Analytic Geometry Unit 4: Common Unit Assessment Directions: Identify the choice that best completes the statement or

answers the question. Page 1 of 3

Multiple Choice Identify the choice that best completes the statement or answers the question.

____ 1. Simplify . Assume that all variables are positive.

a. c. b. d. none of these

____ 2. Multiply and simplify . Assume that all variables are positive. a. c. b. d. none of these

____ 3. Divide and Simplify

a. b. c. d.

____ 4. Which statement is not true? a. If a and b are

non-zero rational numbers than (a)(b) is rational.

b. If a is an irrational number and b is a non-zero rational number than a + b is rational.

c. If a and b are irrational numbers than (a)/(b) is irrational.

d. If a is an irrational number and b is a non-zero rational number then a + b is irrational.

____ 5. A garden has width and length . What is the perimeter of the garden in simplest radical form? a. units c. 91 units b. units d. units Simplify.

____ 6. a. 9 b. c. 3 d.

____ 7. Identify a valid step in the process of solving this equation for x =

a. b.

c. 4x + 1 = 3x + 2 d. 4x + 1 = 3x + 6

Analytic Geometry Unit 4: Common Unit Assessment Directions: Identify the choice that best completes the statement or

answers the question. Page 2 of 3

____ 8. Write the radical expression in exponential form.

a.

b.

c.

d.

____ 9. Write in simplest form. a. c.

b. d. none of these

____ 10. Let and . Find f(x) – g(x). a. 2x – 5 b. 2x + 5 c. 4x – 1 d. 2x – 1

____ 11. Let and . Find 2f(x) – 3g(x). a. c. b. d.

____ 12. Let and . Find and its domain. a. ; all real numbers except x 2

3

b. ; all real numbers c. ; all real numbers d. ; all real numbers except x 6

7

___ 13. Given that x = y, find the area, including units, of the shape below.

a. A = 12x3 cm2 b. A = x2 – 8x + 12 cm2 c. A = x2 + 12x + 8 cm2 d. A = x2 – 2x + 48 cm2

____ 14. Taylor and Susan each have a box that is the shape of a cube. The edges of Taylor’s box are each x cm in length. The edges of Susan’s box are 4 cm longer than Taylor’s box. Which expression represents the area of one of the sides of Susan’s box?

a. A = 4x2 b. A = x2 + 4 c. A = (x + 4)3 d. A = x2 + 8x + 16

Analytic Geometry Unit 4: Common Unit Assessment Directions: Identify the choice that best completes the statement or

answers the question. Page 3 of 3

Simplify the expression. ____ 15.

a. 1 c. b. –1 d.

____ 16. Fill in the blank; is ________ a. rational b. irrational c. imaginary d. All of the above

____ 17. Explain difference between imaginary numbers and irrational numbers. a. Imaginary numbers do not really exist while irrational numbers do not fit on the number line. b. Imaginary numbers are negative when squared while irrational numbers are positive when squared. c. Imaginary numbers do not fit on the number line while irrational numbers do not really exist. d. Imaginary numbers cannot be squared while irrational numbers can be squared.

Write each expression in the form a + bi, where a and b are real numbers.

____ 18. a. c. b. d.

____ 19. a. c. b. d.

____ 20.

a. c. b. d.

Constructed Response: Complete ALL sections of the questions below on a separate sheet. Show all work. Answer

in complete sentences.

21.

a. Explain what it means to raise the number x to the powerb

a

b. Write an equivalent expression for b

a

x 22. Consider (3√5 – 2√3)(3√5 + 2√3) a. Multiply the expression and simplify. b. Explain why your answer does not contain radicals.