Posts Tagged ‘SAT Math’

Discounts and Rate Increases – A Great SAT Strategy

March 29th, 2010 by Marty Rafson

I’ve walked into stores with my wife and she sees a $60 dress but there’s a sign that says there’s a 20% discount on this price. Since I’m a math teacher, she will turn to me and ask what this dress would cost after the discount. Most people will multiply $60 * .20 giving a discount of $12, and then subtract $60 minus $12 yielding the final cost of $48. Absolutely correct – yet, this is not how we at ESC want our students to handle this situation on an SAT test. Ask yourself: If they are reducing the price by 20%, what percent do you pay? Since everything starts at 100%, when you subtract the 20% discount, you actually pay the other 80%. So, just multiply $60 * .80 and you instantly get the final price of $48 (no subtraction necessary since you already subtracted the 20% from 100%).

Now, let’s consider this situation. A woman is earning $60,000 per year but she is getting a promotion and a 20% salary increase. What is her new salary? Similar to the above situation with discounts, we certainly can multiply $60,000 * .20 giving her a salary increase of $12,000 and when we add that to her current salary of $60,000 she will now be getting $72,000. However, once again, there’s a classic SAT strategy. You must always view the current situation as starting at 100% so this additional 20% brings us to 120%. The decimal for 120% is 1.20, so just multiply $60,000 * 1.20 immediately giving the new salary of $72,000.

These strategies are not just useful for the SAT, but they are also great for everyday real-world situations.

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.

A Critical SAT Math Topic: Percent of Change

March 22nd, 2010 by Marty Rafson

The Educational Testing Service has cleverly figured out that students are not sufficiently familiar with the topic of percent of change. Consider this simple problem:

A store owner raises the price of an item from $40 to $50. By what percent did he increase the price? There is a formula that every student must know for the SAT:

Percent of Change = (Change/Original) * 100

In the case of this problem, the price increased by $10, so that’s the change. The classic question that students always have trouble with is whether to put that $10 over the $40 or over the $50. It’s always over the ORIGINAL. Thus, we put 10/40 = .25 * 100 giving us 25%. Then, there’s an interesting follow-up that has appeared on past SAT tests. Suppose this store owner now decides to be nice and bring the price back down to $40. Well, if he had raised the price by 25% surely he must now be lowering the price by the same 25%, right? Wrong!!! Let’s go back to our formula. He is now dropping the price by the same $10 but now the “original” price at the start of the new problem is $50. Therefore, we must put 10/50 this time, giving us .2 * 100, or a 20% decrease in price. Fascinating!

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.

Defeating an SAT Math Question: Plugging in Numbers

March 19th, 2010 by Marty Rafson

Consider this grid-in problem:

If 3x + 2y = 16, what is the value of 9x + 6y?

Suppose you don’t see the solution at first. Since it’s a grid-in problem, there are no choices to try so you might think that you are out of business (remember you do get a penalty-free guess on a grid-in question). Is there anything else you can try? Yes, try plugging in some numbers. The equation 3x + 2y = 16 has an infinite number of solutions. For instance, x=2 and y=5 are “good” numbers since 3 (2) + 2 (5) = 16. Now, just take those values and plug them into 9x + 6y giving you 9 (2) + 6 (5) = 48. Grid the answer 48 and you get your one point for this problem. What was the “pure solution to the problem? Ask yourself how the expression 9x + 6y was chosen. It is precisely 3 times the original expression 3x + 2y or 3 (3x + 2y) = 9x + 6y. Just calculate 3 * 16 = 48 and you’re done!

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.

Can’t Solve the SAT Math Problem? Try the Choices

March 15th, 2010 by Marty Rafson

Every student would like to find a “pure” solution to every problem. However, as SAT math questions get harder, it becomes virtually impossible to find this pure mathematical solution. If you can’t solve the problem outright, what should you do? Train yourself to try the choices.

Consider this problem:

A calculator company finds that 2% of all its calculators are defective. In a certain shipment, 16 defective calculators were found.  How many calculators were in this shipment?

