7 2? 7 2 THE ANSWER KEY IS AT THE END OF THE PACKET. TOPIC: Rationalizing Denominators. 1. Which expression is equivalent to (3) (1) 9 5

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1 NAME: Algebra /Trig Midterm POW #Review Packet #4 DATE: PERIOD: THE ANSWER KEY IS AT THE END OF THE PACKET 1. Which expression is equivalent to TOPIC: Rationalizing Denominators 7? 7 (1) 9 5 (3) () -1 (4) TOPIC: Simplifying Algebraic Fractions. Written in simplest form, the expression x y 4 4 x y is (1) 1 (3) x y 4 4 x y () 0 (4) -1 TOPIC: Equations of Circles 3. The center and radius of the given circle ( x 3) ( x 8) 39 are: (1) (3,-8), r = 39 (3) (-3, 8), r 39 () (-3, -8), r 39 (4) (3,-8), r 39

2 TOPIC: Radical Equation Word Problems 4. The period of a pendulum (T), in seconds, is the length of time it takes for the pendulum to make one complete L swing back and forth. The formula T gives the period T for a pendulum of length L in feet. If you want 3 to build a grandfather clock with a pendulum that swings back and forth once every 3 seconds, how long, to the nearest tenth of a foot, would you make the pendulum? TOPIC: Completing the Square 5. Solve the equation x 6x 1 by completing the square, and express the roots in simplest a + bi form. TOPIC: Using the Discriminant 6. Jacob is solving a quadratic equation. He executes a program on his graphing calculator and sees that the roots are real, rational, and unequal. This information indicates to Jacob that the discriminant is (1) zero (3) a perfect square

() negative (4) not a perfect square TOPIC: Graphing Complex Numbers 7. Fractal geometry uses the complex number plane to draw diagrams, such as the one shown in the accompanying graph.

3 () negative (4) not a perfect square TOPIC: Graphing Complex Numbers 7. Fractal geometry uses the complex number plane to draw diagrams, such as the one shown in the accompanying graph. Which number is not included in the shaded area? (1) 0.5i (3) 0.9 () i (4) i TOPIC: Addition and Subtraction of Complex Numbers 8. Melissa and Joe are playing a game with complex numbers. If Melissa has a score of 5 16 and Joe has a score of 3 4 (1) 8 + 6i (3) 8 6i () 8 + i (4) 8 i, what is their total score? TOPIC: Complex Fractions 9. In a science experiment, when resistor A and resistor B are connected in a parallel circuit, the total 1 resistance is. This complex fraction is equivalent to 1 1 A B (1) 1 (3) A + B () AB A B (4) AB

4 TOPIC: Multiplying Algebraic Fractions 10. A rectangular prism has a length of x x 4, a width of x x 6, and a height of 8 x x. For all 4x x x 4 x 9 values of x for which it is defined, express, in terms of x, the volume of the prism in simplest form. TOPIC: Defining Functions 11. Which relation is not a function? (1) y x 4 (3) x 3y () y x 4x 3 (4) x y x 3 1. The solution set of 3x + 1 contains (1) only negative real numbers () only positive real numbers (3) both positive and negative real numbers (4) no real numbers TOPIC: Absolute Value Inequalities

5 TOPIC: Radical Equations 13. The solution set of the equation x 6 x is (1) {,3} (3) {3} () { } (4) { } TOPIC: Using the Discriminant 14. The roots of the equation x 3x 0 are (1) real, rational, and equal () real, rational, and unequal (3) real, irrational, and unequal (4) imaginary TOPIC: Solving Rationals 15. Working together, Mary and Antoine can solve the problem in 6 minutes. If this situation is represented by the equation 6 6 t t 16 1, where t represents the number of minutes Antoine works alone to solve the problem, how many minutes will it take Antoine to solve the problem if he works by himself?

6 TOPIC: Composition of Functions 16. If f ( x) 5x and g( x) x, what is the value of ( f g)( 8 )? (1) 8 10 (3) 80 () 16 (4) 1, 80 TOPIC: Inverse of Functions 17. If a function is defined by the equation y 3x, which equation defines the inverse of this function? (1) x y (3) y x () y x 3 (4) y 3x TOPIC: Domain and Range 18. What is the domain of h( x) x 4x 5? (1) { x x 1or x 5 } (3) { x 1 x 5 } () { x x 5or x 1 } (4) { x 5 x 1 } TOPIC: Simplifying Complex Numbers The expression ( 1 i ) is equivalent to (1) 3i (3) 1 i () i (4) + i

7 TOPIC: Function Notation 0. The revenue, R(x), from selling x units of a product is represented by the equation R(x) = 35x, while the total cost, C(x), of making x units of the product is represented by the equation C(x) = 0x The total profit, P(x), is represented by the equation P(x) = R(x) C(x). For the values of R(x) and C(x) given above, what is P(x)? (1) 15x (3) 15x 500 () 15x (4) 10x What is the sum of and 18? (1) 5i (3) i 5 () 4i (4) 6i TOPIC: Operations with Radicals. TOPIC: Defining One-to-One Functions

8 TOPIC: Inverse of Functions 3. TOPIC: System of Equations 4. Solve the following systems of equations algebraically.

9 TOPIC: Solving Quadratic Inequalities 5. Which graph best represents the inequality? (1) () (3) (4) TOPIC: Roots of Quadratics 6. Find the sum and product of the roots of the equation. TOPIC: Using the Discriminant 7. Find all values of k such that the equation has real, rational, and equal roots.

A2 HW Imaginary Numbers

Name: A2 HW Imaginary Numbers Rewrite the following in terms of i and in simplest form: 1) 100 2) 289 3) 15 4) 4 81 5) 5 12 6) -8 72 Rewrite the following as a radical: 7) 12i 8) 20i Solve for x in simplest