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 If no money added or withdrawn from the account, answer the following questions.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