 (A) .32     (B) 8     (C) 80     (D) 800     (E) 8000

If you can’t solve this directly, look at the choices. SAT choices are always arranged in order, usually ascending from left to right. A good strategy is to try choice C first, since it is the “middle-sized” choice. Try .02 * 80 = 1.6. This tells you that your choice was too small. Therefore, next try choice D and do .02 * 800 giving you exactly 16 proving choice D was right. Whenever you defeat an SAT question with a strategy like trying the choices, you might in the back of your mind wonder what the pure solution was (although, you got the same one point for bubbling in choice D). Here, one method of solution would have been to write and solve the equation .02x=16 and division by .02 gives x=800.

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.

SAT Math Grid-In Questions: Strategy

March 10th, 2010 by Marty Rafson

When the Educational Testing Service created the “grid-in” questions they faced a new dilemma. While every other question on the math, reading and writing sections was a 5-choice question carrying a ¼ point penalty for a wrong response, what should the penalty be for an incorrect answer to a grid-in question? The penalty for a wrong answer is a deterrent to guessing. What would a student’s chances be of randomly guessing the answer to a grid-in question? With no choices to select from, the probability of guessing the right answer is virtually zero. Thus, it was decided that there is no penalty for an incorrect answer to a grid-in question. Of course, if a student gets a question wrong, he doesn’t get the one point he would have gotten for answering it correctly. However, if a student can’t determine the answer, absolutely go ahead and guess freely, since there is truly no penalty. The grid-ins are scored by just counting how many of these 10 questions you get right and no deduction for the wrong ones. Furthermore, even if you don’t get to finish the last, toughest grid-ins like #17 and #18, just fill in your favorite number. In fact, even if the proctor says to stop working on that section, while you can’t go back and solve the problems later, you can at any time fill in your favorite guess for any grid-in problem that you hadn’t gotten to before being told to put your pencil down.

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.

SAT Math Grid-In Questions – Know the Questions

March 8th, 2010 by Marty Rafson

The “Student Produced Response Questions”, or “Grid-In” questions, are unique to the SAT. These 10 questions can be critical in determining a student’s SAT math score. Therefore, it is essential that every student knows the directions perfectly (and not by reading them on the day of the test). Since the answers are recorded in the four-column grid, 9999 is the largest possible answer to any problem. The least possible answer is zero since the directions explicitly state that there are no negative answers. A classic student question is what to do if your answer contains less than four digits. You can place your answer in any column(s) of the grid; the SAT folks only want to see that you’ve got the right answer. The directions clearly state that some problems may have more than one answer. Therefore, a student shouldn’t sit there with a solution such as x > 3 and wonder what to grid. Just pick your favorite number greater than 3 and move on quickly. 

Mixed numbers are absolutely not to be bubbled into the grid. This is because a scanner can’t tell the difference between 2½ and 21/2. Use 2.5 or 5/2 if you think the correct answer is 2½. Lastly, be sure you know what to do if you think the answer is a non-terminating decimal. Here again, the SAT folks are trying to be nice. As long as you fill all the columns of the grid, they don’t care if you “truncate” your decimal (a good SAT word meaning to cut off the decimal when you run out of room) or properly round off your decimal.

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.

The SAT Math Grid-In Questions – A Brief History

March 7th, 2010 by Marty Rafson

Standardized tests such as the SAT receive a variety of criticism. One classic comment is that these tests just show who is best able to choose the right multiple choice answer. Who says that this is necessarily the brightest person? In the early 1990’s to partially address this critique, the Educational Testing Service sought to create math questions without multiple choices. However, the SAT exam does have to be graded by a scanner, not hand-scored. How could this be done? In 1993, we had the first appearance of the Student Produced Response Questions (students have to “produce” their own responses, not just select a choice). The answers to these questions would be placed in a new four-column grid. Each problem contained no multiple choices. The grid would provide a way for students to enter whatever answer they had determined. In the later SAT revision of 2005, 10 “grid-in” questions took their permanent place as questions #9 through #18 on the 18-question, 25-minute math section.

