Algebra 2 Chapters 1-7 Review

Linear Equations and Systems of Linear Equations

100

This is the equation for a line with a slope of 3 and a point: (—4, 1)

What is y = 3x + 13?

200

This is the equation for a line through points (3, -8) and (8, 2)

What is y = 2x - 14?

300

Are these two lines perpendicular?

y = 2x + 1

(1/2)x + y = -3

Yes: slopes of 2 and -1/2.

400

Solve the system of equations using any method:

9x - 5y = -30

x + 2y = 12

What is (0, 6)?

500

Solve the system of equations using any method:

2x + 3y = -7

-4x - 5y = 13

What is (-2, -1)?

Matrices

100

Multiply the two matrices:

[ 2 15] [-5 12]

[-3 10] [ 1  0 ]

What is

[ 5   24]

[25 -36]

200

This is the determinant of the matrix

[6 -1]

[2  1]

What is 12?

300

This is the determinant of

[3 1 0]

[2 1 1]

[0 3 4]

What is -5?

400

This is the inverse of

[2  3]

[7 11]

What is

[3/4  -1/2]

[-1/4  1/2]

500

This is the inverse of

[-3  6]

[ 2 -4]

What is none: the determinant is zero

Quadratic Functions

100

This is the solution to x² + 11x + 24 = 0

What is x = -3, -8 ?

200

This is the standard form of the following complex number expression:

(3 + 10i)(4 - 9i)

What is 102 + 13i?

300

This is the solution to the quadratic equation (solve by completing the square)

x² + 4x = 3

What is x = -2 + 7^1/2 and -2 - 7^1/2 ?

400

This is the vertex form and the vertex of the following quadratic function:

y = x² - 8x + 17

What is y = (x - 4)² + 1

Vertex: (4, 1)

500

This is the solution to the equation 

x² - 8x + 5 = 0

(300 bonus points if you stand on your chairs and sing the quadratic formula)

What is 4 + 11^1/2, 4 - 11^1/2 ?

Polynomial Equations

100

Simplify (2/3)²•(6xy^-1)³

What is 96x³y^-3 ?

or (96x³)/(y³)

200

This is the distributed and simplified form for the following polynomials:

(x³+ 3)(3x³ + x² + 1)

What is 3x⁶ + x⁵ +10x³ +3x³ +3?

300

Factor and find the real-number solutions of the equation:

x⁴ - 6x² = 27

What is x = 3, -3 ?

400

Use synthetic division to divide

(x³ + 2x² - 57x + 54) / (x + 9)

What is x² - 7x + 6 ?

500

Write a quadratic function in intercept form whose graph has the given x-intercepts and passes through the given point:

x-intercepts: 4, 0 and point (1, -6)

What is y = 2x(x - 4) ?

Power Functions and Function Operations

100

Let f(x) = 2x - 4 and g(x) = x - 2.

This is f(x) + g(x)

What is 3x - 6 ?

200

Let f(x) = 2x - 4 and g(x) = x - 2.

This is f(x) - g(x)

What is x - 2?

300

Let f(x) = 2x - 4 and g(x) = x - 2.

This is f(x) • g(x)

What is 2x² - 8x + 8 ?

400

Let f(x) = 2x - 4 and g(x) = x - 2.

This is f(x) / g(x)

What is 2 ?

500

Let f(x) = 2x - 4 and g(x) = x - 2.

This is f(g(x))

What is 2x - 8 ?