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Section 1.2

Algebra

Simple algebraic expressions, addition, subtraction, multiplication and division; use of brackets; simple algebraic fractions.

Simulation

Squares, Cubes, Roots & Indices

Squares, Cubes, Roots & IndicesFull screen ↗
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Notes

Algebra (Cat A), summary notes

Main ideas
  • Algebra uses letters to stand for unknown or variable quantities, so a single formula can describe every case rather than one specific set of numbers.
  • Only 'like terms' can be added or subtracted, 3x + 2x = 5x, but 3x + 2y cannot be combined any further.
  • Multiplying and dividing terms works on the numbers and the letters separately: 3x × 4y = 12xy, and 6x ÷ 3 = 2x.
  • Expanding brackets means multiplying every term inside the bracket by the term outside.
  • A simple algebraic fraction is simplified by cancelling factors common to the top and bottom.
Key formulas
Collecting like terms
ax + bx = (a + b)x
Expanding a bracket
a(b + c) = ab + ac
Simplifying a fraction
6x / 3 = 2x
Solved examples
  1. Simplify 5x + 3x − 2x.

    All three are like terms in x: (5 + 3 − 2)x = 6x.

  2. Expand 3(2x − 4).

    Multiply both terms inside by 3: 3 × 2x = 6x and 3 × (−4) = −12, giving 6x − 12.

Mind map

Algebra concept map

Algebra (Cat A)

Quiz

Algebra quiz

Algebra (Cat A)

Ref 1.215 of 50Pass 75%
  1. 1. Simplify 3a + 2b − a + 4b.

    2a + 6b
    4a + 6b
    2a + 2b
  2. 2. Simplify 5x + 3x.

    8x
    15x
    2x
  3. 3. Simplify 7y − 2y.

    5y
    9y
    14y
  4. 4. Simplify 4a + 3b + 2a.

    6a + 3b
    9ab
    6a + 3
  5. 5. Simplify 8m − 3m − 2m.

    3m
    13m
    5m
  6. 6. Simplify 2x + 5y − x + y.

    x + 6y
    3x + 6y
    x + 4y
  7. 7. Simplify 6p − 4p + 3q.

    2p + 3q
    10p + 3q
    2p − 3q
  8. 8. Simplify a + a + a.

    3a
    3
  9. 9. Simplify 9c − c.

    8c
    9c
    10c
  10. 10. Simplify 4x + 2y + 3x − y.

    7x + y
    7x + 3y
    x + y
  11. 11. Simplify 5a + 2b − 3a − b.

    2a + b
    8a + 3b
    2a − b
  12. 12. Simplify 10 − 3x + 5x.

    10 + 2x
    10 − 2x
    12x
  13. 13. Simplify 3ab + 2ab.

    5ab
    6ab
    5a²b²
  14. 14. Simplify 7x + 0.

    7x
    0
    7
  15. 15. Simplify 2a − 5a.

    −3a
    3a
    7a