Math 2

Name:________________________

Unit 1 Review LT0: Simplify radicals and apply arithmetic operations (addition/subtraction/multiplication) of square roots.

1) Give a value of x that would make

33  x simplify to a whole number.

2) Circle all of the following that represent like terms:

a)

27

b)  5 3 c) 6 300 d )  8 48 e) 5 75

3) The length of a rectangle is 50 feet and the width is 2 3 feet. What is the simplified representation for the area of the rectangle?

4) Simplify 3 5(2 10  5 3) fully.

5) Find the simplest expression equivalent to

880x9 y10 .

6) In order for a b  c d  e f to be considered like terms, what must be true of b, d ,and f ?

7) Simplify 9 90  8 80  7 70

8) Roger and Joe are asked to solve a problem involving simplifying

x17 . Roger says the

answer is x8 x , but Joe says that Roger is off his rocker and the correct answer is x x16 . Who is correct?

9) List the first 15 perfect squares.

LT1: Use rational exponents to simplify and evaluate expressions, solve equations, and solve equations with given scenarios.

4

10) Solve for x: 7 x 3  57 . Round your answer to the nearest hundredth.

11) Which of the following is the correct way to rewrite the expression exponent?

7

x 4 with a rational

7

a) x 4 b)

x

c) x

7 4

4 7 4

d)

x7

12) Classify the following expressions as rational or irrational.

a)

1 3  125 2 1

b) 64 3  16 7 c)  3 5 9 1

d ) 5 3  25

13) What number could be inserted in for x in 4

x 16

to make an expression that is rational?

14) The number of bacteria in a certain culture increased from 600 to 1800 between 7:00 a.m. and 9:00 a.m. Assuming exponential growth, the number f (t ) of bacteria t hours after 7:00 a.m. t 2

is given by f (t )  600(3) . Estimate the number of bacteria in the culture at 8:00 a.m., 10:00 a.m., and 11:00 p.m.

15) In the expression

2

x5 , identify the root and identify the power.

4

 2 5 16) Evaluate the expression  x 3  .  

3

1

2

151

17) Crissy and Janet were asked to evaluate x 7  x 4  x 5 . Crissy says the answer is x 140 . Janet 3 70

says that just looks weird and that the correct answer is x . Who is correct? What did the person who was correct do right that the other person did wrong?

LT2: Perform and apply arithmetic operations (addition/subtraction/multiplication) on polynomials. 18) Find the sum of  3x 3  5x 2    2 x 3  7 x 2  11 .

19) Find the difference of  x 2  4 x  6     x 2  7 x  3 .

20) The perimeter of a polygon is the sum of the lengths of the sides of the polygon. Find the perimeter of the shape below if all lengths are given in feet. 5x  3

4 x  15 21) Malfoy built a rectangular playground and needs to buy enough fencing to enclose the playground. If the length of the playground is 2 x 2  7 and its width is 3x  1 , find the total amount of fencing he will need to enclose the playground, given the above measurements are in meters.







 x



22) Find the product of x 3  3 x 2  7 .

23) Find the product of 3x 2  4



2

 x  5 .





24) Find the product of x 2  5 x  6 2 x 2  3x  1

25) The area of a rectangle is found using the formula area  lw , where l is the length, in feet, of the rectangle and w is the width, in feet. Find the area of a rectangle given l  5x  1 and w  2 x  3 .

LT 3: Understand, perform and apply arithmetic operations (addition/ subtraction/ multiplication) with complex numbers.

3 26) Identify the real part and the imaginary part of 2  i . 4 27) Find the product of  6  3i  5  2i  . Write the answer in simplest form.

28) Simplify i 93

29) Find the complex conjugate of  7  3i  . Then, use multiplication to verify your answer.

30) Simplify the radical 5 300 using the imangiary unit i .

31) Rewrite the imaginary number using a radical instead of the imaginary unit i for 3i 5 .

32) List four different values for x that would satisfy the expression i x  1 .

33) Which of the following is true about complex conjugate of  a  bi  ? Select all that apply. a. The complex conjugate is  a  bi  b. The complex conjugate is  a  bi  . c. When multiplying  a  bi  with its’ complex conjugate, the answer will be 1. d. When multiplying  a  bi  with its’ complex conjugate, the answer is wholly real.

34) Find the product of 10  2i   i 3 . Write the answer in simplest form.

35) Find the complex conjugate of  i  5 . Then, use multiplication to verify your answer.

36) Complete the following subtraction  7  5i 31    2  9i 50  . Identify whether the difference is wholly real or wholly imaginary, or if it has both a real and imaginary part.

37) Find a value of x that would make the simplified answer for (12  7i15 )  (5  7i x ) Wholly Real. Note: there are many correct answers.

38) Simplify the radical

252 using the imangiary unit i .

39) Find the product of  4  7i  2  3i  . Write the answer in simplest form.

40) Simplify the radical

72 using the imangiary unit i .

41) Find the value of K so that the expression 7  9i  K , when simplified, results in a wholly real number.