{"id":5483,"date":"2020-09-11t11:30:51","date_gmt":"2020-09-11t18:30:51","guid":{"rendered":"\/\/www.catharsisit.com\/sat\/?p=5483"},"modified":"2016-11-13t15:11:43","modified_gmt":"2016-11-13t23:11:43","slug":"sat-math-algebra","status":"publish","type":"post","link":"\/\/www.catharsisit.com\/sat\/sat-math-algebra\/","title":{"rendered":"sat math: algebra"},"content":{"rendered":"
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in short, \u201calgebra\u201d refers to any problem that has an algebraic equation in which none of the powers next to a variable is higher than one. for example:<\/p>\n
\\(y + 5 < -1\\)<\/span><\/center><\/p>\n pretty straightforward, right? the computation underpinning algebra is straightforward, but the sat typically won\u2019t be giving you problems this simple. while you will encounter several problems that ask you to solve for variables, much of the algebra content are real-world word problems that you have to unwrap before solving. for example:<\/p>\n five lemonades and two cookies cost $1.50. two lemonades and five cookies cost $2.70. how much do one cookie and one lemonade cost?<\/p>\n (wondering how to solve this equation? read on and you’ll understand how!)<\/em><\/p>\n<\/div>\n <\/p>\n there are two ways to make sure you’re prepared for algebra questions:<\/p>\n to help you get the swing of things, we\u2019ve broken down and demonstrated the key concepts and skills that will serve you on the algebra questions. feel free to explore these concepts through the clickable table of contents below:<\/p>\n <\/p>\n first thing\u2019s first: in order to interpret real-world scenarios as equations, you\u2019ll need to be super clear on how to balance an equation!<\/p>\n so, in an algebraic equation with an equal sign, think of the equation in balance. if you do anything to one side you do the exact same thing to the other side. if you multiply one side by 4, you have to multiply the other side by 4. if you subtract 3 from one side, you subtract 3 from the other side.<\/p>\n the goal in balancing the equation is isolation. that\u2019s right \u2014 you want to isolate x, or get x (or whatever variable happens to be in the equation) by itself. think of the variable as the unpopular person in the room. everyone \u2013 that is, the other numbers \u2013 want to get away!<\/p>\n \\(4x + 3 = 15.\\)<\/span><\/p>\n to get x by itself, first subtract 3 from both sides of the equation.<\/p>\n \\(4x + 3 – 3 = 15 – 3\\)<\/span><\/p>\n \\(4x = 12\\)<\/span><\/p>\n now divide both sides of the equation by 4:<\/p>\n \\(frac {4x} {4} = frac {12} {4}\\)<\/span><\/p>\n \\(x = 3\\)<\/span><\/p>\n let\u2019s try one more:<\/p>\n \\(sqrt{x} = 9\\)<\/span><\/p>\n notice how x has a square root sign on top of it. we want x to be all by itself. therefore we have to get rid of the square root sign by squaring both sides:<\/p>\n \\((sqrt{x})^2 = 9^2 \\)<\/span><\/p>\n \\(x = 81\\)<\/span><\/p>\n the gist? by knowing how to isolate variables by balancing equations, you’re well on your way to success on the algebra section!<\/p>\nhow to prepare for the sat algebra questions<\/h2>\n
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algebra basics: balancing the equation<\/h2>\n