<p>Are the hard type questions mostly one of a kind of types? (meaning, you won't see them again?) if so, how should i study besides just doing them?</p>
<p>No, SAT questions’ ‘styles’ often repeat. Best thing to do is to do many practice problems and expose yourself to as many ‘styles’ as possible.</p>
<p>Master the fundamentals of all math up to Algebra 2/Trigonometry and you’ll have the skill-set to tackle any “hard” questions.</p>
<p>I think it’s important to look at alternate solutions. Sometimes we get so stuck in reaching for our calculator and solving the hard questions with traditional classroom strategies. But many of them have simple solutions that take a matter of seconds to perform. Once you start to see these simple solutions work, you’ll come at the questions with a different perspective. Realizing this helped me pull up my math score and increase my confidence on the most difficult questions.</p>
<p>The hard questions often “look” very different, but the same strategies can be applied over and over. This is why it is so important to learn all of the SAT specific math strategies. After that it’s important that you practice implementing these strategies as often as possible. You will then start to see patterns, and then the problems will start to “look” the same, even though the words are quite different.</p>
<p>is there a list of strategies here somewhere?</p>
<p>We have 8 general strategies, but they are applicable to different types of questions, regardless of difficulty.</p>
<ol>
<li><p>ANALYZE the Answer Choices
You should always look at the answer choices briefly before starting a question, because they can provide clues about the solution. For example, if the answers all have pi in them, you’ll need to find the area of a circle, the circumference of a circle, or the volume of a cylinder. If the answers are all square roots and the question involves a triangle, expect to use the Pythagorean theorem. I fell victim to this on the SAT back in 2005, when I was just starting my study of the test. The last question had 3 circles and asked for the distance between two lines. The answers all had root 2 or root 3, indicating I needed to find a 45:45:90 or 30:60:90 triangle. Still makes me mad I missed that question because I didn’t ANALYZE.</p></li>
<li><p>BACKPLUG the Answer Choices
If the question is algebraic in nature and the answers are all numbers, try plugging each answer in for the requested variable. Works especially well with exponents, remainders, absolute value and inequalities. </p></li>
<li><p>SUPPLY Numbers
This is by far my most used strategy. When the question gives you a rule (x < 0 or a is a positive even integer), SUPPLY a number to satisfy that rule. Use a small number to avoid a large result. Avoid using 0 and 1 though as they have special properties when multiplied or squared. For the hardest questions, be sure to test several numbers, especially negative numbers, fractions, and negative fractions. The test makers often count on you just SUPPLYING one number for the hard questions.</p></li>
<li><p>TRANSLATE from English to Math
Great strategy for those stronger in verbal skills. And a necessity for most percentage problems on the SAT. The most important translation to know is “of = multiply.” And the most mis-translated phrase is “what percent.” The correct translation is “what percent = x/100.” This is a basic strategy.</p></li>
<li><p>RECORD What You Know
This can mean two things: first, if a problem uses a word that has a formula, immediately write down that formula. You need it. For example, if the problem tells you that the area of the square is 16, write down “area = s^2.” Or if it says the average of x, y, and z is 48, write down “sum/# of #s = average.” It can also mean to to apply familiar values to variables. If the question is “How old will a person be exactly 1 year from now if exactly r years ago the person was s years old?” use your own info. If your age now is 17, then your age one year from now is 18. Let r = 5 years, so r years ago you were 12. Thus, s = 12. Now, go through each answer choice to find the one that equals 18. </p></li>
<li><p>SPLIT the Question into Parts
This is a basic strategy, but one that many students forget. Many algebraic questions, especially function questions, need to be solved in 2 or 3 steps. </p></li>
<li><p>DIAGRAM the Question
The SAT is designed to mess with your short term memory. This is why many figures are only partially labeled. If information is provided in the text (like AB = 6), be sure to illustrate the facts in the pre-existing figure. Also, if a pre-existing figure “is not drawn to scale,” check that it’s at least close to scale. If it isn’t, redraw it. The SAT often makes equilateral triangles look like tall isosceles triangles. Finally, if there isn’t a figure at all, draw one if it will help you solve the question. You may need to provide a figure for counting problems, number lines, geometry, coordinate geometry, and logic questions. </p></li>
<li><p>SIZE UP the Figure
For geometry questions, learn what some benchmark measurements (30, 45, 60, 90, 120, etc) look like so that you can make educated guesses on figures that are drawn to scale. Also use the given lengths of figures to guess at the lengths of other sides in the figure. You can also learn to estimate the area of an entire figure given the area of a portion of the figure and vice versa. You should almost always guess on Geometry questions in which a figure is present. You can also SIZE UP coordinate geometry questions to guess line length, coordinates, and slope. This strategy should be used only in guessing situations or as a way to corroborate your answer. </p></li>
</ol>
<p>Hope that helps!</p>