- always pay attention to the signs and read the questions on the tests very carefully before answering as well as after you’ve finished your test make sure that you reread what you’ve written 2 or 3 times just to be sure that all the signs are correct and you have read the questions properly.
- make sure you pay close attention to the signs while graphing because one mistake with that could mess up your entire graph and make it open up instead of open down
- pay attention to the right triangles in trigonometry and their ratios because if one side of the triangle is not in the proper place then your whole ratio will be messed up and your answer will be very different from the proper answer.
- make sure to always double or even triple check your answers by putting them back into the equation, no matter what it be, factoring, graphing anything of the sorts. It’s always important to make sure you verify the answers just in case you’re not sure the answers right
- pay attention during the lessons because if you decide to sleep through a class or skip or slack off, it will catch up to you in the end and it will bring your grade down substantially.
this week in math we learned about the sine law and cosine law, they’re used when you can’t solve a triangle with simple SOH CAH TOA ratios.
For the top side we have a pretty simple triangle and I show you the steps above and the reason I flipped the equation upside down is because of a trick I was taught, whatever you’re trying to solve whether it be a side or an angle have that on top, so if you’re trying to figure out a side keep the sides on top and if it’s an angle keep the angles on top, work smarter not harder.
and on the bottom another simple triangle and I have demonstrated how the cosine law works there
this week in math we did a little review of last years trigonometry unit and I wanted to share it with you guys.
What we have here with SOH CAH TOA are the ratios dependent on how you can solve which part of the triangle
I have the sides labelled on the big triangle below as well as the ratios in between, naturally hypotenuse will be the longest side, adjacent will always be the side with the reference angle and the right angle, and finally opposite will only have the right angle on it’s side.
on the right side of the picture I have demonstrated how to find an angle and a side using the cosine ratio, as you can see it is fairly simple
During week 15 we learnt how to add and subtract radical expressions, in the picture above I demonstrate the part of addition
For the first example, There is an expression with the denominators being the same so all you have to do is add across. An important note, to subtract or add your denominator must be the same for both sides.
For the second expression the denominators are different so what was done in the example to find the lowest common multiple is we’ve multiplied each side with the opposite denominator so that the denominators become the same and then you simply add across
equivalent rational expressions are basically factoring in a fraction format and then once you have the expressions factored as I have in the second step of the expression and after that you must find the restriction where the denominator cannot be equal to 0 and the restrictions are -5 and 0
after that you cancel the like terms from the nominator and denominator which in this case is (x+5) and the final expression will be the one on the bottom
this week during math we learnt how to graph reciprocal linear and quadratic functions, in the picture above represented are 3 different ones. The first being linear the second being a simple quadratic function and the final being a more complex quadratic function.
the key to reciprocal functions is making sure you know exactly where your asymptotes are located and they will correspond with your interveniant numbers which are 1 and -1 and with your restrictions they represent where the hyperbolas will be located.
so for the first one x=3 and y=0 those will be our restrictions and the hyperbolas are set.
for the second one it’s more difficult because it’s a quadratic function but basically your asymptotes are what give you boundaries or sections and usually with a quadratic function it will be 6 sections as to which the parabola could be located in and simply which ever section the parabola is found in that’s where and which direction you draw the hyperbola the same goes for the bottom quadratic function
This week in math we learnt how to determine x-intercepts using the substitution method.
the very first step is you have to isolate a variable, in the equations above a variable has already been isolated for us which is “y” and from that step is the second where you substitute the letter variable which is “y” in the second equation to the equation above.
after that step 3 is distributing and and putting the equation in a form you can factor and then factor it to the point of being able to determine the x-intercepts and after that you do the math and the x-intercepts should be -5/4 and 1 for these equations
this week we learnt how to solve quadratic inequalities and how to test if the equation represented is true
above we have a standard quadratic equation but instead of being = to it is saying that the equation is greater than 0
so to test that we first have to find the x intercepts and from there we find a number lower than the lowest x intercept, a number in between the x intercepts, and a number greater than the greatest x intercept and we input them in the equation and see if the answer given is a positive or negative which will then tell us if the answer is greater or less than 0
we have now tested all three of the numbers we chose and it says that we have a positive, a negative, and another positive answer. We are looking for the positive answers to make this equation true.
after that you just state what is true which is….. X<-4 and x>2 making the equation true
the only way to find the x-intercepts is to bring it to factored form whether it be from standard form or general form and once you have it in factored form it’s simply like doing an equation between the brackets
The discriminant is related to the x-intercepts in the way that the discriminant will tell you how many intercepts you may have but in the factored form you figure out what the intercepts really are.