paper 1 algebra leaving certificate helpdesk 20 th september 2012
TRANSCRIPT
General Content for Algebra
• Simultaneous Equations• Modulus Equations • Inequalities • The Nature of Roots of a Quadratic Equation• Complex Numbers
Simultaneous Equations: Example 1
Solve the simultaneous equations:
_______________________________________Step 1: Eliminate one of the variables.
Step 2: Solve for either or using the following equations:
Step 3: Solve for by subbing for in the equation:
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.
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
212
xx
(2 𝑥−1)2𝑥
2 𝑥−1<−2(2𝑥−1)2
Complete all multiplication and tidy up the expression:
Solve the quadratic to find the roots and sketch the curve:
Quadratic Roots Example 1
The equation has equal roots. Find the possible values of k.
0)1(2 kxkkx
Solution: Equal roots: