Final Exam Review

Order of Operations, Complex numbers, and Scientific Notation

100

(30+4²)/2=

23

200

write 589700 in scientific notation

5.897 x 10 ⁵

300

foil (3i +4) (2i-6)

-30-10i

400

solve 3[(2+4)²-3]

99

500

write 0.000734 in scientific notation

7.34 x 10^-4

Polynomials and Factoring, and Rational Expressions

100

9x²+25

(3x-5i)(3x+5i)

200

9x³+27x²+36x

9x(x²+3x+4)

300

(x³+x²+x+1)-(x³-2x²-5x+3)

3x²+6x-2

400

(x²+4x+3)/(x+1)

x+3

500

factor the trinomial given in the numerator of a rational expression (x²+3x-10) divide by (x-2)

x+5

Exponents and Radicals

100

cbrt(5⁴)

5sqrt(5)

200

cbrt(16)

2cbrt(2)

300

(2x⁴y^-3)/16x^-2

(x⁶)/(8y³)

400

Rewrite in Radical form and simplify if possible 3^8/3

cube root 3⁸

500

Rewrite in exponential form 

sq200

200^1/2

Graphing, transformations, circles, midpoint, distance, and slope

100

Graph

y=(x+3)²-4

Parabola=3 left, 4 down

200

Find  y=2x-3

a)slope of the line

b)perpendicular slope

a)2

b)-1/2

300

Rewrite from general form to standard form of a circle

x²+y²-6x+4y-12=0

(x-3)²+(y+2)²=25

400

Find the midpoint of (2,-3) and (8,5)

(5,1)

500

Find the distance between these two points (2,-3) and (8,5)

10

Systems of Equations, Matrices, and Logarithms

100

Find the value of x and y in the following systems of equation:

y+x=16

y=3x

x=4

y=12

200

Find the value of x

3^x=27

x=3

300

log₃9=

2

400

Turn this matrix into equations

|1 3 4 | 2|

|2 5 6 | 5|

|6 1 2 | 4|

x+3y+4z=2

2x+5y+6z=5

6x+y+2y=4

500

If the Gauss-Jordan elimination is the following, what is the answer?

|1 0 0| 3|

|0 1 0| 2|

|0 0 1| 5|

x=3,2,5