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.

The 18-Question Math Section – The Key to Your SAT Math Score

March 4th, 2010 by Marty Rafson

One of the 3 math sections of the SAT contains 18 questions. The first 8 are multiple choice and the last 10 are “grid-ins” (more on these later). The 8 multiple choice questions are again arranged in almost perfect order of increasing difficulty – #1 is easy and #8 is quite difficult. The problem on this 18-question section is the fact that the hard questions like #7 and #8 are sitting right in the middle of the section. Once again, the student must be honest about his/her potential score. If you’re a candidate for a 700, you need to attack every question. What if you’re shooting for a 500 which requires about half the questions to be answered correctly? To be candid, you should SKIP #7 and #8. Students are always told not to spend too much time on a problem that they find difficult. Correct. However, #7 and #8 are guaranteed to be difficult, so we say the average student should spend zero time on them. Right after #8, you will find the start of the 10 grid-in questions. They begin easy, then come the medium ones and end with the hardest. You need to preserve time for these grid-ins. If you waste time on #7 and #8, you’re taking time away from grid-ins that you can definitely do if you left yourself enough time. The 18-question math section is the key to your math score and not spending too much time on the first 8 multiple choice questions is the key to handling this section.

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.

Time Versus Score – Strategy on SAT Math Sections

February 28th, 2010 by Marty Rafson

SAT’s are scored in the range from 200-800. The national average math score is approximately 500. Many students enrolled in SAT prep classes are seeking to improve to a score over 500. Some students are unaware of the fact that a score of 500 is achieved by getting about ½, 50%, of the questions right. If a student scores 50% on a classroom math test, that’s an “F” (and trouble with parents at home). Half right on the SAT is 500, the national average, and quite respectable. SAT math sections are arranged with the questions almost in perfect order of increasing difficulty. Approximately the first 1/3 are easy, the next 1/3 medium difficulty, and the last bunch are downright difficult. Consider the 20-question, 25-minute section. If a student is seeking a 500, s/he would want 10 points out of this section (each correct answer is worth one point). Where will these points come from? A conscientious SAT prep company has to be blunt here – these points are not coming from that last group of hard questions. These are just too hard for the average student. Therefore, your best strategy is to take your time and plan to spend your 25 minutes on the first 15 questions. It is out of this group of easy and medium level questions that you will find the 10 points you are seeking. Rushing to get through all 20 is silly for the average student because those last 5 are guaranteed to be hard every time. Incidentally, you would need about 2/3 of the questions correct to score 600. Even then, all you would need is to get all the easy and medium ones right. To get 700, you need to attack all the questions (about 48 of the 54 points on the full math test is needed for a 700).

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.

SAT Math Prep

February 26th, 2010 by Marty Rafson

What do the letters SAT stand for? Right now they are just three letters. However, they used to represent the “Scholastic Aptitude Test.” Why isn’t this used as the present-day name of this test? There’s a sensitivity to using the word “aptitude.” An aptitude test is a test of your intelligence, your basic ability. After working hard to compile a solid high school transcript, this single four-hour test helps tell a college what capabilities you have. The Educational Testing Service used to say that you can’t possibly increase your aptitude. This has been dramatically proven wrong. A well-planned program of practice will increase your SAT score. Educational Services Center can help you maximize your score on the reading, writing, and math sections of the SAT. There’s a strategy to approaching the math questions. We’ll review your arithmetic, algebra and geometry. We’ll also show you how to employ other approaches when you don’t see a “pure” mathematical solution to a problem. With dedicated practice, you can definitely improve your SAT score.

Marty Rafson wrote the ESC math curriculum and has been an SAT math teacher, tutor, and curriculum developer for 30 years. He has been a high school math teacher for 36 years and a math department chairman for 25 years. He was also an adjunct professor at City College of New York School of Education.