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Algebra Lesson 1 Junior Certificate Mathematics 1 Topics To be Covered The Use of Letters Translating from a spoken phrase to an Algebraic Expression 02 May 2015

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Algebra helps us to solve problems. In algebra we use letters to stand for numbers. I think of a number, add seven to it and the result is 11. If we let x stand for the number we can write this as follows : Do you know what the number is? The answer is 4 202 May 2015

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Here we simply remove the multiplication symbol. Some examples 3 The x here has different values in each question, we call this letter a variable. Notation: We write instead of Also instead of 02 May 2015

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Try Exercise From Text Book Translating from a spoken phrase to an algebraic expression. 4 x plus 2 times y 4 times x minus 8 x decreased by 9 6 less than 3 times k 02 May 2015

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Algebra Lesson 2 Junior Certificate Mathematics 5 Topics To be Covered Replacing Letters with Numbers 02 May 2015

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Remember Multiply and divide before you add and subtract Replacing letters with numbers 6 Ex 1 02 May 2015

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Remember Any number when multiplied by 0 is 0, e.g. 12 x 0 = 0 Try the following yourself 7 Ex 2 02 May 2015

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Try Exercise From Text Book 802 May 2015

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Algebra Lesson 3 Junior Certificate Mathematics 9 Topics To be Covered Adding and Subtracting like Terms 02 May 2015

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2 cars + 2 cars = 4 cars Let x be a car then this is 2 x + 2 x = 4 x 2 cars + 2 cars = 4 cars Let x be a car then this is 2 x + 2 x = 4 x Adding Like Terms 1002 May 2015

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2 cars + 1 truck Let x be a car and y be a truck = 2x + y It cannot be reduced further 2 cars + 1 truck Let x be a car and y be a truck = 2x + y It cannot be reduced further Unlike Terms cannot be added 1102 May 2015

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5 x + 4 y are left just as they are Like Terms can be added and subtracted. Unlike Terms cannot be added together or subtracted from each other. 1202 May 2015

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Try Exercise From Text Book Simplifying Algebraic Expressions 13 Ex 1 02 May 2015

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Algebra Lesson 4 Junior Certificate Mathematics 14 Topics To be Covered Removing Brackets Removing Brackets & then Simplifying 02 May 2015

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Everything inside the brackets is multiplied by the number outside Removing Brackets 15 Here we did what was inside the brackets first. Here we multiplied everything inside the bracket by 5. The final result is the same as Method 1. In this section we may not be able to reduce what is inside the bracket further, so Method 2 is what we use. Method 1 Method 2 02 May 2015

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A minus outside the bracket changes the sign of each term inside the bracket Removing Brackets 16 Ex 1 Ex 2 Ex 3 02 May 2015

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Like signs when multiplies together give a positive result. Unlike signs when multiplied together give a negative result. Try the following yourself 17 Q 1 Q 2 Q 3 02 May 2015

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Try Exercise From Text Book Remove Brackets and Simplify 18 Ex 4 02 May 2015

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Algebra Lesson 5 Junior Certificate Mathematics 19 Topics To be Covered Multiplication involving Powers 02 May 2015

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The power is the number at the top of the letter Multiplication involving Powers 2002 May 2015

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Multiply the numbers in front of letters and add the powers at the top of the letters. Multiplication involving Powers (cont.) 21 When multiplying two similar letter together we add the powers When multiplying two similar letter together that have numbers in front of them we multiply these numbers infront together, and add the powers as before. 02 May 2015

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Bring like terms together, and reorder with highest power terms first Multiplication involving Powers (cont.) 22 Ex 1 Ex 2 Ex 3 You have a new substitute teacher today as PowerPoint Sir is not well. 02 May 2015

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Try Exercise From Text Book Try the following yourself 23 Q 1 Q 2 Q 3 02 May 2015

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Algebra Lesson 6 Junior Certificate Mathematics 24 Topics To be Covered Calculating Expressions with x 2 02 May 2015

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For a x 2 you always find x 2 before you multiply by a. Calculating Expressions with x 2 25 Here we have squared -2 first, then multiplied by 4. 02 May 2015

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Here we had to square both x and y Calculating Expressions (cont.) 26 Ex 1 Find the value of: Ex 2 Find the value of Nice to be back 02 May 2015

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Remember to work out the power before you multiply. Try Exercise From Text Book Try the following yourself: 27 Q 1 Find the value of: Q 2 Find the value of Well done 02 May 2015

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Algebra Lesson 7 Junior Certificate Mathematics 28 Topics To be Covered Multiplying Compound Expressions 02 May 2015

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Multiply each term in the second bracket by each term in the first bracket Multiplying Compound Expressions 29 When multiplying compound algebraic expressions together, we multiply each term in the second bracket, by each term in the first bracket. (i) Write down the second bracket twice. (ii) Multiply the 1 st term in the 1 st bracket by the 2 nd bracket. (iii) Multiply the 2 nd term in the 1 st bracket by the 2 nd bracket. (iv) Remove the brackets(by multiplying) (v) Bring like terms together 02 May 2015

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When the highest power of x is 2. This is called a Quadratic Expression 30 EX 1 Multiply 02 May 2015

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When the highest power of x is 2. The Expression is called an Quadratic Expression? 31 EX 2 Multiply Answer: The highest power of x is 2. Why is the resulting expression called a quadratic expression? 02 May 2015

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When the highest power of x is 2. The Expression is called an Quadratic Expression? 32 EX 3 Multiply Answer: The highest power of x is 2. What is the highest power of x in the expression? 02 May 2015

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Try Exercise From Text Book 33 Q 1 Try the following yourself. Multiply: 02 May 2015

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7.1Variable Notation.

7.1Variable Notation.

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