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Algebra Lesson 1

Algebra Lesson 1. Junior Certificate Mathematics. Topics To be Covered The Use of Letters Translating from a spoken phrase to an Algebraic Expression. In algebra we use letters to stand for numbers. I think of a number, add seven to it and the result is 11.

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Algebra Lesson 1

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  1. AlgebraLesson 1 Junior Certificate Mathematics Topics To be Covered The Use of Letters Translating from a spoken phrase to an Algebraic Expression

  2. 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 Algebra helps us to solve problems.

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

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

  5. AlgebraLesson 2 Junior Certificate Mathematics Topics To be Covered Replacing Letters with Numbers

  6. Replacing letters with numbers Ex 1 RememberMultiply and divide before you add and subtract

  7. Try the following yourself Ex 2 RememberAny number when multiplied by 0 is 0,e.g. 12 x 0 = 0

  8. Try Exercise From Text Book

  9. AlgebraLesson 3 Junior Certificate Mathematics Topics To be Covered Adding and Subtracting like Terms

  10. Adding Like Terms 2 cars + 2 cars = 4 carsLet x be a car then this is 2x + 2x = 4x

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

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

  13. Simplifying Algebraic Expressions Ex 1 Try Exercise From Text Book

  14. AlgebraLesson 4 Junior Certificate Mathematics Topics To be Covered Removing Brackets Removing Brackets & then Simplifying

  15. Removing Brackets Method 1 Here we did what was inside the brackets first. Method 2 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. Everything inside the brackets is multiplied by the number outside

  16. Removing Brackets Ex 1 Ex 2 Ex 3 A minus outside the bracketchanges the sign of each term inside the bracket

  17. Try the following yourself Q 1 Q 2 Q 3 Like signs when multiplies together givea positive result. Unlike signs when multiplied together givea negative result.

  18. Remove Brackets and Simplify Ex 4 Try Exercise From Text Book

  19. AlgebraLesson 5 Junior Certificate Mathematics Topics To be Covered Multiplication involving Powers

  20. Multiplication involving Powers The power is the number at the top of the letter

  21. Multiplication involving Powers (cont.) 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. Multiply the numbers in front of letters and add the powers at the top of the letters.

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

  23. Try the following yourself Q 1 Q 2 Q 3 Try Exercise From Text Book

  24. AlgebraLesson 6 Junior Certificate Mathematics Topics To be Covered Calculating Expressions with x2

  25. Calculating Expressions with x2 Here we have squared -2 first, then multiplied by 4. For a x2you always find x2 before you multiply by a.

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

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

  28. AlgebraLesson 7 Junior Certificate Mathematics Topics To be Covered Multiplying Compound Expressions

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

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

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

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

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

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