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# 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                 .
1. Axis of Symmetry
2. End Behavior
3. Concave Up
4. Concave Down
4.
Which of the following describes a quadratic function that has been shifted to the left 4 units?
1. $f(x)=x^2 +4$
2. $f(x)=x^2-4$
3. $f(x)=(x-4)^2$
4. $f(x)=(x+4)^2$
5.
If y = f(x) is transformed to y = f(x) - 2, the function                     .
1. Shifts up 2 units
2. Shifts down 2 units
3. Shifts left 2 units
4. Shifts right 2 units
6.
Does the function shown here have an inverse that is also a function?
1. Yes, the inverse is a function.
2. No, the inverse is not a function.
7.
Which restriction would make the function $y=1/2x^2$ invertible?
1. $x>0$
2. $y>0$
3. $y<0$
4. $x<1/2$
8.
Find the inverse of $g(x)=-3x$.
1. $g ^(-1) (x)=x+1$
2. $g ^-1 (x)=-3x-3$
3. $g ^-1 (x)=x-1$
4. $g ^-1(x)= -1/3 x$
9.
$f(x) = sqrt(x+3)$ and $g(x)=2x$. Find $(f @ g)(4)$.
1. $2sqrt14$
2. $sqrt11$
3. $sqrt14$
4. $2sqrt7$
10.
Find the domain of the composite function $f(g(x))$.

$f(x)= x+3$
$g(x)= 2/(x+6)$
1. $(-oo,3) uu (3,oo)$
2. $(-oo,oo)$
3. $(-oo,-6) uu (-6,3) uu (3,oo)$
4. $(-oo,-6) uu (-6,oo)$
11.
Simplify the expression $(7x^2-63)/(x+3)$.
1. $(x+3)/7, \ x!=-3$
2. $(7x^2-9)/(x), \ x!=-3$
3. $7(x+3), \ x!=-3$
4. $7(x-3), \ x!=-3$
12.
Solve. Check for extraneous solutions.

$x/(x-1)=(x+3)/(-2x+2)$
1. $x=-1 or x=-2$
2. $x=-1$
3. $x=1$
4. $x=1 or x=-1$
13.
Which function is an example of exponential growth?
1. $g(x)=0.4(1.3)^x$
2. $f(x)=1.6(0.85)^x$
3. $h(x)=0.5(0.95)^x$
4. $k(x)=1.2(1-.25)^x$
14.
Determine the y-intercept of the following exponential function. $y=2^x+3$
1. (0,4)
2. (0,3)
3. (0,2)
4. (4,0)
5. none of these are correct
15.
What is the value of $x$ in the equation $9^(3x+1)=27^(x+2)$ ?
1. $1$
2. $1/3$
3. $1/2$
4. $4/3$
16.
Write $log_5 36=x$ in exponential form.
1. $36x = 5$
2. $5^x = 36$
3. $x^5 = 36$
4. $10^x = 36$
17.
Evaluate. $log_3 (1/9)$

18.
Evaluate. Write in simplest form. $10^(log_(10) 3)$
1. 3
2. 10
3. 1000
4. 1/3
5. none of these are correct
19.
Which expression is equivalent to $log((3x^2)/y^4) ?$
1. $2 log(3x) + 4 log(y)$
2. $2 log(3x) - 4 log(y)$
3. $log(3) + 2 log(x) + 4 log(y)$
4. $log(3) + 2 log(x) - 4 log(y)$
20.
Express as a single logarithm. $3log a - 2log b - 4logc$
1. $log (3a - 2b - 4c)$
2. $log (a^3 - b^2 - c^4)$
3. $3log a - 2log b - 4logc$
4. $log ((a^3)/(b^2c^4))$
5. none of these are correct
21.
What is the domain of the function $f(x)=3log_2 x ?$
1. $[0,oo)$
2. $(0,oo)$
3. $(3,oo)$
4. $[2,oo)$
5. $(-oo,oo)$
22.
Solve. $log_4 x- log_4 5= log_4 60$
1. 3
2. 12
3. 120
4. 300
23.
Solve the system.
$x+y+z=6$
$x=2y$
$z=x+1$

24.
Solve the following system of equations:

$x - 2y + 3z = 3$
$2x + y + 5z = 8$
$3x - y - 3z = -22$

25.
The variables x and y are inversely proportional, and y = 6 when x = -2. What is y when x is 2?
1. 4
2. 12
3. -9
4. -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.

