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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
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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

Collecting like terms

What happens if there is more than one term?

  • Terms can be added and subtracted 

    • The numbers in front of the letters are called coefficients

  • Each term has a positive or negative sign in front

    • In 2x – 3y the sign of the x term is positive and the sign of the y  term is negative

  • Subtractions can be thought of as adding a negative 

    • 2x – 3y is the same as 2x + (-3y)

      • Just like 20 – 30 is the same as 20 + (-30)

  • The order of two terms can be swapped, but the signs must move with their terms 

    • 2x – 3y is the same as -3y + 2x

      • A plus is now needed in front of the 2x

      • Just like 20 – 30 is the same as -30 + 20

  • If no number appears in front of a term, then its number is 1

    • x  is the same as 1x

What is a like term?

  • Like terms are terms with exactly the same letters and powers

    • The numbers in front can be different

      • For example:

      • 2x and 3x

      • 4x2 and 6x2

      • 5xy and -7xy

    • These are not like terms:

      • 2x and 3y (different letters)

      • 4x2 and 6x4 (different powers)

      • 5xy and 7xyz (different letters)

  • Remember multiplication can be done in any order

    • xy and yx  are like terms

      • So are 2xy and 3yx

How do I collect like terms?

  • Collecting like terms means simplifying by adding or subtracting the numbers in front 

    • 2x + 3x becomes 5x

    • 4y – 10y  becomes -6y

      • A negative sign is needed here

  • If there are different types of like terms, collect them separately

    • For 2x + 4y + 5x – 3y 

      • Collecting the x‘s gives 2x + 5x = 7x

      • Collecting the y‘s gives 4y – 3y = y

      • The answer is 7x + y

Examiner Tips and Tricks

  • Don’t leave terms like 1x in your final answer in an exam – always simplify them to just x.

Worked Example

Simplify

8 a minus 5 b minus 6 a plus 4 b

 Collect the a terms first

8 a minus 6 a equals 2 a 

Then collect the b terms
Don’t forget the minus sign in front of the 5b

negative 5 b plus 4 b equals negative b 

Add together the two answers

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