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Algebra II – Chapter 8 Test Review Standards/Goals: A.SSE.2: I can take the structure of an expression and identify different ways to rewrite it I can use the FOIL method to multiply binomials that have radical expressions. I can multiply binomial expressions using conjugates. N.RN.2: I can rewrite expressions involving radicals and rational exponents using the properties of exponents. A.REI.2: I can solve simple rational and radical equations in one variable. I can show how to arrive at ‘extraneous’ solutions. A.CED.4.: I can rearrange formulas to highlight a quantity of interest, using the same techniques and methods as you would use to solve an equation. F.BF.1.b.: I can combine standard function types using arithmetic operations, such as addition, subtraction, multiplication, and division. F.BF.1.c.: I can use the idea of composition to evaluate radical functions. F.BF.4.a.: I can solve an equation for a simple function that has an inverse. I can write an expression for the inverse of a simple function. F.IF.7.b.: I can graph square and cube root functions. I can determine the transformations of the graph of a radical function. 1. What is the real cube root of -216? 81 2. What is the real fourth root of − ? 625 3. 4. 5. 6. What is the simplified form of the expression: √81𝑥 12 𝑦 26 ? What is the simplified form of the expression √112𝑥 9 𝑦10 ? 3 3 What is the simplest form of √48𝑤𝑧 4 √4𝑤 2 ? What is the simplest form of 5√63 − 3√18? 7. What is the simplest form of √45𝑥 7 √125𝑥𝑦 4 ? 8. What is the simplest form of (2 – 3√5)(3 + 4√5)? 9 9. What is the simplest form of ? 1 3 4 3 3 + √7 10.What is 𝑤 𝑧 in simplest form? 11.Let f(x) = -3x + 16 and g(x) = 2𝑥 2 . a. What is (g – f)(x)? b. What is the domain of (g – f)(x)? 𝑔 c. What is the domain of (x)? 𝑓 d. What is g ᵒ f (x)? e. What is f ᵒ g(x) f. What is f ᵒ g(-3)? 12. What is the inverse of y = -2(x + 6)? 13. Consider the following function: 𝑦 = −3√𝑥 + 9 − 16 a. What is the domain for the function given in the previous problem? b. What are the transformations for the following function? 4 14. What is the DOMAIN of ? 5−√𝑥+10 15. Rationalize the denominator and simplify: 5+√10 5+√2 16. Simplify the following expression: 3 4 √216𝑤 7 √81𝑦 8 √12𝑤 12 𝑦 6 17. Simplify the following expression: √ 25𝑟 4 𝑠 5 48𝑡 5 18. Suppose that a, b, and c are real numbers where 𝑏 = 𝑐 3 and 𝑎 = 𝑏 5 . Write the following in terms of c: 4 4 √𝑐𝑎 + √𝑏 6 19. Solve the following: a. √5𝑥 − 2 − 7 = 3 b. √5𝑥 − 2 + 7 = 3 1 c. 3𝑥 2 − 10 = 2 d. √3𝑥 + 7 = 𝑥 − 1 e. √3𝑥 = √𝑥 + 6 20. Simplify: 2 + √5−3𝑥 3−√𝑥+7 21. A spherical water tank holds 9000 square feet of water. What is the 3 6𝑉 diameter of the tank? (Use the formula: 𝑑 = √ ) 𝜋