Functions and algebra: Solve algebraic equations and inequalities
Subject outcome
Subject outcome 2.3: Solve algebraic equations and inequalities
Learning outcomes
- Solve quadratic equations by means of:
- Factorisation
- Completing the square
- Using the quadratic formula.
- Solve simultaneous equations with two unknowns algebraically and graphically, where the one equation is linear and the other equation is quadratic.
- Solve quadratic inequalities in one variable and represent the solution in the following ways:
- In set builder notation
- Interval notation
- On the number line.
Unit 1 outcomes
By the end of this unit you will be able to:
- Apply the zero-product law.
- Solve rational quadratic equations which have fractions with the unknown in the denominator.
- Factorise quadratic expressions to solve for the unknown variable.
Unit 2 outcomes
By the end of this unit you will be able to:
- Solve a quadratic equation by completing the square.
Unit 3 outcomes
By the end of this unit you will be able to:
- Understand when to use the quadratic formula to solve quadratic equations.
- Apply the quadratic formula when necessary.
Unit 4 outcomes
By the end of this unit you will be able to:
- Solve simultaneous equations algebraically where the one equation is linear and the other equation is quadratic.
- Solve simultaneous equations graphically where the one equation is linear and the other equation is quadratic.
Unit 5 outcomes
By the end of this unit you will be able to:
- Find the critical values.
- Solve quadratic inequalities using the table and graphical methods.
- Represent the solution using set builder notation, interval notation and on a number line.
