= (Type exponential notation with positive exponents)

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Archibald O’Connor’
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1 1. Subtract. Simplify by collecting like radical terms if possible. 2 2 = (Simplify your answer) 2. Add. Simplify if possible. = (Simplify your answer) 3. Divide and simplify. = (Type exponential notation with positive exponents) 4. Rationalize the denominator. Assume that all expressions under radicals represent positive numbers. = (Simplify your answer). Find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function. F(x) = -2x^2 + 2x + The x-coordinate of the vertex is? (Type a simplified fraction) The y-coordinate of the vertex is? (Type a simplified fraction) The equation line of symmetry is? (Type an equation) The maximum/minimum of f(x) is? (Type a simplified fraction) Is the value f ( ) = is maximum or minimum? 6. Simplify by removing factors of 1.

2 The simplified form is? 7. Convert to decimal notation. 8.6 x 10^7 = (simplify answer) 8. Solve for x. 4x (x 6) x (x ) = -2 X=, or is there no solution? 9. Multiply and simplify. = (Type exponential notation with positive exponents) 10. Factor completely. 17s^ sg + 343g^2 = 11. If the sides of a square are lengthened by 6cm, the area becomes 196cm^2. Find the length of a side of the original square. The length of a side of the original square is how many cm? 12. Simplify by taking roots of the numerator and the denominator. Assume that all the expressions under radicals represent positive numbers. 3 = (or is the root not a real number?) 13. Skip 14. Multiply. (b + ) (b + ) = (simplify answer)

3 1. Rewrite the following expression with positive exponents (16xy)^ 16. Factor completely. 36t^ t = (or is the expression not factorable) 17. Subtract. Simplify if possible. - = (simplify your answer) 18. Add. (3v^4 3v^3 + 2v^2 + 14v 8) + (v^ + 9v^3 + 9v^2 2v + 6) + (-6v^4 + v^2 10v 6) The answer is? (Simplify your answer) 19. Skip 20. Factor the trinomial. S^3 4s 32s = (Factor completely/ or is the trinomial not factorable) 21. Television sets. What does it mean to refer to a 20-in TV set or a 2 inch TV set? Such units refer to the diagonal of the screen. A 1-in TV set also has a width of 12 inches. What is the height? What is the height of a 1in TV? (INCHES)

4 22. Express using a positive exponent. U^ -7 = (simplify your answer. Type a positive exponent) 23. Evaluate the polynomial for x = -4. 2x^2 3x + 9 = (simplify your answer) 24. Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. 3 3 = (simplify your answer. Type in radical form) 2. Solve. b^2 b 14 = 0 The solution is b =, or is there no solution 26. Find all the numbers for which the rational expression is undefined. The numbers for which the rational expression is undefined are? Answer: 7, If a pro basketball player has a vertical leap of about 3 inches, what is the hang time? Use the hang time function V = 48 T^2. His hang time is how many seconds? (simplify your answer. Type an integer or a decimal. Round to the nearest tenth.) Answer: 0.9

5 28. Solve. = x + The solution is x =, or is there no solution Answer: Factor C^2 + 12c + 36 = (Factor completely. Or is the polynomial prime?) Answer: (c+6)^2 30. Multiply. (-3t)^2 (2t^8)^3 = Answer: 72t^ Simplify. = (Simplify your answer. Or is the root not a real number?) Answer: -1/2 32. Use rational exponents to simplify. 4 = (simplify your answer) Answer: x^ 33. Solve. 2x^4 20x^2 + 3 = 0 The solution is x =? / or is there no solution? Answer: 1, 1,, 34. Jack usually mows his lawn in 7 hours. Marilyn can mow the same yard in 4 hours. How much time would it take for them to mow the lawn together? They could mow the lawn in how much time if they do it together? (Simplify answer)

6 Answer: 2 6/11 (mixed number) 3. Rewrite the rational exponent. ^4 = (simplify your answer) Answer: 18 1/4 36. Factor completely. 36r^2 2 = (Factor completely. / or is the binomial not factorable?) Answer: (6r-)(6r+) 37. Solve. (x + 17)(x 8)(x + 9) > 0 What is the solution set? / Or is the solution all real numbers? / Or is there no solution? Answer: {x/ -17<x<-9 or x>8} 38. Multiply. (3x + 4)(x^2 + 8x + 6) = (simplify your answer) Answer: 1x^3+44x^2+40x Factor completely. 8x^7 64x^6 + 32x^ The complete factorization is? (type your answer in factored form) Answer: 8x^(x^2-8x+4) 40. Factor a + a^2 = (factor completely/or is the trinomial not factorable?) Answer: (a-8)(a-6) 41. Solve. T^2 + 2t 48 = 0 The solution(s) is/are t = / or is there no solution? Answer: -8,6

7 42. Find the following. 16 = (simplify your answer/ or is the root not a real number?) Answer: Simplify by removing factors of 1. The simplified form is? Answer: n + 1 7n Skip 4. Perform the indicated operations and simplify. Answer: - + = 9 v Multiply and simplify. Assume variables represent nonzero real numbers. X^13 Answer: x^ Multiply. (3 9 ( + 1 = (simplify your answer) Answer: Skip 49. Find the vertex, the line of symmetry, and the maximum or minimum value of f(x). Graph the function. F(x) = (x + 8)^2 + 4 The vertex is? (Type an ordered pair) The line of symmetry is? (Type an equation)

8 What is the maximum/ minimum value of f(x)? Is the value, f (-8) = 4, a minimum or maximum? Answers: Vertex = (-8,4), line: x=-8, max/min=4, minimum 0. Find the greatest common factor for the group of terms. 18a^3, 3a^ The greatest common factor is? Answer: 3a^3 1. Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2 + bx + c = 0. Solution: 8, only solution The equation is? Answer: x^2-16x Use the quadratic formula to solve the equation. 2x^2 x = -1 The solution set is? (Express complex numbers in terms of i. Use integers or fractions for any numbers in the expression.) Answer: 1+ 7i 1 7i, Divide. (42b^3 + 23b^2 + 38b + 44) (6b + ) Answer: 7b^2-2b+8 +4/(6b+) 4. Find the variation constant and an equation of variation where y varies directly as x and y = 30 when x = 10. The variation constant is k =

9 The equation of variation is y = Answer: k = 3, equation : y = 3x. Multiply. (v + f)(v^2 vf + f^2) = (simplify your answer) Answer: v^3+f^3

Never leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!!

Never leave a NEGATIVE EXPONENT or a ZERO EXPONENT in an answer in simplest form!!!!! 1 ICM Unit 0 Algebra Rules Lesson 1 Rules of Exponents RULE EXAMPLE EXPLANANTION a m a n = a m+n A) x x 6 = B) x 4 y 8 x 3 yz = When multiplying with like bases, keep the base and add the exponents. a