Schurz Finals Review

Solving Linear Systems

100

Solve the linear system: x+y=15, 9x-y=15

x=3, y=12

200

Solve the linear system: x-y=-15, x+5y=9

y=4, x=-11

300

Find the solution to the system: x+y=17, 5x+12y=120

x=12, y=5

400

Solve the linear system: y=3x+12, y=5x+2

x=5, y=27

500

Solve the linear system: 2y+3x=7, 6x+4y=14

Infinite Solutions

Zeros and Vertecies

100

What are the roots of the the quadratic: x²+10x+21=0

x=-7, x=-3

200

Find the roots of the parabola described by the quadratic: 2x²-x=10

x=5/2, x=-2

300

Find the roots of the parabola y=12x²+30x

x=0, x=5/2

400

Find the roots and the vertex of the following parabolic function: y=x²+4x-12

Is is concave up or concave down?

x=-6, x=2

vertex: (-2, -16)

Concave up

500

Find the roots and the vertex of the parabolic function: f(x)=-2x²+4x

Is it concave up or concave down?

Roots: x=0, x=2

Vertex: (1, 2)

Concave down

Convert to Slope-Intercept

100

Turn -x+y=-15 into slope-intercept form.

y=x-15

200

Turn 2y+3x=12 into slope intercept form.

y=-3/2x+6

300

Turn 10x-12y=24 into slope-intercept form.

y=5/6x-2

400

What is the slope of a line parallel to 8x-16y=30?

m=1/2

500

What is the slope of a line perpendicular to 2y+4x=16?

(hint: the slopes of perpendicular lines are "opposite-reciprocals" to each other)

m=-1/2

Multiplying Polynomials

100

Find the product of the monomials: 4x⁴y and x²y

4x⁶y²

200

Find the product of the monomials: -15x²y¹³ and 6x⁷y³

-90x⁹y¹⁶

300

Multiply the binomials: (3x+2)(2x-12)

6x²-32x-24

400

Multiply the binomials: (3x²+10)(4x+5)

12x³+15x²+40x+50

500

Multiply the polynomials: (x²+3x+1)(5x-3)

5x³+12x²-4x-3

Add/Subtract Polynomials

100

(2x²+5)+(x²+12)

3x²+17

200

(x²+2x-1)+(5x²+12x-12)

6x²+14x-13

300

(3x-13)-(6x+1)

-3x-14

400

(-x²+12x-1)-(5x²+5x-4)

-6x²+7x+3

500

(2x²-3x+20)+(-x³+4x-12)

-x³+2x²+x+8