SP#7: Unit Q Concept 2: Finding All Trig Functions when given one Trig Function and Quadrant ( Using Identities)

This SP7 was made in collaboration with Christine N. Please visit her awesome posts on her blog by going here.

SP:#6 Unit K Concept 10: writing a repeating decimal as a rational number using geometric series

 

Unit K Concept 10: writing a repeating decimal as a rational number using geometric series

 

 

 

When doing these problems remember to not worry about the number in front of the decimal right away: forget about it in the beginning. Since it is a 3 digit repeating decimal it goes on top of 1000 making r=1/1000. You solve it and plug it into the formula and one you get your answer you add it to the umber in front which you previously ignored in the beginning.

SP#5 Unit J Concept 6: Partial Fraction Decomposition with repeated factors

UNIT J CONCEPT 6

PARTIAL DECOMPOSITION WITH REPEATED FACTORS

Problem difficulty 8out of 5! :)

When doing this problem dont forget to factor out the common denominator completely. Also remember that since they are repeated factor that you must count UP for how many times they reoccur. Also remember that you will end up with two three variable systems in which you can solve them. You will be using elimination to solve them. After you get one answer all you have to do in just plug bak in your answer to find the rest.

SP #4 Unit J concept 5:Partial decomposition with distinct factors

Partial Decomposition with distinct factors

PART ONE

PART TWO

PART THREE

PART FOUR

When completing these problems you must be distribute properly and when decomposing remember to factor out the denominator FULLY. You must then separate them and use letter variables instead.Your common demoninator must be made up of the factors you need and you multiply them to the top. Dont forget that every factor it doesnt have must be multiplied. Dont forget once you start crossing off like terms that the x's cancel out. rememeber to set them equal to the same original factor it corresponds too in the original. Finally if your rref doesnt match the original numbers then you made a mistake.

SP3:Unit I Concept 1 Graphing functions and identifying x-intercept, y-intercept, asymptotes, domain, range

  Graphing functions and identifying x-intercept, y-intercept, asymptotes, domain, range

1) To solve these problems first you must identify the parts of the equation and label them. Since this is an exponential graph the asymptote is y=k. To find the x intercept you plug in y=0 however you must take notice if the graph will cross the x axis if not there will be none. To find the y intercept we use x=0 and solve. The domain is not restricted so it will be all real numbers, however our range is so it will depend on if the graph is above or below the asymptote.

SP#2: Unit E Concept 7 - Graphing a polynomial and identifying all key parts

1) This problem is about graphing polynomials and including the x-intercepts,y-intercept, the zeroes(with their multiplicities) and the end behavior.To start the problem you must first factor the equation out. Then with the answers you get you will be able to sketch the graph.

2) When doing this type of problem you must first remember to factor it all out. Once you get the remaining value you must solve to zero and then you have your zeroes. You must remember that if it has  multiplicity of 1 then it goes through and if it has one of two then it bounces off.The y intercept is gotten by setting all the x's equal to zero(in this case your answer is zero). The end behavior in this case is even positive therefore the graph will face negative when going to the right and left.

SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts

1)this is a quadratic in standard form. The standard form is  f(x)=ax^2=bx=c. In order to graph them more sufficiently we must complete the square so that they can be in the parent function form. The graph will include 2 and 4 points:the vertex, the y-intercept, and up to two x-intercepts, as well as one dotted line which s the axis of symmetry

2).Once you have completed the square, to identify the points and intercepts you need to understand how to find them. to find the vertex you must use the equation (h,k) It could be  a maximum or a minimum. The x-intercepts are the solutions. You set the equation equal to zero and then you solve. To find the y intercept you use the standard form of the problem and plug in 0 for x and then solve  Finally the axis of symmetry divides the parabola so you set it up like x=h.