Twenty-five years ago, only a few kids studied for the SAT. The rest of us just showed up and did our best. But as the competition to get into college has gotten stiffer, the test stakes have risen. Today, it’s all but required for students to spend time and money on preparing for this important exam.

I know from personal experience that practicing pays off. As a private SAT math tutor, I regularly saw students improve their math scores by ten to twenty percent. There was no magic – just the students’ commitment to hard work.

So has it become necessary to enroll your child in an expensive program? There’s no doubt that businesses like Kaplan and The Princeton Review give their students a leg up, especially when it comes to information on the new writing section. But if your child is motivated, it’s possible for him to study independently for the math section of the SAT. For insight on this option, we interviewed award-winning math teacher Gregg Whitnah. Mr. Whitnah has taught SAT preparation courses for twenty-eight years, in both private and group settings. Here are some tips he offered about how to prepare.

  1. Before taking the SAT, complete Algebra and Geometry. It’s optimal to have also taken the first few weeks of Algebra II.
  2. Carve out plenty of time to practice. Plan on at least thirty hours of studying for the math section alone.
  3. Buy the College Board book, ‘The Official SAT Study Guide.’ It offers a complete list of the topics that will be tested, as well as practice problems and eight real tests. Take all of the practice tests from start to finish; it’s the best way to become familiar with the instructions and organization of the test.
  4. Get to know the test format. The math test has three sections, each lasting twenty to twenty-five minutes. Most questions are multiple-choice, but a few are free-response. Each section starts out easy and gets progressively harder. It’s important to remember that the easy questions are worth just as much as the hard ones; it does no good to get #25 right if you are going to miss #1.
  5. Beware of guessing; the SAT doesn’t reward random guesses. Getting a multiple-choice question wrong deducts a quarter to a third of a point from your score. Test makers are good at creating ‘wrong answers.’
  6. Don’t rely on computer preparation programs alone because they don’t simulate the test experience. It’s important to practice with paper-and-pencil materials.

Next, your student needs to get to know which areas of math to study. The specific topics listed by the College Board are numerous, but can be grouped into the following categories: Computations, Algebra, Probability/Statistics, Functions, and Geometry. Below are five practice problems that demonstrate the types of questions on the test. You can find other free problems on the College Board's SAT Question of the Day.

Computation: A student’s test scores are 70, 90, 65, 85, and 75. What score must she get on the next test to raise her average to 80?

a) 73      b) 85         c) 90         d) 92.5      e) 95
 

The correct answer is e. An average is defined as the sum of the parts, divided by the number of parts. We can therefore write the equation: 80 = (70+90+65+85+75+x)/6. Simplifying further, we get: 80 = (385+x)/6. Solving for x, we get 480 = 385+x, or x=95.

Algebra: If x+y = 7 and x-y = 10, then 2x =
 

a) 70        b) 17       c) 3          d) -3         e) -17

The correct answer is b. This is an example that shows how the test makers offer chances to be clever. Most people approach this problem by using substitution to isolate and solve for x. But the skillful student saves time by seeing that she only needs to add the two equations, because the y-terms cancel each other.
 
   x+y = 7
+ x-y = 10
                       2x = 17
 

Probability/Statistics: Two marbles are drawn at random without replacement from a jar containing 8 red marbles and 6 red marbles. What is the probability of drawing two red marbles?

This is a student response question. Please fill in the answer grid below:

 
 
 
 

The correct answer is:

4
/
1
3

The probability of an event can be written by the following fraction:

(The Number of Desired Outcomes)/ (The Number of Possible Outcomes)

In this problem, there are 14 marbles total. The probability of drawing the first red marble is 8/14. Once it is gone, the probability of drawing the second red marble is 7/13. Because we need both to happen, we multiply the two fractions to get 56/182, which reduces to 4/13.

Functions: Find the point at which the function f(x) = 3x-4 intersects the line y = 5.

        a) (5, 3)         b) (0, 5)       c) (-3, 5)       d) (3,5)          e) (0, 4/3)

 The correct answer is d. Students with graphing calculators might solve this problem by setting f1 = 3x-4, and f2 = 5. By studying the graph, they could find the point of intersection. But it’s also easy to solve with old-fashioned methods. In the Cartesian coordinate system, points are listed as (x,y.) So if our point is on the line y=5, the point must be (x, 5). Then, we must find the value of x which makes 3x-4 = 5. Solving, we get 3x=9, or x=3. Therefore, the correct point is (3,5).

Geometry: If p, q, and r are the degree measures of the three angles of an isosceles triangles and p = 100, then q = ??

This is a student response question. Please fill in the answer grid below:

 
 
 
 

The correct answer is:

 
 
4
0


This problem requires two geometry facts. First, that an isosceles triangle has two equal sides and two equal angles. And, that the angles in any triangle add up to 180. If p = 100, then there are 80 degrees left. So q+r = 80, and since q and r must be equal, q = r = 40.

As you can see from just these five problems, there’s a lot of review to do before your student takes the SAT. She’s sure to benefit from a formal course, or you can collect your own materials and set aside time at home. But one thing is for certain – there’s no shortcut for practice when it comes to helping your student do her best on what might be the most important test she’ll ever take.