SAT Math: Sum of Consecutive Integers

Consecutive Integers are those which occur in numerical order. (like 3,4,5,6,…)

One type of consecutive integer question tells you the sum total of a group of consecutive integers and asks you to find one of these integers.

To answer Sum of Consecutive Integer questions:

1. Divide the sum total by the number of integers to find the midpoint of the sequence.

2. Then count up or down from this midpoint to find the integer asked for by the question.

Example:

Answer and explanation below.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide that test this SAT Math topic.

SAT Math: It’s more important to be accurate than complete

Many students make the mistake of rushing too quickly through the SAT Math section to finish, and in the process miss earlier, easier questions simply because they are not careful enough.

On SAT Math, it’s more important to be accurate than complete.

It’s far more important to answer the SAT Math questions you know correctly, than worry about finishing the entire section. Because SAT Math questions appear in order of difficulty, failing to finish the very last questions on the SAT math section simply means that you haven’t been able to answer the hardest questions.* Better to take a little bit of extra time checking your work on the earlier questions than rush and lose points.

Concentrate on trying to answer the first 2/3 of math questions on each section correctly, and then cherry pick the hard questions. According to the 2007-2008 Official SAT Practice Test raw score conversion table, you only need 67% of the total points to earn a scale score of 600 on SAT Math. This means that you only need to answer 13 or 14 questions correctly on a 20 question section, and skip the rest, to be on track for a 600.

Given enough time, most students can usually answer many of the first 2/3 of SAT math questions in any given section, which are easy to medium difficulty questions. Score as many points as you can on these earlier questions, and then see if there are any hard questions at the end you can answer that will help add to your total.

If you get stuck on a question, skip it and come back.

Every question counts the same regardless of difficulty, so there is no point wasting too much time on any single question when there are other points to the earned.

*Remember:

On the section with both multiple choice and grid-in questions, the questions at the beginning of each of the multiple choice and grid-in parts are the easy questions, while the questions at the end of each part are the hard ones.

From my SAT training guide: SAT Unlocked.

SAT Math: Repeating Sequences (w/ example)

The SAT will occasionally include a sequence where the numbers repeat themselves in a pattern. In repeating sequence questions, you’re usually asked which of the repeating terms lies at a point far down the sequence.

1. Figure out how many terms it takes before the sequence repeats;

2. Divide the number of the term you need by the total number of repeating terms;

3. Use the remainder to find which number in the repeating sequence is the correct term.

Answer and explanation below.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide that test this SAT Math topic.

SAT Math: Geometric Sequences (w/ example)

Sequences which multiply the same number over and over again are known as ‘geometric’ sequences.

Tip:

It is often easier simply to multiply out the geometric sequence until you get to the term you need.

Answer and explanation below.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide that test this SAT Math topic.

SAT Math: Arithmetic Sequences (w/ example)

Sequences which add the same number over and over again are known as ‘arithmetic’ sequences.

Answer and explanation below.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide that test this SAT Math topic.

SAT Math: Number Sequences (w/ example)

The SAT will sometimes include a question that asks you to figure out the pattern of a sequence of numbers.

Read the question carefully for clues as to what the sequence should be. Then plug in numbers for the variables until you get the right combination.

Example:

Answer and explanation below.

Answer:

From my SAT guide SAT Unlocked, which includes a complete list of Official SAT Study Guide practice questions that test this SAT Math topic.

SAT Math: Always Factor the Difference of Two Squares

SAT math tests only basic factoring skills, and you rarely if ever have to factor or FOIL complicated quadratic equations. However, there is one type of quadratic equation you definitely need to be able to recognize and factor for the SAT:

How to factor the difference of two squares:

ALWAYS factor the difference of two squares when you see it.
The SAT test makers just LOVE using the difference of two squares in their questions. Whenever an SAT math question includes the difference of two squares, like a² – 4, factoring the expression, (a + 2)(a – 2), is almost always the key to figuring out the correct answer.

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