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SAT Readiness

Discover how to simplify and evaluate algebraic expressions with this comprehensive guide. Learn how algebra can model real-world scenarios, such as scoring in basketball, representing distances, and calculating travel times. Understand key operations using algebraic terms, and practice combining like terms. With detailed examples, including word problems and step-by-step evaluations, you'll become proficient in creating and simplifying expressions. Polish your skills with interactive exercises and enhance your understanding of algebra leading to better SAT readiness.

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SAT Readiness

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  1. SAT Readiness

  2. Simplifying Algebraic Expressions 1.4

  3. Objectives • Simplify and evaluate algebraic expressions

  4. Why Learn This? • You can model the total point scored in a basketball game by using an algebraic equations • Example f + 2g +3t f = number of 1 point free throws g = number of 2 point shots t = number of 3 point shots

  5. Translating Real-World  Algebraic Expressions

  6. Words for Operations • + : Add, Combine, Plus, And, Total • - : Subtract, Minus, Less than, Difference, • x : Multiply, Product, Times • ÷ :Quotient, Divide, Divided by

  7. Write an Algebraic Equation to Represent each equation • The distance remaining for a runner after m miles of a 26.2 mile marathon. 26.2 - m 2) The number of hours it takes to fly 1800 miles at an average rate of n miles per hour. 1800/n

  8. Algebraic Expressions (Cont.) 3) Lucy’s age y years after her 18th birthday 18+y 4) The number of seconds in h hours. 3600h

  9. PEMDAS 1) Parentheses and grouping symbols 2) Exponents 3) Multiply and Divide from left to right 4) Add and Subtract from left to right

  10. Evaluating Algebraic Expressions Ex) x + 3xy -2y for x = 4 and y=7 = (4) + 3 (4)(7) – 2(7) = 4 + 84 – 14 = 74 Ex) b2z-2bz+z2 for b = 6 and z =2 Answer: 52

  11. Combine Like Terms • Simplify the Expressions by adding or subtracting Like terms. • Example: 3x2 -9xy + 2 +4x2 -1 3x2 -9xy + 2+4x2-1 • Answer: 7x2 -9xy -1

  12. Like versus Unlike • 4xy2 and -7xy2 like • 2xy2 and 2x2y unlike • 1 and -8 like • 3x and (1/2)x like • 7xy and 4yx like

  13. Simplify the Following Expressions • x2 + 5x + 2y +7x2 Answer: 8x2 + 5x + 2y • b(5a2 -2a) -11a2b+2ab Answer: -6a2b

  14. Word Problems a) Holly’s hybrid car gets 45 miles per gallon on the highway and 25 miles per gallon in the city. Write & simplify an expression for the total number of miles she can drive if her fuel tank hold 15 gallons of gas. Let h = # gallons used on the highway. Answer: 45h +25(15-h) = 20h + 375 b) How many total miles can she drive on one tank of gas if she used 5 gallons on the highway? Answer: 20(5) + 375 = 475

  15. Closure • Simplify the expression: -8x + 10x + 2(3-9x) • Evaluate when x = 2 • Homework: Simplifying Expressions & Word Problems Packet

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