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# Algebra II Review, #2 (Grades 11-12)

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## Algebra II Review, #2

1.
Given $f(x) = 3x +4 and g(x) = 6x^2 - 9$, find $(f-g)(x)$.
1. $-6x^2 + 3x + 13$
2. $-3x - 5$
3. $6x^2 - 3x - 13$
4. $-3x^2 + 13$
2.
Find $(g//f)(x)$ given that $f(x) = sqrt(3x-5) and g(x) = sqrt(2x^2+3)$.
1. $(2x^2+3)/(3x-5)$
2. $sqrt(3x-5)/sqrt(2x^2+3)$
3. $sqrt(2x^2+3)/(sqrt(3x-5)$
4. $(3x-5)/(2x^2+3)$
3.
For $f(x) = 3x^2 - 1$ and $g(x) = sqrt(2x-5)$, find $(g@f)(x)$.

4.
Let $f(x)=x^2$ and $g(x)=x-3$. Find $(g@f)(3.5)$.

5.
Find the inverse of the function $g(x) = -4x + 1$.
1. $g^(-1)(x) = 1 /(x+3)$
2. $g^(-1)(x) = 3 /(x+2)$
3. $g^(-1)(x) = 1 /(x+2)$
4. $g^(-1)(x) = (-x+1) /4$
6.
For the function $f(x)=(2x^2)/5+1$ find the inverse and tell whether or not it is a function.

7.
What domain restriction on the function $f(x)=(x-2)^2$ would make the inverse also a function?

8.
Which function matches the following description?
An absolute value function that has been reflected about the x-axis, and then shifted up 5 units.
1. $f(x)=|x|+5$
2. $f(x)=-|x| +5$
3. $f(x)=-|x+5|$
4. $f(x)=-|x-5|$
9.
Given $f(x)=e^x$, let $g(x)$ be the transformed function under the following transformations on $f(x)$: a reflection over the x-axis, and then translated 3 units up and one unit left. Write the equation of $g(x)$ and then graph both functions.

10.
Which function represents exponential decay?
1. $f(x) = 2^x$
2. $f(x) = 8(0.9)^x$
3. $f(x) = 6x^2$
4. $f(x) = 0.9 * x$
11.
Evaluate the function $y = 1/2 *3^x$ for x = 8.
1. 85
2. 3,280.5
3. 6,561
4. 13,122
12.
Solve for x. $e^(4x+2)=1$
1. $1$
2. $e$
3. $-1/2$
4. $2$
5. none of these are correct
13.
Solve.
$(8^x)/4=(16^x)/(2^(2x-1))$
1. $x=3$
2. $x=6$
3. $x=4$
4. $x=-4$
14.
Write $5^3=125$ in logarithmic form.
1. $log_3 125 = 5$
2. $log_5 3 = 125$
3. $log_3 5 = 125$
4. $log_5 125 = 3$
15.
What expression is equivalent to $3log_4x + log_4y - 4log_4z?$
1. $log_4 ((3xy)/(4z))$
2. $log_4((x^3y)/z^4)$
3. $log_4x^3yz^4$
4. $log_4x^3 + y - z^4$
16.
Solve: $log_6(x^2-6x)=log_6(-8)$
1. -4, -2
2. 4, 2
3. 4
4. No real solution
17.
Solve the logarithmic equation.

$5 log(x-2)=11$
1. $x=160.5$
2. $x=158.5$
3. $x=2.2$
4. $x=0.34$
5. $x=2.34$
18.
Add and simplify. $(x+2)/(x-1)+(x-3)/(x+1)$
1. $(x^2-3x+1)/(x^2-x+4)$
2. $(2x-1)/(2x)$
3. $(x^2-x-6)/(x-1)$
4. $(2x^2-x+5)/((x-1)(x+1))$
19.
What are the restrictions on $x$ for the expression $(x-4)/(x^2-x-12)$?
1. $x != 4, -3$
2. $x != -4, 3$
3. $x != -3$
4. $x != 3$
20.
Divide and simplify the expression $(x-2)/(5x+10)-:(3)/(3x+6)$.
1. $5/(x-2), \ \ x!=-2$
2. $(3(x-2))/(15(x+2)^2)$
3. $(x-2)/5, \ \ x!=-2$
4. $(3(x-2))/(15(x+2))$
21.
Rationalize the denominator. $(3+sqrt8)/(2-2sqrt8)$

22.
Tell whether x and y show direct variation, inverse variation, or neither.

xy = 5

23.
Suppose d varies directly as u and the square of v, and inversely as w. Given that d = 1.8 when u = 4, v = 6 and w = 28, find d when u = 18, v = 5 and w = 24.

