Algebra II Review (Grades 11-12)
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Algebra II Review
1.
Define the domain of a function.
2.
Define the range of a function.
3.
The appearance of the graph of a function as x approaches positive infinity or negative infinity is called the .
- Axis of Symmetry
- End Behavior
- Concave Up
- Concave Down
4.
Which of the following describes a quadratic function that has been shifted to the left 4 units?
- [math]f(x)=x^2 +4[/math]
- [math]f(x)=x^2-4[/math]
- [math]f(x)=(x-4)^2[/math]
- [math]f(x)=(x+4)^2[/math]
5.
If y = f(x) is transformed to y = f(x) - 2, the function .
- Shifts up 2 units
- Shifts down 2 units
- Shifts left 2 units
- Shifts right 2 units
6.
Does the function shown here have an inverse that is also a function?

- Yes, the inverse is a function.
- No, the inverse is not a function.
7.
Which restriction would make the function [math]y=1/2x^2[/math] invertible?
- [math]x>0[/math]
- [math]y>0[/math]
- [math]y<0[/math]
- [math]x<1/2[/math]
8.
Find the inverse of [math]g(x)=-3x[/math].
- [math]g ^(-1) (x)=x+1[/math]
- [math]g ^-1 (x)=-3x-3[/math]
- [math]g ^-1 (x)=x-1[/math]
- [math]g ^-1(x)= -1/3 x[/math]
9.
[math]f(x) = sqrt(x+3)[/math] and [math]g(x)=2x[/math]. Find [math](f @ g)(4)[/math].
- [math]2sqrt14[/math]
- [math]sqrt11[/math]
- [math]sqrt14[/math]
- [math]2sqrt7[/math]
10.
Find the domain of the composite function [math]f(g(x))[/math].
[math]f(x)= x+3[/math]
[math]g(x)= 2/(x+6)[/math]
[math]f(x)= x+3[/math]
[math]g(x)= 2/(x+6)[/math]
- [math](-oo,3) uu (3,oo)[/math]
- [math](-oo,oo)[/math]
- [math](-oo,-6) uu (-6,3) uu (3,oo)[/math]
- [math](-oo,-6) uu (-6,oo)[/math]
11.
Simplify the expression [math](7x^2-63)/(x+3)[/math].
- [math](x+3)/7, \ x!=-3[/math]
- [math](7x^2-9)/(x), \ x!=-3[/math]
- [math]7(x+3), \ x!=-3[/math]
- [math]7(x-3), \ x!=-3[/math]
12.
Solve. Check for extraneous solutions.
[math]x/(x-1)=(x+3)/(-2x+2)[/math]
[math]x/(x-1)=(x+3)/(-2x+2)[/math]
- [math]x=-1 or x=-2[/math]
- [math]x=-1[/math]
- [math]x=1[/math]
- [math]x=1 or x=-1[/math]
13.
Which function is an example of exponential growth?
- [math]g(x)=0.4(1.3)^x[/math]
- [math]f(x)=1.6(0.85)^x[/math]
- [math]h(x)=0.5(0.95)^x[/math]
- [math]k(x)=1.2(1-.25)^x[/math]
14.
Determine the y-intercept of the following exponential function. [math]y=2^x+3[/math]
- (0,4)
- (0,3)
- (0,2)
- (4,0)
- none of these are correct
15.
What is the value of [math]x[/math] in the equation [math]9^(3x+1)=27^(x+2)[/math] ?
- [math]1[/math]
- [math]1/3[/math]
- [math]1/2[/math]
- [math]4/3[/math]
16.
Write [math]log_5 36=x[/math] in exponential form.
- [math]36x = 5[/math]
- [math]5^x = 36[/math]
- [math]x^5 = 36[/math]
- [math]10^x = 36[/math]
17.
Evaluate. [math]log_3 (1/9)[/math]
18.
Evaluate. Write in simplest form. [math]10^(log_(10) 3)[/math]
- 3
- 10
- 1000
- 1/3
- none of these are correct
19.
Which expression is equivalent to [math]log((3x^2)/y^4) ?[/math]
- [math]2 log(3x) + 4 log(y) [/math]
- [math]2 log(3x) - 4 log(y) [/math]
- [math] log(3) + 2 log(x) + 4 log(y) [/math]
- [math]log(3) + 2 log(x) - 4 log(y)[/math]
20.
Express as a single logarithm. [math]3log a - 2log b - 4logc[/math]
- [math] log (3a - 2b - 4c)[/math]
- [math]log (a^3 - b^2 - c^4)[/math]
- [math]3log a - 2log b - 4logc[/math]
- [math]log ((a^3)/(b^2c^4))[/math]
- none of these are correct
21.
What is the domain of the function [math]f(x)=3log_2 x ?[/math]
- [math][0,oo)[/math]
- [math](0,oo)[/math]
- [math](3,oo)[/math]
- [math][2,oo)[/math]
- [math](-oo,oo)[/math]
22.
Solve. [math]log_4 x- log_4 5= log_4 60[/math]
- 3
- 12
- 120
- 300
23.
Solve the system.
[math]x+y+z=6[/math]
[math]x=2y[/math]
[math]z=x+1[/math]
[math]x+y+z=6[/math]
[math]x=2y[/math]
[math]z=x+1[/math]
24.
Solve the following system of equations:
[math]x - 2y + 3z = 3[/math]
[math]2x + y + 5z = 8[/math]
[math]3x - y - 3z = -22[/math]
[math]x - 2y + 3z = 3[/math]
[math]2x + y + 5z = 8[/math]
[math]3x - y - 3z = -22[/math]
25.
The variables x and y are inversely proportional, and y = 6 when x = -2. What is y when x is 2?
