Tuesday is the day that I set aside for Algebra. Since the easy level does not use actual material from an Algebra course, I have included things that students need to know for an algebra course (fractions and decimals, order of operations, etc.). I have also tried to make the arithmetic challenging in that section to make the actual task a little harder than normal.

Easy:

First, calculate the value of

*m*and

*n*using the values of

*a*and

*p*. Reduce the fractions once you have found them.

2617736

*m*=

*–––––––*

20775

*a*

*n*=

*––––*

277

*p*

*Now, solve for*

*y*and

*z*using the rules for subtracting and dividing fractions.

*y*=

*m*-

*n*

*z*=

*m*÷

*n*

*m*= _____

*n*= _____

*y*= _____

*z*= _____

Medium:

Substitute the values of

*p*and

*h*into the following equation, and then solve for the value of

*t*.

*p*(

*ht*+ 705) = (3

*t*- 56)(6

*h*- 2

*p*)

^{3}

*t*= _____

Hard:

First, find the value of

*q*

_{0}using the value of

*p*from yesterday.

9

*p*+ 47*q*

_{0}

*=*

*–––––––*

2

Now,

*q*

_{0 }is the zeroth term in a geometric sequence. The recursive formula for this sequence is the following:

*q*n = (½)

*q*n-1

Knowing the values of the geometric sequence, simplify the following rational function (you can leave it factored, but make sure

*x*is the only variable):

(

*x*-

*q*

_{11})(

*x*-

*q*

_{9})

*f(x)*=

*––––––––––––––––––––––*

(

*q*

_{11}

*x*+

*p*)(

*x*-

*q*

_{10})(

*x*+

*q*

_{11})

Now, determine the vertical and horizontal asymptotes of this function. Use

*x*

_{1},

*x*

_{2},

*x*

_{3 }and so on for the equations for the vertical asymptotes (if the asymptotes were 2 and 5, but

*x*

_{1}= 2 and

*x*

_{2}= 5), and

*y*

_{1},

*y*

_{2},

*y*

_{3 }and so on for the equations for the horizontal asymptotes. Make sure that the asymptotes are arranged from least to greatest in relation to the variable subscripts.

I am not going to put down the variables to find with the blank. Just find as many values of

*q*,

*x*, and

*y*that exist or are necessary for the problem.

_{}

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