Algebra Math Presentation
Transcript: List of variables with: no equals sign - expression equaks sign - equation inequality sign ( greater than or less than) - inequality # Expression Description 1 a ± b A number (b) added to or subtracted from another number (a) 2 (a ± b) ± c Expression #1 plus or minus another number (c) 3 (a ± b)^c Expression #1 multiplied by itself (c) amount of times 4 ab A number multiplied by another number 5 (ab)^c Expression #4 multiplied by itself (c) amount of times 6 ab ± c Expression #4 plus or minus another number (c) 7 ab/c Expression #4 divided by another number (c) 8 (a ± b)/c Expression #1 divided by another number (c) 9 a/b A number (a) divided by another number (b) 10 a^b/c A number (a) multiplied by itself (b) amount of times then divided by another number (c) 11 √ a The square root of a number (a) Equations that involve fractions To solve you need Lowest Common Denominator Distributive Law Equations which have a range instead of an equal sign Solved the same as a linear equation Graphed For example: “A farmer has c chickens, e eggs, 2 roosters, and n nests. The number of eggs is 2 times the number of hens, the number of hens is 3 more than the number of nests, and the number of nests is 10 times the number of roosters. How many eggs are there?” You would rewrite it as: e = 2h, h = n + 3, n = 10 x 2. n = 20, so e = 2 x (20 + 3) e = 46 Some Formulae to remember (a + b)^2 = a^2 + 2ab + b^2 (a – b)^2 = a^2 – 2ab + b^2 (a + b)(a – b) = a^2 – b^2 (x + a)(x + b) = x^2 + (a + b)x + ab “(a+b)^c” has the coefficient pattern of Pascals Triangle where to the 0 is 1 and the exponent pattern of a^c, c-1, c-2, etc until 0 and b^0, 0+1, 0+2, etc until c. Uses the balance method Does the same thing to both sides but reverses the sign (positive to negative) Also known as exponent laws They explain how to simplify exponents in an equation Replacing a variable with a number Often occurs when some numbers and one variable are in a question You rewrite the question in terms of the variable and solve Or you can check your work by going through and replacing the variable with your answer Simplifying For example: a > 2 is graphed as a < 2 is graphed the same but facing the other direction a >= 2 is the same line but the circle is coloured in Problem Solving For example: (2 + x)(7 + y) = (2)(7) + (2)(y) + (x)(7) + (x)(y) = 14 + 2y + 7x + xy = xy + 7x + 2y + 14 For example: a + a + b + b you could simplify it as 2a + 2b because if you count it up there are 2 “a”s written and 2 “b”s. Whereas a x a = a^2, a x a x a = a^3, etc. Mixture Problems For example: 3^a = 27 we need to have 27 as a power of 3. We know that it is 3^3 so we know that 3^a = 3^3 so a = 3. a^0 = 1 but only if a != 0 a^-b = 1/a^b 1/a^-b = a^b a^-1 = 1/a a^b/c = c√a^b Exponential Equations a^b x a^c = a^(b+c) a^b / a^c = a^(b-c) (a^b)^c = a^bc (ab)^c = a^c b^c (a/b)^c = a^c/b^c For example: “How much water(a) must be added to 1L of 5% cordial to make a 4% cordial mixture?” a + 95% x 1 = 96% x (a + 1), a/1 x 100/100 + 95/100 = 96/100 x a + 95/100, 100a + 95 = 96a + 96, 100a – 96a = 96 – 95, 4a = 1, a = 1/4L For example: 5x + 7 = 32 5x +7 – 7 = 32 – 7 5x = 25 5x/5 = 25/5 X = 5 Notation Linear Equations Index Laws Algebra When the variable is in the exponent Solved the same as linear equations Rational Equations Substitution Gathering like terms Values are only sepatated by addition or subtraction signs Any multiplication or division can be simplified. Upon completion order answer form greatest to lowest Incorporates rewriting equations in terms of a variable Involve using one equation to solve another Taking a word problem and turning it into an equation then solving it This is done by: determining the variable(s) determining the operations writing it out solving it For example: In 5 years, I will be twice as old as I am today. How old am I? Unknown: age = x Operation: +, x Written out: x + 5 = 2x Solve: x + 5 – 5 = 2x – 5 x = 2x – 5 x = 5 Problem solving tool that uses letters to represent unknown values called variables For example: 5^1/2 = 2√5 (the square root of 5 to the 1) Equations Linear Inequations Expanding brackets One acronym is FOIL: First, Outside, Inside, Last Meaning you multiply the values in that order
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