Semester 2 Final Exam Review

Polynomials

100

Given that roots of polynomial are x = -9 and 5, identify the factors.   

(x+9)(x-5)

200

Given factors of (x+3)(2x-5), identify the zeros.  

x = -3 and 5/2

300

A polynomial, when graphed, crosses the x-axis at -5 and -1 and only touches (turning point) at x = 7.  Is this an even degree or odd degree function?

Even degree

400

Perform synthetic division and identify the quotient and remainder (if there is one).

 3x³−17x²+13x+23 ÷ x−4

3x²−5x−7−5/(x-4)

500

If f(x) = x³−3x²−36x−32 and f(-1) = 0, identify the remaining zeros of the function.  

x = -4 and 8

Logarithms

100

Convert to exponential form:

log₃(729) = x

3^x = 729

200

Convert to logarithmic form:

6^x+2 = 2

log₆(2) = x+2

300

Solve for the variable:

log₆(3x) + log₆(2) = log₆(18)

x = 3

400

Solve for the variable:

log₅(4x) - log₅(8) = log₅(3)

x = 6

500

Use the common base method to solve for x:

8^x−2= 64^-2x+2

x = 6/5

Trigonometry

100

Convert 11π/6 to degrees.

330°

200

Convert 375° to radians.

25π/12

300

Given the side lengths of a right triangle below, identify the 3 primary trig ratios.

Hypotenuse = 7, Opposite = 4, Adjacent = 3

sin = 4/7

cos = 3/7

tan = 4/3

400

Identify the reference angle of -770°

50°

500

Identify cos(-5π /6)

-√3/2

Random Review

100

Who is your favorite teacher?

Mr. Lee, of course.

200

What is the quadratic formula?

x = (-b±√(b²-4ac))/(2a)

300

Solve for the variable:

√(7x+50)−9 = -1

x = 2

400

Solve for the variable:

2x²-18 = -36

x = ±3i

500

Find (f(g(x)):

f(x) = 2x²+5x+15

g(x) =-x+5

2x²−25x+90