1. Surds and Quadratics
AS 91577

2. Surds
Adding
Subtracting
Multiplying
Dividing

3. Adding and subtracting surds

4. Multiplying Surds Example 1:

5. Multiplying Surds Example 2:

6. Dividing surds (Rationalising) Example 1
Multiply top and bottom by

7. Dividing surds (Rationalising) Example 2
Multiply top and bottom by

8. Recognising terms

9. Worksheet 1

10. Quadratics
General formula:

11. Example 1.
Solving for the roots (i.e. y = 0)
Method 1: Factorising

12. Method 2: Quadratic Formula

13. Equation Mode F2: Polynomial Degree: 2 (F1) Enter 1, -2, -3 Solve (F1)
Method 3: Graphics Calculator
Equation Mode
F2: Polynomial
Degree: 2 (F1)
Enter 1, -2, -3
Solve (F1)

14. Equation has 2 real solutions x = 3, -1

15. Example 2
Method 1: Factorize

16. Method 2: Quadratic Formula

17. Equation has two equal solutions: x = 3

18. Example 3
Equation cannot be factorised.

19. Using quadratic formula
We use the substitution
A complex number

20. Equation has 2 complex solutions
Real part
Imaginary Part

21. Note: Because the coefficients are real, solutions come in conjugate pairs i.e.

22. Equation has 2 imaginary solutions.

23. Forming quadratic equations from 2 solutions.
If solutions are

24. Example 1
Quadratic equation is

25. Example 2
Quadratic equation is

26. Example 3

27. Worksheet 2