Algebra 2 Honors Semester 1 Review
Find the domain: f(x) = x-3 / x^2+10x-24
(-∞,-12)U(-12,2)U(2,∞)
Solve and give the solution: 3x - 5 ≤ 4 and -6x + 2 ≥ -4
(-∞,1]
Find the domain: f(x) = x^2+3+4 / x-5
(-∞,5)U(5,∞)
f(x) = x+1/x^2+2
(-∞,∞)
Solve and write the solution in INTERVAL NOTATION: 2x - 1 ≥ 9 or 4 - 3x < -2
(2,∞)
-3 + 4(x-1) > x + 5 or 4x + 5(x + 4) > x + 44
(3,∞)
Factor 27g^3 + 64h^3
(3g + 4h)(9g^2 - 12gh + 16h^2)
Factor 27x^3 - 8
(3x - 2)(9x^2 + 6x + 4)
Factor completely 4x^4 - 13x^2 + 9
(x + 1)(x - 1)(2x + 3)(2x - 3)
Factor completely x^4 - 13x^2 + 36
(x + 3)(x - 3)(x + 2)(x - 2)
-3^0
-1
f(x) = -2x^2 + 8x - 5
-15
Which is an approximate solution to the equation 2x^2 + 5x - 1 = 0?
-2.686
Solve for x: 4/x+3 - x-1/x^2-4x-21 = 5/x-7
-22
(2x^4y^2)^3(-3x^4y)
-24x^16y^7
(-15a^4b^2 / 5a^10b^-3)^3
-27b^15 / a^18
g(x) = -x^2 - 9x + 3
-33
For f(x) = { 6 - x^2 for x ≥ 1 ; x - 3x^2 for x < 1 }
-4
If the polynomial 2x^2 - 13x + 15 is factored into (2x + A)(x + B) then what is the value of B?
-5
Give the slope of the line parallel to 5x + 2y = 12
-5/2
25a^13b^4 / -5a^2b^3
-5a^11b
Simplify for x ≥ 0: 4√7x^2 + √63x^2 - 4√28x^2 (4 radical seven x squared plus square root of sixty three x squared minus four radical twenty-eight x squared)
-x√7
Solve 2x^3 - 50x = 0
0, 5, -5
(3a^-5b^2 / 12a^3b^-4)^0
1
How many solutions does this equation have? 3x^2 - 6x + 3 = 0
1 real
3^4 / 3^7
1/27
2^-3 · 2
1/4
Simplify for t > 0: (4t^2 / 100t^10)^1/2
1/5t^4
Use f(x) = 4x^2 - 2 and g(x) = 3x + 4: Give an expression for g(f(x))
12x^2 - 2
Use f(x) = 4x^2 - 2 and g(x) = 3x + 4: Give an expression for f(x) · g(x)
12x^3 + 16x^2 - 6x - 8
Use f(x) = 4x^2 - 2 and g(x) = 3x + 4: Find the value of f(-2).
14
Add the complex numbers (5x - i) + (12 - i)
17 - 2i
How many solutions does this equation have? 5x^2 - 4x + 3 = 0
2 imaginary
How many solutions does this equation have? 6x^2 - 12 = 0
2 real
A taxi-cab company charges $20 as a fixed charge, and the first five miles are included. Each additional mile is $0.80 per miles. If the taxi charge was $33.60 (tax is not charged) then how long was the trip, in miles?
22
Find the quotient 7/4-3i
28+21i/25
(4 + 3i)(2 - i)
2i + 11
Factor completely 30x^3 - 26x^2 + 4x
2x(5x - 1)(3x - 2)
Simplify ^3√48x^6y^4 (cube root of 48 x to the sixth y to the fourth)
2x^2y√6y (2 x squared 2 y square root 6 y)
Simplify for denominators not equal to 0. x/2 - 4 / x/3 - 8/3
3/2
Give the positive solution of 4x^3/2 + 1 = 33
4
Give the solution to the quadratic equation x^2 + 25 = 8x
4 ± 3i
Simplify 2/3x-1/2 / 1/x + 1/6
4-3x / x+6
What is the value for c would complete the square? x^2 + 7x + c
49/4
Use f(x) = 4x^2 - 2 and g(x) = 3x + 4: Give an expression for f+g
4x^2 + 3x + 2
Use f(x) = 4x^2 - 2 and g(x) = 3x + 4: f-g
4x^2 - 3x - 6
The trinomial 14x^2 + 33x - 5 is factored as (7x + A)(Cx + B). What is the value of B?
