Tip #8 to Get a Top SAT Math Score

Students come into my office and say, "I can't do this question because I don't know what 'consecutive' means." I get to say, "Oh cool, it just means numbers in a row, like 4, 5, 6." Then the question becomes easy. In fact, for some questions, the only hard part is knowing the vocabulary, and once you know the terms, the questions are easy. That's why I love this strategy; memorize these terms and practice using them in the drills, and you will absolutely gain points, guaranteed. Also, once you know the terms, watch for them and underline them when they appear. That will eliminate many careless errors.

Here are the first nine math vocabulary terms:

Real number—any number: –3, –2.2, 0, , π

Constant term—this term really throws some kids, but it just means a letter in place of a number, kinda like a variable, except that it won't vary.

Integer—number without decimals or fractions: –3, –2, –1, 0, 1, 2, 3,… This is the single most common SAT math vocab word!

Even/odd—even numbers: 2, 4, 6, 8,… ; odd numbers: 1, 3, 5, 7,…

Positive/negative—positive numbers are greater than 0; negative numbers are less than 0.

Consecutive numbers—numbers in a row: 7, 8, 9, 10.

Different numbers—numbers that are… ummm… different.

Prime—a number whose only factors are 1 and itself. 2, 3, 5, 7, 11, 13, 17,… are prime.

Note:

only

Units digit—just a fancy term for the "ones" digit in a number, like the 2 in 672.

Let's look at this question:

Solution: List the primes: 2, 3, 5, 7, 11, 13, 17, 19, 23. Only the number 2 is prime and even. No other primes can be even, since every even number (besides the number 2) has factors other than 1 and itself.

Example Problems

Easy

If 2 consecutive integers have a sum of 9, what is the larger number?
How many different integers satisfy the equation x² = 9 ?
1. 0
2. 1
3. 2
4. 3
5. 4
How many positive integers less than 100 have a units digit of 3 ?
1. 100
2. 50
3. 33
4. 11
5. 10

Medium

If 2 consecutive prime numbers have a sum of 60, what is the larger number?
Two consecutive even integers have a sum of –26. Which of the following must be true?
1. Both numbers are negative.
2. The lesser number is –12.
3. The lesser number is –14.
1. I only.
2. II only.
3. I and III only.
4. II and III only.
5. I, II, and III.

Hard

Let S equal the set of all positive integers less than 12. How many members of S are not consecutive odd prime numbers?

Answers

5 This question simply tests whether you know the words "consecutive" and "integer." Many students do not and wind up intimidated and having to skip this very easy question. Since you know what these two words mean, use simple trial and error to solve this question. 4 + 5 = 9.
C Most people know that since 3² = 9, there is at least one answer to this question. But the term "different" is the keyword here. It is the tipoff that perhaps there is more than one answer. That should be enough to jog your brain to realize that (–3)² = 9 also. So there are two possible answers to the question, 3 and –3.
E Lots of students don't know the term "units digit" and get this wrong; since you know, it's easy. Just list the possibilities: 3, 13, 23, 33, 43, 53, 63, 73, 83, 93.
31 This question intimidates many people. I know so many students who would immediately say, "I have no chance," and move on. I think that this is something the SAT is testing: can you be intimidated? Shout with me now, "NO WAY!" So once we're done with that, this is easy. Just list a bunch of prime numbers: 2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 27, 29, 31 and look for two in a row (consecutive) that add up to 60. So 29 + 31 = 60. Cake, if you stay relaxed, focused, and confident.
C Probably best to just find the 2 numbers. If that seems difficult, "Use the Answers" as hints, that is try –12 and –14. The two numbers are indeed –12 and –14, so I and III are true. II is a trick that the SAT tried and that we can totally predict. –12 might seem less than –14, since 12 is less than 14, but the bigger the negative number, the smaller it is; like the more you owe, the bigger the debt. This sort of trick is discussed more in Skill 43.
8 There are 11 positive integers less than the number 12. How many of these are consecutive odd prime numbers? List the prime numbers that are less than 12: 2, 3, 5, 7, 11. Of these numbers, 3, 5, and 7 are consecutive odd numbers, so 11 – 3 = 8 are not.

Go to: Tip #9

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