Paper 1 Algebra Leaving Certificate Helpdesk 20 th September 2012

General Content for Algebra Simultaneous Equations Modulus Equations Inequalities The Nature of Roots of a Quadratic Equation Complex Numbers

Simultaneous Equations: Example 1 Step 1: Eliminate one of the variables.

Simultaneous Equations in Three Variables Method: Select one pair of equations and eliminate one of the variables. Select another pair and eliminate the same variable. Solve these two new equations simultaneously. Use answers to find third variable.

Simultaneous Equations: Example 2 Solve the simultaneous equations

Simultaneous Equations: Example Paper 1 Q1(a)

Method: Turn the rational inequality into a quadratic inequality by multiplying both sides by a positive expression. Example: Solve the inequality Note: multiplying both sides by a squared value ensures that the inequality sign is not affected. Rational Inequalities

Modulus Equations / Inequalities

The Nature of Roots of a Quadratic Example: 2009 Question 2 (b)(i)

The Nature of Roots of a Quadratic

Quadratic Roots Example 1 The equation has equal roots. Find the possible values of k.

Quadratic Roots Example 2 Sample Paper 2012 Paper 1 Q3