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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

Finding regions using inequalities

What are 2D inequalities?

  • Recall that an inequality in one variable (1D inequality) represents a relationship that is not equal

    • An inequality of x < 7, represents all values smaller than 7

      • There are an infinite number of values than can satisfy this inequality

  • A 2D inequality represents a relationship between two expressions that is not equal

    • The inequality y > x represents all pairs of numbers x and y where the y value is greater than the x value

      • There are an infinite number of pairs of values that would satisfy this inequality

      • These pairs of numbers can be thought of as coordinates

      • On a graph, all coordinates above the line y = x would satisfy this inequality

  • If a 2D inequality includes either the symbol ≤ or ≥, then coordinates on the line itself also satisfies the inequality

    • E.g. y ≤ 2x represents all of the pairs of numbers where the value of y is less than two lots of the value of x

      • This is the region below the line y = 2x, but also being on the line y = 2x satisfies the inequality

How do we draw inequalities on a graph?

  • A set of 2D inequalities can be shown graphically using straight lines and shaded regions

  • To draw the correct lines:

    • Replace the inequality sign with “=” and draw that line

      • Use a solid line for ≤ or ≥ (to indicate the line is included)

      • Use dotted line for < or > (to indicate the line is not included)

  • To decide which side of the line is the wanted side:

    • if “y ≤ …” or “y < …” then the wanted region is below the line

    • if “y ≥ …” or “y > …” then the wanted region is above the line

    • If you are unsure

      • substitute the coordinates from a point on one side of the line into the inequality

      • determine whether or not the inequality holds true on that side

    • For vertical lines:

      • the wanted region for x less than k is to the left of x equals k

      • the wanted region for x greater than k is to the right of x equals k

  • To do the shading:

    • Shade the unwanted sides of each line (unless the question says otherwise)

      • You are shading away any parts you don’t want

      • This will leave behind a clear region that is the wanted region (rather than trying to look for the wanted region under multiple shades)

      • Label the wanted region R (unless the question says otherwise)

  • (Be careful if using graphing software, as some shade the wanted sides)

Worked Example

Show, graphically, the region that is satisfied by all three inequalities below:

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