Algebra II Accel Sem 1 Final Review 25-26

Unit 1 - Functions

100

Use f(x) = 2x² - x + 5 and g(x) = 2x - 3 to find (f+g)(-2)

8
f(-2) =15
g(-2) = -7

200

Find the Average Rate of Change of g(x) = 2x - 3 from x = 1 to x = 3

f(3) = 3
f(1) = -1
(3+1) / (3 - 1) 

m = 2

300

Use f(x) = 2x² - x + 5 and g(x) = 2x - 3 to find
f o g(-1)

60
g(-1) = -5
f(-5) = 60

400

Write the function h(x), whose graph is the graph f(x) = sqrt(x) but shifted left 3 units, reflected over the x axis, and shifted up 7 units.

h(x) = sqrt(x+3) + 7

500

Given a point (-1,5) on a function f(x), what point is on the function f(x-5)+3 ?

right 5, up 3
(4,8)

Unit 2 - Quadratics

100

Solve for x: 4x² + 12x = 0

4x(x+3) = 0
x = 0, -3

200

Solve for x:
2x² - 23 = x² - 11

x² = 12
x = +/- 2sqrt(3)

300

Perform the indicated operation: (1+5i)(7-4i)

7+35i-4i-20i²
27 + 31i

400

Perform the indicated operation: (3-2i)²

(3-2i)(3-2i) = 9 - 12i + 4i²
5 - 12i

500

Using the function f(x) = 3x² - 6x + 5, find the vertex of the function, and write the equation in vertex form, a(x-h)² + k

V_x = -b / 2a = 6/6 = 1
V_y = f(1) = 2
Vertex: (1,2)
a value: 3
Vertex Form: 3(x-1)² + 2

Unit 3 - Polynomials

100

Perform the Indicated Operation: (3x² + 8x - 3) + (-5x² + 4x + 6)

-2x² + 12x + 3

200

Perform the Indicated Operation: (2x -7)(2x + 7)

4x² - 49

300

Is x+1 a factor of x⁴ - x³ + 2x - 8?

f(-1) = -8, No! 

400

Factor and solve: x⁴ - x² - 72

(x²-9)(x²+8)
x = +/- 3, +/-2i sqrt(2)

500

Find a degree 3 polynomial function with the following zeros:  2 and -3i. Give the polynomial function in standard form.

(x-2)(x+3i)(x-3i)

(x-2)(x²+9)

x³-2x²+9x-18

Unit 4 - Rationals

100

Simplify:
(x² - 25) / 2x² - 8x - 10

(x+5)(x-5) / 2(x-5)(x+1)

= (x+5) / 2(x+1)

200

Simplify: (x² - 2x - 8 / 8x³ + 16x²) * (2x² - 8 / x² - 6x + 8)

= (x+2) / 4x²
((x-4)(x+2) / 8x²(x+2)) * ((2(x-2)(x+2) / (x-4)(x-2)) 

300

Solve for x:
-4 / (x+4) = -3 / (x+6) 

-3(x+4) = -4(x+6)
-3x - 12 = -4x - 24
-x = 12
x = -12

400

Simplify:
((x-1) / (x+2)) - (3 / (x+1))

(x²-3x-7) / (x-1)(x+2)

500

Solve for x:
(3 / (x²+5x+6)) - (7 / (x+3)) = ((x-1)/(x+2))

LCD: (x+3)(x+2)

3 - 7(x+2) = (x+3)(x-1)

x² + 9x + 8 = 0
x = -8,-1

Unit 5 - Radicals / Exponents

100

Simplify x^5/4 / x^5/3

1/x^5/12

200

Simplify / Evaluate:

(8)^1/4 + 9(8)^1/4

10(8)^1/4

300

Convert and Simplify:
cbrt(64²)

cbrt(64) = 4
4² = 16

400

Solve for x:
sqrt(x+3) + 2 = 5

x + 3 = 9
x = 6

500

Solve:
x^2/5 + 10 = 14

x^2/5 = 4
x = 4^5/2 (even root, +/-)
x = 2⁵ = +/- 32