Month: April 2017

The eleventh week of Foundations of Mathematics and Pre-Calculus is based on reviewing and understanding the concepts of the previous units for the upcoming midterm. Some important materials from each unit include: prime factorization, great common factors, lowest common multiples, number systems, entire radicals, mixed radicals, exponent laws, integral exponents, rational exponents, substitutions in formulas, referents, conversions, surface area and volume of given objects, trigonometric ratios, using SOHCAHTOA,  solving triangles, multiplying polynomials, simplifying polynomials, finding common factors, factoring trinomials, and difference of squares. The arrangement of these units is made where some the previous unit materials, may be found in further units. For example, great common factor was learned in the Numbers Unit, but reappeared in the Factoring Polynomials Unit. Another example is surface area, volume, perimeter, and area, from the Measurement Unit, which was shown in the Polynomial units for a few word problems. There are far more examples of connections/overlaps between the units.

Image: 

During the tenth week of Foundations of Mathematics and Pre-Calculus, I learned how to factor trinomials in the form  . Some important points to understand before are: if the product is positive, then the two integers must be either both positive or both negative, and if the product is negative, then one integer is positive and the other is negative. To factor  , some things to do first is check if the products are negative or positive. To factor this form, you must know how the FOIL (factored) version, example: , of the trinomial. To factor this, there are easy ways to determine the factored version, find two integers which have a product equal to c, and a sum equal to b. Note: if there is a great common factor in the trinomial, factor it out first, then continue factoring. Finally, always watch if factoring the trinomial is possible.

Image: 

During the ninth week of Foundations of Mathematics and Pre-Calculus, I learned how to multiply three binomials. A binomial is an algebraic expression that consists of two terms, example: . To multiply three binomials, FOIL comes into play. Rather than using FOIL once, after you get your answer with the middle binomial, with your new answer, do it again with the remaining binomial to get the full expansion. For example: , this has three binomials, as discussed in previous lessons, use FOIL for the full expansion. The full expansion of the three binomials above is .

Image: 

During the eighth week of Foundations of Mathematics and Pre-Calculus, I learned how to multiply two binomials. This can be completed by the correct use of distributive property. The method that is used in the distributive property can be simplified into noticing that the four monomial products (a + b)(c + d) = ac + ad + bc + bd can be memorized using the acronym FOIL. For example: , to find this product, simply use FOIL. Your answer is . FOIL stands for F: first term in each bracket, O: outside terms, I: inside terms, and L: last term in each bracket.

Image:

During the seventh week of Foundations of Mathematics and Pre-Calculus, I learned how to use a calculator to find the value of trigonometric ratios. To find trigonometric ratios, you first must have a calculator, and then it must be in degree mode. Then you put your number in your calculator, and choose which ratio you are going to use. On different calculators, the steps of finding the ratio could be reversed to ratio then number. If your number has many decimal places, the most accurate approximation can be to four decimal places. Using this simple method can help you find angles of sides easily on a right triangle. The three ratios I learned were sine, cosine, and tangent.  A helpful acronym that is useful is SOHCAHTOA.

Image: