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

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Algebra II Review, #2

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





4. 
Let [math]f(x)=x^2[/math] and [math]g(x)=x-3[/math]. Find [math](g@f)(3.5)[/math].





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





7. 
What domain restriction on the function [math]f(x)=(x-2)^2[/math] 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. [math]f(x)=|x|+5[/math]
  2. [math]f(x)=-|x| +5[/math]
  3. [math]f(x)=-|x+5|[/math]
  4. [math]f(x)=-|x-5|[/math]
9. 
Given [math]f(x)=e^x[/math], let [math]g(x)[/math] be the transformed function under the following transformations on [math]f(x)[/math]: a reflection over the x-axis, and then translated 3 units up and one unit left. Write the equation of [math]g(x)[/math] and then graph both functions.

Coordinate Plane - 5x5 -  Blank





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

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





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

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





28. 
Given the matrices below, find [math]AB[/math].

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





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





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





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





35. 
Simplify the complex number radical expression [math]sqrt(-350)[/math].
  1. [math]-5sqrt14[/math]
  2. [math]-5isqrt14[/math]
  3. [math]5isqrt14[/math]
  4. [math]5sqrt14[/math]
36. 
Simplify. [math] i^13[/math]
  1. [math]i[/math]
  2. [math]-i[/math]
  3. [math]1[/math]
  4. [math]-1[/math]
37. 
Plot the following complex number. Be sure to label the axes. [math] -3 + 7i[/math]
Graph 10x10





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





40. 
Subtract the complex numbers. [math] (4 - 2i) - (6 - 7i)[/math]





41. 
Multiply. [math](3 - 4i)(-2 + 6i)[/math]





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





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





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





46. 
Factor. [math]27x^3 + 64[/math]
  1. [math](3x-4)(9x^2 + 12x + 16) [/math]
  2. [math](3x + 4)(9x^2 - 12x + 16)[/math]
  3. [math](3x+4)(9x^2 + 12x + 16)[/math]
  4. [math]"Can't factor further"[/math]
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 [math]3 + 6 + 12 + 24 + ...[/math], 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: [math]x^2-4x-4y^2+8y=4[/math].
  1. Parabola
  2. Circle
  3. Hyperbola
  4. Ellipse

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