Revision Seminar ALGEBRA Why Algebra Algebra is everywhere
Revision Seminar ALGEBRA
Why Algebra ?
Algebra is everywhere CALCULUS SERIES AND SEQUENCES COORDINATE GEOMETRY ALGEBRA ARITHMETIC TRIGONOMETRY
Addition and Subtraction Two Key Rules 1) Only like terms can be added or subtracted. 2) Group together your positive like terms and your negative like terms and then subtract The rest is easy!!
Your Turn •
Multiplication & Division Rules 1) To Multiply Add the Powers • Your Turn •
2) To Multiply or divide + or – letters use the following rules •
3) To Divide Subtract the Powers. • Your Turn
Brackets Mean Multiply STEP 1) Multiply the signs together STEP 2) Multiply the numbers together STEP 3) Multiply each letter (variable) together
Your Turn •
Simplify Means Multiply & Tidy Up •
Your Turn •
Express as a Single Fraction Approach: Get the Common Denominator and Tidy Up Example:
Your Turn •
Example •
FACTORISE • Type 1: Highest Common Factor.
Grouping •
Trinomials If the last sign is +, the signs inside the brackets are both the same. They are the same as the middle sign. Pick the factors that add to give the middle term. • •
If the last sign is – the signs inside the brackets are opposite: The larger factor is the same as the middle sign. Pick the factors that subtract to get the middle term. • Your Turn •
• Your Turn •
4. The Difference of Two Squares • Your Turn
Solving Equations • Type 1: Linear Equations Method: Multiply out and tidy up.
Your Turn •
If necessary cross multiply but only across an equals sign. •
Your Turn •
Type 2: Quadratic Equations •
Formula •
Type 3: Simultaneous Equations • Method: Set up the equation:
Example •
• When you add the two line the y’s will cancel and you get
Solving Linear Inequalities • Inequalities are treated in the very same way as equations, with one exception!! • When you multiply or divide across an inequality by a negative you must turn the inequality sign around.
Example • -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
• -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
• Multiply both sides of the equation by LCD (i. e. 12) -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Number systems •
Number systems •
Rearranging Formulae • Key: Treat formulae the same as equations. Example: Express p in terms of q and r.
Your Turn • Express q in terms of p and r.
Substitution • Given that 3(b + a) = t(6 – a), • Calculate the value of a when t = 3 and b = − 4
Your Turn •
Also •
Rules for Indices • •
More Rules of Indices • •
2013 OL LEAVING CERTIFICATE (b) Each tank is 1 m in height. Find how long it takes to fill each tank.
(c) For each tank, write down a formula which gives the depth of water in the tank at any given time. State clearly the meaning of any letters used in your formulas. (d) For each tank, draw the graph to represent the depth of water in the tank over the 2 minutes.
(e) Find, from your graphs, how much time passes before the depth of water is the same in each tank. Answer: 60 seconds (f) Verify your answer to part (e) using your formulas from part (c).
2011 Ordinary Level Leaving Certificate Project Maths Q 6
- Slides: 54