Worksheet Chapter 2: Factorisation and Algebraic Fractions

1. True or False: The algebraic fraction x + 2x² - 4 simplifies to 1x - 2.

2. True or False: The algebraic expression x² + 9 can be factorised into (x + 3)(x - 3).

3. Express as a single fraction in its simplest form: (3x) - (2 / (x + 1)).

4. The total area of a square is (4x² + 12x + 9) cm². (a) Find an expression for the length of one side of the square. (b) Find the perimeter of the square when x = 3 cm.

5. Fill in the blank: The process of expanding (a + b)(a - b) gives ________.

6. Simplify: [x² - 163x] ÷ [x - 46x²].

7. Expand and simplify: (2x - 3)² - (x + 1)(x - 4).

8. A triangular park has a base of (2x + 6) meters and a height of (x - 2) meters. (a) Express the area of the park in terms of x in expanded form. (b) If x = 5 meters, calculate the numerical area of the park.

9. Factorise by grouping: 3ps + 3pt - 2qs - 2qt.

10. Factorise completely: 4x² - 36.