SAT Problem Solving (General Methods)

Learning to sit for the math part of the SAT exam is comparable to learning to play an Internet game.  Regarding internet games, at first a game seems like a daunting task, but as you begin to understand the game, you develop skills that help you play quickly and skillfully.  The same can be said for the SAT math part.  As you understand the test and how to begin and problems, you will develop test taking skills and you will be able to do problems quickly.  Remember that even though learning to take the SAT can be compared to playing an Internet game, it’s a very serious test since the results can change your life.  The student has to learn not just to do the problems correctly, but also to do them as quickly as possible since time is a limited resource on this exam.

Below are some problem solving approaches and one problem of each type.  I teach the student to solve problems by taking a general approach to a type of problem.  Listed below are general approaches to solving specific problem types and a brief explanations of each.  I’ve included 4 of them, but there are dozens more.

1)  Make it look like problems:  <There are usually 1 to 4 of these on most SAT exams>

If x+ 2y = 8 and x + 3z =10 and y + z = 20 what is the value of 2x + 3y + 4z?

This is a make it look like problem.  The first clue you have is that the problem is less than 1 line long.  99 out of 100 problems that are 1 line long, or less, are make it look like problems.  Make it look like problems require the student to use one of the five familiar operations(+, -, *, /, /\) to convert one or more given statements into what is being asked for.  The student has to first compare what is given with what is asked for and be able to say the differences.  In this example each of the given equations does not have all three variables x, y and z.  The result does.  So you first have to ask yourself how I can use the three given equations to find one equation that contains all three variables.  If you said addition has to be done, you’re halfway home.  Note that this is not taught in school.

Add the three equations giving 2x + 3y + 4z = 38

2)  Arithmetic mean problems.  If the average (arithmetic mean) of x and y is 6 and the average of x, y and z is 20, find z.

Always begin with arithmetic mean = sum/count.

Since 6 = (x+y)/2  => x+y = 12.�� Also 20 = (x+y+z)/3 => x+y+z = 60.  Therefore z = 48

3) Find the area of a square with diagonal 8.  A = d/ 2 (always use this formula when area of a square is requested and the diagonal of the square is given.)

A = 32.  <If you don’t remember this formula, memorize it>

4) Find the hypotenuse of a right triange that has sides of 24 and 45.  The common factor of 24 and 45 is 3 since the sum of the individual digits of both numbers is divisible by 3.  2 + 4 = 6 and 4 + 5 = 9.  24/3 = 8, 45/3 = 15.  Thiis is an 8, 15, 17 triangle so the answer is 3 x 17 = 51.  Students should know the 3-4-5, the 5-12-13 and the 8-15-17 right triangles.  If you don’t know how to use them, you should know.  My students always walk into the SAT exam knowing them.