Finals Review Algebra II

Simplify the rational expression. State any restrictions on the variable 8x ----------- 72x^2 - 8x

1 ------ 9x-1 A, 0, 1/9

Solve the equation 6^x =7

1.0860

Find the two real solution of the following equation x^2= 16

4, -4

Write the expression below as a single natural logarithm ln7 + ln6

ln 42

Write an exponential function to model the following situation. A population of 120,00 grows 4% per year for 15 years. How much will the population be after 15 years?

120,000 1.04 216, 113

g(x)= 3x and h(x) = x^2 +5 (g o h) (0)

15

Solve the equation 2 ^3x = 4^x +1

2

Suppose you deposit $2,500 in a savings account that pays interest at an annual rate of 4%. If no money added or withdrawn from the account, answer the following questions.

2,924.65 4,682.45 5 9

Simplify the following rational expression. Use absolute value symbols when needed. 3√64/216

2/3

Multiply and simplify. Assume that all variables are positive.√5x ^6 *√12x ^7

2x ^6√15x

f(x) = 2x -9 and g(x) = x+4 f(g(x)) and g(f(x))

2x-1 2x-5

x=√ 3x-9 +3

3,6

Evaluate the following logarithm log (base)16 64

3/2

Write in logarithmic form 125= 5^3

3= log (base)5 125

Write as an exponential equation log (base)3 81 =4

3^4

Simplify. Assume that all variables are positive. √63x ^13

3x ^6√7x

Multiply the pair of conjugates (3-√5) (3+√5)

4

f(x) = 4x^2 - 11x+6 g(x)= x-2 (f*g) (x)

4x^3 - 19x^2 + 28x -12 C

Find the value of the logarithmic expression log (base)2 32

5

Solve. Check for extraneous solutions √ 2y + 1 -6=5

60

Convert the expression from exponential form to radical form. x 5/6

6√x ^5

Simplify 343 1/3

7

√4x-3 = 5

7

√x^2 +15 = x +1

7

Simplify 512 1/3

8

Simplify the product √3 *√27

9

Perform the indicated operation and simplify 5√5 -2√6 6√5 + 5√6

90 +13√30

Solve q + 7 ---- = -8 q

A, -7, -1

Solve the equation. 1/y + 1/2 = 3/2y

A, 1

Solve the equation. Check each solution y/5 +y/2 =7

A, 10

Simplify the sum. State any restrictions on the variable. 3v +8 9v +9 ---------- + -------- v-4 v-4

A, 12v +17 ------------, 4 v-4

Solve the following equation. Check your solution 9 x+3 ------- = --------- x+1 x+1

A, 6

f(x)= (x-4)^2

B No

Expand the logarithm. Simplify is possible log (base) 8 ab

c log(base)8 a + log(base)8 b

Write the expression below as a single natural logarithm ln3 + ln6

ln 18

Write the expression as a single natural logarithm 5 ln m - 4 ln n

m^5/n^4

Multiply √7 *√3

√21

Solve. √5 - x =4

-11

Multiply. (2-√6) (2+√6)

-2

Subtract. Assume all variables represent nonnegative real numbers. 3√x - 6√x

-3√x

f(x) = x -3 and g(x) = 4x^2 (f-g) (x)

-4x^2 +x - 3 C

Multiply and Simplify (7-4√5) (3+6√5)

-99 + 30√5

Subtract 9/x^2-9x - x/9x-81

-x +9 ----------- 9x

Let f(x)= -2x-1 and g(x) =x ^2 -1 (f o g)(0)

1

Simplify the expression shown below y^ 3/5 / y ^ 3/10

y^3/10

Rewrite the expression with rational exponents 4√x^3

x 3/4

What is x^2 +8x +16 in simplest form? State any restrictions ----------------- x^2 -4x -32

x+4 ------ x-8 A, 8, -4

Simplify the expression shown below x^2/5 * x^1/10

x1/2

f(x) = x- 3 and g(x) = 4x^2 (f+g) (x)

x^2 + 5x +3 B

F(x) = 5x +3 and g(x)= x^2 (f+g) (x)

x^2 +5x +3