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Topic: Algebraic Manipulation (Foundation - Unit 3)

Specification References: N5.1

N5.1 Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors.


Candidates should be able to:

  • understand that the transformation of algebraic expressions obeys and generalises the rules of generalised arithmetic
  • manipulate an expression by collecting like terms
  • multiply a single term over a bracket
  • write expressions to solve problems
  • write expressions using squares and cubes
  • factorise algebraic expressions by taking out common factors

Notes

Candidates will not be required at Foundation tier to expand the product of two linear expressions.

Examples

  1. Simplify 3x + 5 – x – 4.

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  1. Expand and simplify 2(3x – 5) + 3(5x + 7).

  2. Factorise 12x2 + 8x
    or
    Factorise 15xy2 – 25x2y. 
  3. This rectangle has dimensions as shown.

      
          The perimeter of the rectangle is 68 centimetres.
          Use this information to form and solve an equation to work out the dimensions of the
          rectangle.

  1. The base of a triangle is three times the height.
    The area of the triangle is 75 cm²
    Work out the length of the base of the triangle.
  1. A rectangle has base (2x + 1) cm and width (3x –2 ) cm

a.  Explain why the value of x cannot be 2/3

b.  Work out the area of the rectangle when x = 7