on All of these five things are critical for Math 10, if you want success in the course. Spending time and effort on these five things will help you perform well in all math courses.
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on During the fifteenth week of Foundations of Mathematics and Pre-Calculus, I learned how to use the slope formula to calculate the slope of line segments. Slope is the measure of the steepness of a line. Slope is the ratio of the vertical change over the horizontal change (rise over run). To calculate slope use the slope formula: m= y2 – y1 over x2 – x1 (m stands for slope). Although, if a variable is given rather than a number, find the value of the variable to calculate the missing length by applying the value of the slope. Labeling the y and x values first can help.
Slope Formula:
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on During the fourteenth week of Foundations of Mathematics and Pre-Calculus, I learned how to use Function Notation to determine values. If the function “f” maps an element x in the domain to an element y in the range, you can write f: x -> y. Note: f(x) does not mean f times x. To determine values using Function Notation, a formula must first be given. Once the formula is given, you can determine the x if f(x) is given, or you can determine the value of f(x) if x is given. If f(x) is given, replace it with the variable. If f(x) is not given, but a number that is equal to it, use the formula of the function to determine f(x). You can write a function in the form f(x) = 2x + 1, it also means y = 2x + 1.
Good To Know:
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on During the thirteenth week of Foundations of Mathematics and Pre-Calculus, I learned how to identify functions. Identifying functions is not to difficult, there are only a few things you need to do. The ways to can identify functions are arrow diagrams, ordered pairs, and graphs. On arrow diagrams, if one input is mapped to more than one output, it’s not a function. For ordered pairs, if the input value is repeated, it’s not a function. Finally, for graphs any vertical line that crosses the graph at more than one place, it’s not a function. This method is called the vertical line test. Some things to know first are: input, output, domain, and range.
Mapping Example:
Ordered Pairs Example:
Graph Example:
Which ones are functions?
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on During the twelfth week of Foundations of Mathematics and Pre-Calculus, I learned how to represent the relations between two quantities. To represent two quantities, there are six different ways that can be represented. The ways are: in words, a table of values, a set of ordered pairs, a mapping diagram, an equation, or a graph. These diagrams can help you find the independent and dependant variables, as well as the inputs and outputs. Therefore, these ways can show the relations, then you can determine further values of different numbers. In my opinion the best way to determine relations is using a graph, and then checking your answers by using an equation, but first the table of values for the first set of numbers should be completed.
Different Ways To Represent Relations:
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on 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.
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on 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.
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on 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 
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on 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.
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