24.
Solve the following system of equations:
x + y = 9
y + z = 7
z + x = 5

25.
Solve the following system of equations:
3x - 2y + 5z = -1
4x + 3y - 2z = -13
3x + 5y - 4z = -12

26.
For $A = [[16, 8, 32], [4, 0, 12], [8, 24, 20]]$, find $1/4 A$.
1. $[[4, 2, 8],[4, 0, 12], [8, 24, 20]]$
2. $[[ 4, 8, 32],[1, 0, 12],[2,24,20]]$
3. $[[4,2,8],[1,0,3],[2,6,5]]$
4. $"Does not exist (because of 0 in matrix)"$
27.
Evaluate the following.

$[[5,2],[4,9],[0,3]] - [[2,9],[1,7],[6,5]]$

28.
Given the matrices below, find $AB$.

$A=[[5,4],[3,2]] , \ \ B=[[1,9],[3,1]]$

29.
Evaluate, if possible.
$[[3,4,8],[1,3,1]] + [[6,1],[9,2],[3,4]]$
1. $[[9,2],[13,5],[11,5]]$
2. $"Not possible"$
3. $[[9,5],[10,5]]$
4. $[[7,4],[12,6],[4,12]]$
30.
Evaluate the determinant of $[[-1, 6], [-2, 5]]$.

31.
What is the determinant of $[[1,-3,4],[6,2,-1],[0,3,5]]$ ?
1. 25
2. 175
3. 40
4. -25
32.
Find the inverse of the matrix $[[0,6],[2,8]]$.
1. $[[4/6,2/4],[2/12,6/0]]$
2. $[[-2/3,1/2],[1/6,0]]$
3. $[[0,1/2],[1/6,2/3]]$
4. $[[96,-72],[-24,0]]$
33.
Find the inverse of $A = [[4,6],[2,3]]$, if it exists.

34.
What is the value of the imaginary unit, i?

35.
Simplify the complex number radical expression $sqrt(-350)$.
1. $-5sqrt14$
2. $-5isqrt14$
3. $5isqrt14$
4. $5sqrt14$
36.
Simplify. $i^13$
1. $i$
2. $-i$
3. $1$
4. $-1$
37.
Plot the following complex number. Be sure to label the axes. $-3 + 7i$

38.
Multiply and simplify the complex numbers. $-6i(70-85i)$
1. $510+420i$
2. $510-420i$
3. $-510+420i$
4. $-510-420i$
39.
Evaluate. $(3 + 4i) + (5 - i)$

40.
Subtract the complex numbers. $(4 - 2i) - (6 - 7i)$

41.
Multiply. $(3 - 4i)(-2 + 6i)$

42.
What is the complex conjugate of $3 + 4i ?$
1. $-3 - 4i$
2. $-3+4i$
3. $4i + 3$
4. $3-4i$
43.
Divide and simplify. $(4-7i)/(2+4i)$

44.
Divide using polynomial long division. $(3x^4 + 14x^3 - 7x^2 - 10x - 4)/(3x+2)$

45.
Use synthetic division to divide the polynomials. $(3x^3 - 7x + 4)/(x+3)$

46.
Factor. $27x^3 + 64$
1. $(3x-4)(9x^2 + 12x + 16)$
2. $(3x + 4)(9x^2 - 12x + 16)$
3. $(3x+4)(9x^2 + 12x + 16)$
4. $"Can't factor further"$
47.
The sum of the first 10 terms of an arithmetic progression is 40. If the first term is -5, then what is the common difference?
1. -3
2. -1
3. 2
4. 4
48.
Given the geometric series $3 + 6 + 12 + 24 + ...$, find the sum of the first 17 terms.

49.
Write the equation of a circle with a center (3,-2) and a radius of 3.

50.
Identify the following conic: $x^2-4x-4y^2+8y=4$.
1. Parabola
2. Circle
3. Hyperbola
4. Ellipse
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