

      • (Or rearrange to x2 = 9 and use ±√ to get x = ±3)

  • Factorising can often be the quickest way to solve a quadratic equation

When should I use the quadratic formula?

  • Use the quadratic formula when the question says to leave solutions correct to a given accuracy (2 decimal places, 3 significant figures etc)

    • This is a hint that the equation will not factorise

  • Use the quadratic formula when it may be faster than factorising

    • It’s quicker to solve 36x2 + 33x – 20 = 0 using the quadratic formula than by factorisation

  • Use the quadratic formula if in doubt, as it always works

When should I solve by completing the square?

  • Use completing the square when part (a) of a question says to complete the square and part (b) says to use part (a) to solve the equation

  • Use completing the square when making x the subject of harder formulae containing both x2 and x terms

    • For example, make x the subject of the formula x2 + 6x = y

      • Complete the square: (x + 3)2 – 9 = y

      • Add 9 to both sides: (x + 3)2 = y + 9

      • Take square roots and use ±: x plus 3 equals plus-or-minus square root of y plus 9 end root

      • Subtract 3: x equals negative 3 plus-or-minus square root of y plus 9 end root

  • Completing the square always works

    • But it’s not always quick or easy to do

Examiner Tips and Tricks

  • If your calculator solves quadratic equations, use it to check your solutions

  • If the solutions on your calculator are whole numbers or fractions (with no square roots), this means the quadratic equation does factorise

Worked Example

(a) Solve x squared minus 7 x plus 2 equals 0, giving your answers correct to 2 decimal places. 

“Correct to 2 decimal places” suggests using the quadratic formula
Substitute a = 1, b = -7 and c = 2 into the formula
Put brackets around any negative numbers 

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