5
(3i - 8)^2
55 - 48i
Simplify (-8)^1/3 + 4^3/2
6
(8x^3)^2
64x^6
Simplify √-72 (square root of -72)
6i√2 (6i radical 2)
Solve: √8x+12 = 4√6-x (square root of 8x plus 12 equals four radical six minus x)
7/2
Give the positive solution of 2x^4/3 = 32
8
Use f(x) = 4x^2 - 2 and g(x) = 3x + 4: Give an expression f(g(x))
86x^2 + 96x + 62
(2x - 3)(4x^2 - x + 5)
8x^3 - 14x^2 + 13x - 15
(-3x^2y^5)^2 (negative three squared y to the fifth and then all squared)
9x^4y^10 (nine x to the fourth y to the tenth)
What type of equation is this? 4x = x
Conditional
What type of equation is this? x - 3x = 6 - 3(x + 2) + 1
Conditional
What type of equation is this? 1 - 3x = 6 - 3(x + 2) + 1
Identity
What type of equation is this? 8x - 4 = -2(5 - 4x)
Inconsistent
Solve: |8x - 1| ≤ 2x + 11
[-1,2]
For g(x) = { 2x - 1 for x < -1 ; 4x + 3 for x > 0 } a.) Evaluate g(-3). b.) Evaluate g(2).
a.) -7 b.) 11
(-15a^4b^2 / 5a^10v^-3)^-2
a^12/9b^10
What is an example of a piece-wise function that has a domain of all real numbers? (answer is going to be a specific one from the exam review)
h(x) = {4x - 1 for x ≤ -1 ; 3x for -1 < x < 1 ; 6 - x^2 for x ≥ 1}
Describe the graph and slope of the line with the equation y = -1.
horizontal line, zero slope
What does ∩ mean?
intersection (or "and")
Choose an expression for f(m + 2) given f(x) = x^2 - 7x + 2.
m^2 - 3m - 8
Solve for t and give the restrictions: L = 2k(mt + m^2π)
t = L/2km - mπ, k ≠ 0, m ≠ 0
What does U mean?
union (or "or")
Describe the graph and slope of the line with the equation x = -1.
vertical line, undefined slope
Write the equation in standard form of the line through point (-1,3) with the slope 1/4.
x - 4y = -13
-3 +4(x - 1) > 10x + 5 or 4x +5(x + 4) > 2x + 48
x < -2 or x > 4
Solve |4x + 5| = 9. Check for any extraneous solutions.
x = -7/2 or x = 1
Solve 4(x + 3)^2 = 36
x = 0, x = -6
Solve x^2 - 2x = -26
x = 1 + 5i or x = 1 - 5i
Solve the equation to the nearest thousandth place: 6x^2 - 8x - 7 = 0.
x = 1.936, x = -0.603
What is the solution(s) of the quadratic equation 6x^2 - x - 12 = 0
x = 3/2, -4/3
Solve for x and give restrictions: V = 1/3xh + 2
x = 3v-6/h
Solve -3 < 2x -1 < 5
x > -1 and x < 3
Solve and graph the solution set. 2(x - 3) < 5x - 6
x > 0
Solve and graph |5x - 4| ≥ 6
x ≤ -2/5 or x ≥ 2
Solve: 2|x - 5| +1 ≥ 3
x ≤ 4 or x ≥ 6
Solve -7 ≤ 3 - 5x ≤ 8
x ≥-1 and x ≤ 2
Use f(x) = 4x^2 - 2 and g(x) = 3x + 4: Find g^-1(x) (inverse of g)
x-4 / 3
x^14 / x^3
x^11
Factor completely x^4 - 12x^3 + 20x^2
x^2(x - 10)(x - 2)
Simplify ^3√5x^6y^12z^2 (cube root of five x to the sixth times y to the twelfth times z to the second)
x^2y^4√5z^2 (x squared times y to the fourth radical five z squared)
What is the equation of the line, in point slope form which contains points (9,10) and (21,14)?
y - 10 = 1/3(x - 9)
Which line is parallel to the graph of y = -1/2x + 8?
y = -1/2x + 8
Which equation is of a line perpendicular to the graph of y = 4x - 1 and which passes through the point (-8,1)?
y = -1/4x - 1
What is the equation of the line in slope-intercept form which has slope -2/5 and through the point (-10,5)?
y = -2/5x + 1
Which is an equation for the line through the points (9,3) and (5,-5)?
y = 2x - 15
What is the domain of the relation {(1,2), (-1,7), (-3,6)}?
{1, -1, -3}
What is the range of the inverse of {(1,2), (-1,7), (-3,6)}?
{1, -1, -3}
What is the domain of the inverse of {(1,2), (-1,7), (-3,6)}
{2, 6, 7}
What is the range of the relation {(1,2), (-1,7), (-3,6)}?
{2, 7, 6}
Solve 2x^2 - 13x + 15 = 0
{5,3/2}
Solve x^2 - 7x + 6 = 0
{6,1}
Find the domain of the rational function. x+0 / x^2+4x
{x|x ≠ 0, x ≠ -4}
Solve: 4x - 1 = -2(1 - 2x)
ø