Equations and Inequalities

Check list:

Solve exponential equations and surd equations of the form \(\sqrt {x + b} = ax + c\) ; \(a,\;b,\;c\; \in \;\mathbb{Z}\).
Quadratic equations (by factorisation, by completion of the square and by using the quadratic formula).
Quadratic inequalities in one unknown (Interpret solutions graphically on number line, and interval notation).
NB: It is recommended that the solving of equations in two unknowns is important to be used in other equations like hyperbola-straight line as this is normal in the case of graphs.
Equations in two unknown, one of which is linear and the other quadratic.
Nature of roots.

Learn the concepts:

This section spends a lot of time teaching you what to do if you're not able to factorise a quadratic equation. There are two ways to tackle these equations, the manual way (completing the square) or by using a formula. In every exam, you should have at least one question that asks you to solve an equation by completing the square, so make sure you know all the steps!

Simultaneous equations (where one of the equations is a quadratic equation) just takes practice. You will use this skill in many other sections, so make sure you can do these with your eyes closed.

This section also includes quadratic inequalities and how to determine the nature of the roots of an equation. Have fun!

Videos from learn.mindset.co.za

Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 1 Page 22 (Completing the square)
Exercise 2 Page 23 (Completing the square)
Exercise 3 Page 26 (Maximum and minimum values)
Exercise 4 Page 27 (Solving quadratic equations)
Exercise 5 Page 29 (Completing the square)
Exercise 6 Page 31 (Using the quadratic formula)
Exercise 7 Page 32 (Equations with fractions)
Exercise 8 Page 36 (Nature of roots)
Exercise 9 Page 41 (Simultaneous equations)
Exercise 10 Page 44 (Word problems)
Exercise 11 Page 45 (Linear inequalities)
Exercise 12 Page 51 (Quadratic inequalities)