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