27.
If the matrix $[[2,8,12],[3,4,0],[8,10,4]]$ is multiplied by the scalar 1/2, what is the result?
1. $[[4,16,24],[6,8,0],[16,20,8]]$
2. $[[12,8,2],[0,4,3],[4,10,8]]$
3. $[[4,6,16],[16,8,20],[24,0,8]]$
4. $[[1,4,6],[1.5,2,0],[4,5,2]]$
28.
Matrices must have the same dimensions in order to add or subtract them.
1. True
2. False
29.
Evaluate. $[(2,-3), (-4,2)] - [(-1,-5), (-3,2)]$
1. $[(3,2),(-7,4)]$
2. $[(-3,2),(-7,4)]$
3. $[(3,2),(-1,0)]$
4. None of the above
30.
Multiply the following.

$[(0,2),(-2,-5)] * [(6,-6),(3,0)]$
1. Undefined
2. $[(0,6),(-27,12)]$
3. $[(6,0),(-27,12)]$
4. None of the above
31.
For $A = [[1,3],[4,6]]$, find $|A|$.
1. -6
2. 6
3. 18
4. -1
32.
Find the determinant of the following.

$[(-11,3,10),(19,2,-4),(-8,-10,20)]$
1. -2478
2. -2784
3. 2784
4. none of the above
33.
Find the inverse of the matrix, if it exists.

$[[-4,-2],[7,8]]$
1. $"Does Not Exist"$
2. $[[4/9,1/9],[-7/18,-2/9]]$
3. $[[2/9,1/9],[-7/18,-4/19]]$
4. $[[-4/9,-1/9],[7/18,2/9]]$
34.
Simplify the complex number radical expression $sqrt(-96)$.
1. $-4isqrt6$
2. $4sqrt6$
3. $4isqrt6$
4. $-4sqrt6$
35.
Which of the following is equal to $i^3$?
1. $-i$
2. $i^2$
3. $1$
4. $-1$
36.
The complex number $2-5i$ is in which quadrant?
1. $I$
2. $II$
3. $III$
4. $IV$
37.
Add. $(5-2i) + 3i$
1. $11$
2. $6 + 15i$
3. $5 + i$
4. $5 - 5i$
38.
Multiply and write the result in standard form.
$4i(3i - 2)$
1. $-12i-8$
2. $12+8i$
3. $-12-8i$
4. $12i+8$
39.
Multiply $6+5i$ by its conjugate.
1. $61$
2. $61i$
3. $36+22i+25i^2$
4. $82i^3$
40.
Divide and simplify the following complex number expression. $(-5-9i)/(9+8i)$
1. $-117/145+41/145i$
2. $-117/145-41/145i$
3. $117/145+41/145i$
4. $117/145-41/145i$
41.
Factor. $x^2+12$
1. $2sqrt3i$
2. $(x-4i)(x+4i)$
3. $+-sqrt12$
4. $(x+2sqrt3i)(x-2sqrt3i)$
42.
Use synthetic division to divide the polynomials: $(y^2+14y+49)/(y+7)$.
1. $y-7$
2. $y^2+7$
3. $y+7$
4. $y+(7)/(y+7)$
43.
Solve using long division.

$(x^3+7x^2-5x-6)/(x+2)$

44.
Factor. $x^4 - 16$

45.
Factor.
$x^3 - 8$

46.
Find the sum of the first 50 terms in the sequence 2, 6, 10, 14...
1. 5000
2. 198
3. 2500
4. 500
47.
What is the sum of the first 5 numbers in the series $1+2+4+8+16+32+... ?$
1. 16
2. 31
3. 32
4. 63
48.
Identify the following shape.
$x^2+xy-y^2-10x-3y+5=0$
1. Circle
2. Hyperbola
3. Parabola
4. Ellipse
49.
Identify the directrix of $y=-2x^2.$
1. $y=-2$
2. $y=1/2$
3. $y=1/8$
4. $y=-1/8$
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?
1. $x^2/4+y^2/9=1$
2. $x^2/20.25+y^2/4=1$
3. $x^2/9+y^2/4=1$
4. $x^2/4+y^2/20.25=1$
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