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Accelerated Geometry B/Advanced Algebra
UNIT TEST STUDY GUIDE
Unit 1: Extending the Number System
The following are the standards for Unit 1:
1. Perform arithmetic operations on polynomials
2. Extend properties of exponents to rational exponents
3. Use properties of rational and irrational numbers
4. Perform arithmetic operations with complex numbers
Section 1: Polynomial Operations – add, subtract and multiply polynomials, area and volume models
Simplify completely
1) (7 x 2  3x  8)  (4 x 2  3x  2)
2) (2 x 4  3x  6)  ( x 3  2 x  1)
3) (2x + 1)(2x – 1)
4) (3x – 2)(x + 7)
2
5) (x + 4)(2x – 2x + 5)
6) Find the area of the square:
x+9
7) Draw an area model for (x + 5)(x + 8)
x+9
Section 2: Rational Exponents – simplify expressions using properties of exponents
Simplify completely
8) (27)
4
3
 3
9)  3 2 
 
2
7
2
3
1
2
10) x  x  x

1
4
11)
x
2
5
12)
x5
x
4
5
Section 3: Rational and Irrational Numbers – simplify radicals of nth roots
Simplify completely
13)
4
32 x 16 y 13
14)
3
216a 13
b15
15)
3
4x 2  3 2x 7
16)
3
250  3 54
Section 4: Complex Numbers – add, subtract, multiply and divide complex numbers (a + bi)
Make sure you know the powers of i: i = i, i2 = -1, i3 = -i, i4 = 1,…(remember the pattern repeats)
Simplify completely
17)  50
18) i 42  i 67
19) What is the conjugate of -3-5i?
20) -9(2 + i) – 3(4 + 2i)
21) (4 – 3i)(4 + 5i)
22) (4 – 11i)2
23)
7i
1  2i
***If you complete all of these problems, the station problems in class and all of the homework problems
that have been assigned throughout the unit, you should be well prepared for the test!!