PC Junior Final Exam Review

Logarithms

100

The base of the common log.

What is 10?

200

The base of the natural log

What is e?

300

Condense the logarithm:

6log₅x + 24log₅y

log₅(y²⁴x⁶)

400

Expand the logarithm

log₃(a/b⁵)³

3log₃a - 15log₃b

500

Solve the equation:

log₉5x - log₉4 = 1

36/5

Polynomials

100

A rule used to determine the number of positive & negative roots of a polynomial.

Descartes Rule of Signs

200

These are the steps to determining the number of positive & negative zeros of a polynomial.

Pos: Count the sign changes of the terms

Neg: Replace x with -x; simplify; count the sign changes

300

Divide the polynomial by the binomial:

(2x⁴ +13x³+18x²-11x-21)/(x+4)

2x³+5x²-2x-3- (9/(x+4)

400

Divide the polynomial by the binomial:

(5x⁵ -30x⁴+28x³-10x²-26x+1)/(x-5)

5x⁴-5x³+3x²+5x-1 - (4/(x-5))

500

Divide the polynomial by the binomial:

5x⁵+9x⁴-17x³-3x+13 / (x+3)

5x⁴-6x³+x²-3x+6- (5/(x+3))

Exponentials

100

The formula for Continuous Growth/Interest

A = P e^rt

200

The formula for compound interest.

A = P (1 + (4/n))^nt

300

This is the value of Euler's Constant

2.718281....

400

Alishan invests $4,772 in a savings account with a fixed annual interest rate of 3.12% compounded continuously.  What will the account balance be after 9 years?

$6,3109.03

500

Shevon invests $5,269 in a savings account with a fixed annual interest rate of 7.25% compounded 3 times per year.  What will the account balance be after 9 years?

$10,040.04