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.