this week in math 10 we learned how to factor perfect trinomials. the first step to factoring it is to square root the first and last terms of the trinomial (when identifying and factoring the perfect square trinomial make sure to use CDPEU). the next step is checking your answer to do this you make sure the two binomilas are identical then you multiply the first term in the first binomial and the last term in the second, then you multiply the last term in the first binomial and the first term in the second binomial if the two terms you got from that add to the second term in the starting trinomial then you know you factored it right.
This week in math 10 we learned how to factor ugly polynomials. And a quick way to do it.
a phrase that will help you make sure you are doing all the steps correctly and in order is CDPEU a way to remember these letters in order is: can divers pee easily underwater. The C in the phrase stands for common which means you need to figure out if the numbers have anything of common. The D stands for difference of squares, the way you know if it is a difference of squares question is if is it a binomial is there a subtract symbol and are they all perfect squares. The P is pattern for this you look to see if there is a pattern to solve the question easier. The E is easy so just look to see if it is an easy question. Then lastly U which stands for ugly this is when there is a non square number in front of the polynomial if it is this one you can’t use the rest of the rules.
For factoring an ugly polynomial the first step is to try and find if it has anything in common with all the terms and divide. Then you rewrite the question but in the simplified form and you want to put that number you divided the terms by in front of the bracket. Then you make a square divided into four parts, the first term in your polynomial is going to go in the top left box and the last term is going to go in the bottom right box, then you multiply those coefficient together after finding the answer you want to find the factors of that number and pick the factors that add to the middle term if the answer you got from multiplying the coefficients is a negative you just make the bigger factor of the two a nagative and add them. Then you put those factors into the remaining boxes and you have to add an x to the end of both the numbers. Then you go across the rows and down the collombs finding the common factor in the numbers writing the answer alonf the vertical and horzontal part on the outer sides of the square then you put those numbers into the brackets putting the verticals factors into a bracket and the horizontal factors into a bracket and you put the number you divided the first terms with at the front of the first bracket and then you have your factored ugly polynomial.
this week in math 10 i learned multiple ways to solve a polynomial. we leaned the box method, distibutive property, the foil method and algebra tiles. to use the box method you put the first part of the equation on the top of the box and the second on the side and make the box four squares. then you solve each box with the opposite of it. then simplify the alike terms. to solve an equation using distriputive property the first thing you do is distribute the fist term in the first part of the equation with the terms in the second part(you multiply the numbers). After writing down the numbers from before you do the same with the other numbers from the first part of the equation with the second term in the first part of the equation. after distibuting you simplify by adding alike terms. to solve it using algebra to use algebra tiles the numbers should be 5 or less and have a degree 1 or less. the first thing you do is set up the tiles, you wite the first part of the equation goes on thee top of the setup and the second part is on the side. you write down the tiles, if it has and x then it is a long rectangle and if it doesnt have an x and it is just a number it is a small square. after that, you draw a line between each tile, then you will be left with your answer in tiles. the big squre is an x2(squared)and the number of them will be the number in front, if it is a long rectangle then it is an x with the number of them in the front and if it is a small square then it is just a regular number.
this week in math 10 i learned how to find a missing angle in a right triangle. to find the angle the first thing you do is determine whether you use sine, cosine or tangent you do this using the abbreviations SOH CAH TOA the first letter in the abbreviation is which main function you will use (sine, cosine, tangent). the second and third letters are for opposite, hypotenuse and adjacent and which one goes over which for example you have an opposite of 24m long and a hypotenuse of 30m long you would use sine because you only have the opposite(O) and the hypotenuse(H) and 24 would go over 30. after that you move the sin to the other side of the equation but you use inverse sin (sin-1) so its x=sin-1 (24/30) then you use your calculator to determine the answer.
this week in math 10 i learned how to find the missing side length of a right triangle. to do this the first step is to label the hyponenuse, adjacent and the opposite the hypotenuse is the side accross from the right angle, the opposite is the side accross from the angle given and the adjacent is the last side. for step two you find which sides you use for the equation, the two sides you use are the labeled slides. step three you put it into an equation using sin, cos and tan depending on the sides given. for example, tan then the angle = x/the side length given. for step four you multiply both sides of the = by the bottom #. then you are left with somthing like 16(tan34)=x then you type the first part of the equation into your calculator.
this week in math 10, i learned how to find the volume and surface area of a sphere, to find the SA (surface area) you do 4 times /pi times the radias squared. to find the volume you multiply by 4 over 3 by /pi then you multiply it by the radius cubed.
a question i had a problem with was question 9 of lession 9 where you have to find the diameter when you only have the volume, when i got help with it i realized it is super easy you just divide by the first part of the formula (the 4 over 3 and /pi) then you square root the answer to find the radius then multiply it by 2 to find the diameter.
this week in math 10, i learned how to find the surface area of a triangular prism and also all the unit conversions. unit conversions are the thing you need to know most for this unit so it is very important, it tells you the formula you use to convert one measurment into another. to find the surface area of a triangular prism you first find the sum of the area of all the sides, this involves using Pythagorean Theorem and multiplying, the formula for finding the surface area of a triangular prism is 2 times b time height divided by two plus legth time width times legth time width time legth time width then you fill in the spots with the correct numbers and do the equation, then you have your answer.
this week in math 10 i learned all the laws of exponents. there are 5 laws, multiplication, division, power of power, zero exponent law and negative exponents law. the multiplication exponent law (M) is, you add the exponents when the base is the same, the division exponent law (D) is similar, we subtract the exponents when the base is the same. the power of a power exponent law (PP) tells us to multiply exponents by the exponent of the bracket, and you only multiply the exponents inside the bracket. the zero exponent law (Z) is, when the exponent of the number is zero the number becomes 1 no matter what. the fianl rule is the negative exponent law (N) this tells us that when the exponent is negative you find the reciptical and the exponent become posative.