- 4
- 12
- -9
- -6
26.
W varies directly as the square of V and inversely as R. When V = 1.5 and R = 1.25, W = 1.8
(a) Express W in terms of V and R
(b) Find W when V = 0.8 and R = 12.
(a) Express W in terms of V and R
(b) Find W when V = 0.8 and R = 12.
27.
If the matrix [math][[2,8,12],[3,4,0],[8,10,4]][/math] is multiplied by the scalar 1/2, what is the result?
- [math][[4,16,24],[6,8,0],[16,20,8]][/math]
- [math][[12,8,2],[0,4,3],[4,10,8]][/math]
- [math][[4,6,16],[16,8,20],[24,0,8]][/math]
- [math][[1,4,6],[1.5,2,0],[4,5,2]][/math]
28.
Matrices must have the same dimensions in order to add or subtract them.
- True
- False
29.
Evaluate. [math][(2,-3), (-4,2)] - [(-1,-5), (-3,2)][/math]
- [math][(3,2),(-7,4)][/math]
- [math][(-3,2),(-7,4)][/math]
- [math][(3,2),(-1,0)][/math]
- None of the above
30.
Multiply the following.
[math][(0,2),(-2,-5)] * [(6,-6),(3,0)][/math]
[math][(0,2),(-2,-5)] * [(6,-6),(3,0)][/math]
- Undefined
- [math][(0,6),(-27,12)][/math]
- [math][(6,0),(-27,12)][/math]
- None of the above
31.
For [math]A = [[1,3],[4,6]][/math], find [math]|A|[/math].
- -6
- 6
- 18
- -1
32.
Find the determinant of the following.
[math][(-11,3,10),(19,2,-4),(-8,-10,20)][/math]
[math][(-11,3,10),(19,2,-4),(-8,-10,20)][/math]
- -2478
- -2784
- 2784
- none of the above
33.
Find the inverse of the matrix, if it exists.
[math][[-4,-2],[7,8]][/math]
[math][[-4,-2],[7,8]][/math]
- [math]"Does Not Exist"[/math]
- [math][[4/9,1/9],[-7/18,-2/9]][/math]
- [math][[2/9,1/9],[-7/18,-4/19]][/math]
- [math][[-4/9,-1/9],[7/18,2/9]][/math]
34.
Simplify the complex number radical expression [math]sqrt(-96)[/math].
- [math]-4isqrt6[/math]
- [math]4sqrt6[/math]
- [math]4isqrt6[/math]
- [math]-4sqrt6[/math]
35.
Which of the following is equal to [math]i^3[/math]?
- [math]-i[/math]
- [math]i^2[/math]
- [math]1[/math]
- [math]-1[/math]
36.
The complex number [math]2-5i[/math] is in which quadrant?
- [math]I[/math]
- [math]II[/math]
- [math]III[/math]
- [math]IV[/math]
37.
Add. [math] (5-2i) + 3i[/math]
- [math]11[/math]
- [math]6 + 15i[/math]
- [math]5 + i[/math]
- [math]5 - 5i[/math]
38.
Multiply and write the result in standard form.
[math]4i(3i - 2)[/math]
[math]4i(3i - 2)[/math]
- [math]-12i-8[/math]
- [math]12+8i[/math]
- [math]-12-8i[/math]
- [math]12i+8[/math]
39.
Multiply [math]6+5i[/math] by its conjugate.
- [math]61[/math]
- [math]61i[/math]
- [math]36+22i+25i^2[/math]
- [math]82i^3[/math]
40.
Divide and simplify the following complex number expression. [math](-5-9i)/(9+8i)[/math]
- [math]-117/145+41/145i[/math]
- [math]-117/145-41/145i[/math]
- [math]117/145+41/145i[/math]
- [math]117/145-41/145i[/math]
41.
Factor. [math]x^2+12[/math]
- [math]2sqrt3i[/math]
- [math](x-4i)(x+4i)[/math]
- [math]+-sqrt12[/math]
- [math](x+2sqrt3i)(x-2sqrt3i)[/math]
42.
Use synthetic division to divide the polynomials: [math](y^2+14y+49)/(y+7)[/math].
- [math]y-7[/math]
- [math]y^2+7[/math]
- [math]y+7[/math]
- [math]y+(7)/(y+7)[/math]
43.
Solve using long division.
[math](x^3+7x^2-5x-6)/(x+2)[/math]
[math](x^3+7x^2-5x-6)/(x+2)[/math]
44.
Factor. [math]x^4 - 16[/math]
45.
Factor.
[math]x^3 - 8[/math]
[math]x^3 - 8[/math]
46.
Find the sum of the first 50 terms in the sequence 2, 6, 10, 14...
- 5000
- 198
- 2500
- 500
47.
What is the sum of the first 5 numbers in the series [math]1+2+4+8+16+32+... ?[/math]
- 16
- 31
- 32
- 63
48.
Identify the following shape.
[math]x^2+xy-y^2-10x-3y+5=0[/math]
[math]x^2+xy-y^2-10x-3y+5=0[/math]
- Circle
- Hyperbola
- Parabola
- Ellipse
49.
Identify the directrix of [math]y=-2x^2.[/math]
- [math]y=-2[/math]
- [math]y=1/2[/math]
- [math]y=1/8[/math]
- [math]y=-1/8[/math]
50.
Which equation represents the ellipse with foci on the x-axis, major axis 9 units long, minor axis 4 units long, and center at the origin?
- [math]x^2/4+y^2/9=1[/math]
- [math]x^2/20.25+y^2/4=1[/math]
- [math]x^2/9+y^2/4=1[/math]
- [math]x^2/4+y^2/20.25=1[/math]
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