← Back to MathematicsSection 1.2 Simulation Squares, Cubes, Roots & IndicesFull screen ↗ Notes Mind map Quiz
Algebra
Simple algebraic expressions, addition, subtraction, multiplication and division; use of brackets; simple algebraic fractions.
Squares, Cubes, Roots & Indices
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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
Simplify 5x + 3x − 2x.
All three are like terms in x: (5 + 3 − 2)x = 6x.
Expand 3(2x − 4).
Multiply both terms inside by 3: 3 × 2x = 6x and 3 × (−4) = −12, giving 6x − 12.
Algebra concept map
Algebra (Cat A)
Algebra quiz
Algebra (Cat A)
Ref 1.215 of 50Pass 75%
1. Simplify 3a + 2b − a + 4b.
2a + 6b4a + 6b2a + 2b2. Simplify 5x + 3x.
8x15x2x3. Simplify 7y − 2y.
5y9y14y4. Simplify 4a + 3b + 2a.
6a + 3b9ab6a + 35. Simplify 8m − 3m − 2m.
3m13m5m6. Simplify 2x + 5y − x + y.
x + 6y3x + 6yx + 4y7. Simplify 6p − 4p + 3q.
2p + 3q10p + 3q2p − 3q8. Simplify a + a + a.
3aa³39. Simplify 9c − c.
8c9c10c10. Simplify 4x + 2y + 3x − y.
7x + y7x + 3yx + y11. Simplify 5a + 2b − 3a − b.
2a + b8a + 3b2a − b12. Simplify 10 − 3x + 5x.
10 + 2x10 − 2x12x13. Simplify 3ab + 2ab.
5ab6ab5a²b²14. Simplify 7x + 0.
7x0715. Simplify 2a − 5a.
−3a3a7a