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 Topic Helpful Information Example Absolute Value Absolute value = the distance a number is from 0 on a number line The absolute value of 5 and -5 equals 5 because they are both 5 units from 0 Axiom-Additive axiom If a > b, then a + c > b + c. Axiom-Positive multiplication axiom: If c > 0, then a > b   if, and only if, ac > bc. Axiom-Transitive axiom If a > b and b > c, then a > c Binomials-Multiplying two binomials Formula = (a+b) (c+d) =ac + ad + bc + bd Use the FOIL method First Outside Inside Last (b+2) ( b +3) F b*b = b2 O b*3 = 3b I 2*b =2b L 3*2 =6 Combine: b2 + 5b +6 Combining like terms In order to combine they must have like variables and exponents. 1. Place like terms together. 2.Combine each set 3. Put the answers to each combine set together 2a + 4b + 5a – 2b - 2c + 4c Step 1.2a + 5a +4b – 2b -2c + 4c Step 2. 2a + 5a= 7a 4b -2b =2b 4c -2c =2c Step 3. Combine 7a + 2b + 2c Equations-Linear equations Slope-intercept form y = mx +b Standard form ax + by =c Y = 3x + 9 where m=3 and b=9 4x + y = 20, a=4 and b=1 and c = 20 Equations-Solving Equations Step 1 All variables can be moved to the left of the equal sign and the numbers can be on the right.   Move integers by adding the opposite sign of the integer. Step 2. Divide both sides by the coefficient. Step 1. 2b + 3 =7 -3 -3 Step 2 2b = 4 b =2 Equations-Solving literal equations Step 1 The desired variable should be on the left Place all other variables on the right of the equal sign by adding opposites Step 2 Divide both sides by the value of any other variable on the left to “isolate” the desired variable. Solve for a x = aw aw =x a =x/w Equations-Writing Equations Look for key words, for example “the product of” means you should place the constant before a variable “less than” and “ more than” means you should flip the order Substitute equal when you see “is” If there are not any key words create an equation in the order that the words are written. The product of 5 and x is 14 5x = 14 y more than three is 15 3 + y =15 Ten less than x is 5 x - 10 = 5 The sum of 11 and y is 13 11 + y =13 Exponents   And Rules for Exponents Exponents tell you how many times to use the number in multiplication   The Rules xm * xn = x(m+n) (xn)m = x(nm) (xy)m = xmym 3^2 = 3*3 =9 3^3 = 3*3*3= 27 3^4 = 3*3*3*3 = 81     22 * 23 = 2(2+3) = 25 (23)2 = 2(2*3) = 26 (2*3)3 = 23*33 = 8*27 = 216 Exponents-Negative exponents Move the term to the denominator, make the exponent positive then apply the power. 3-2 = 1/3*3 = 1/9   3-3 = 1/3*3*3= 1/27