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Unit 1: Rational Numbers Test

This comprehensive guide focuses on the principles of rational numbers, powers, and polynomials, essential topics in algebra. Students will learn to represent polynomials geometrically, simplify polynomial expressions using exponent laws, and add, subtract, and multiply polynomials. Key terminology including algebraic expressions, variables, coefficients, powers, and degrees will be explored. Practice exercises will reinforce understanding, providing ample opportunities to check comprehension at various stages, ensuring a solid foundation in these foundational algebra concepts.

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Unit 1: Rational Numbers Test

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  1. Unit 1: Rational Numbers Test Wednesday September 26th

  2. Unit 2: Powers and Polynomials Goals: - Represent polynomials geometrically - Simplify polynomial expressions using exponent laws - Add and subtract polynomials - Multiply a polynomial by a monomial

  3. Terminology • Algebraic expression - a mathematical phrase made up of numbers and variables, connected by + or - • Variable - a quantity whose value can change, a letter • Constant • Coefficient - Factor the variable is multiplied by

  4. Terminology • Power • Exponent • Base

  5. Representing Powers • Term – part of an algebraic expression, separated by addition or subtraction • Degree of a term – is the sum of the exponents on the variables has degree 4

  6. Representing Algebraic Expressions

  7. You try: Check your understanding pg. 80 #1,2 Practising pg. 81 #3,4,5, 6 *the opposite of square is square root = x

  8. Multiplying and Dividing Powers • Powers in expanded form • When multiplying Powers, add the exponents

  9. Dividing Powers • When dividing powers, subtract the exponents

  10. Representing expressions involving powers • Simplify = = = = = 4

  11. Write as a single power = ( = ( = ( =

  12. Simplify when x = 2, y = 3. = = = =xy = (2)(3) = 6

  13. You try: Check your understanding pg.89 #1,2,3,4 Practising pg. 90 #5-9 (bc), 10, 11-12 (bc)

  14. Power of a Power • Is a Power raised to an exponent • 2 • when expanding a power of a power, multiply the exponents

  15. Simplify , when x is 3, y is 4. = = = = = = (2)( = (2)(8)(4) = 64

  16. You try: Check your understanding pg. 96 #1,2 Practising pg.96-97 #3-12 (ab)

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