Test Review

3D Graphing

100

An equation of the form ax+by+cz=d forms what shape graphically?

A plane

200

What shape is formed by the intersection of a line and a plane?

A point

300

Give an equation of a plane parallel to

 3x-4y+10z=  60

3x-4y+10z = d

400

What shape is formed by two planes intersecting each other?

A line.

500

What is the minimum number of planes needed in order to form a point at their intersection?

3

Systems of Equations

100

What is the minimum number of equations needed to solve a system of equations with three unknowns?

3

200

What is the first step one should always take when solving a system of equations?

Choose which variable to eliminate.

300

Solve the following:

x + y + z = 2

2x + 3y + 5z = 3

-4x - y + 2z = -8

(1,2,-1)

400

Solve he following:

2x + 3y - z = -16

5x - y + 2z = 34

3x + 2y - 2z = -15

(3,-5,7)

500

Jeopardy (bet up to your max score or 500 pts)

Find the equation of the parabola that passes through (2,16), (3,59) and (4,102)

y = 5x² + 8x - 10

Logarithm Basics

100

Rewrite x^2y=16 in logarithm form.

log_x16=2y

200

Rewrite log₅x = y in exponential form.

5^y = x

300

When a log has no base listed, what is the base's value?

10

400

Find the inverse of y = log₂x and put in y= form.

y = 2^x

500

Find the inverse of y = 145^x and put into y= form.

y = log₁₄₅x

Expanding and Condensing Logarithms

100

Fully expand log xyz

log x + log y + log z

200

Fully condense log m - log n - log a

log (m/na)

300

Fully expand log (x²/y⁵z⁴)

2log x - 5logy - 4logz

400

Fully condense 3log a - 2log b + 5log c

log (a³c⁵/b²)

500

Fully expand log 5sqrt(x/y)

log 5 + 1/2 log x + 1/2 log y

Logarithmic Equations

100

Solve log 5x = log (2x + 9) 

x = 3

200

Solve −6log ₃ (x − 3) = −24 

x = 42

300

Solve 5^2x+1=125

x=1

400

Solve −10 + log ₃ (n + 3) = −10 

n = -2

500

Solve 6 + 2log ₂ (2r) = 0 

r = 1/16