SAT Mathematics Test

To identify the skills that need extra work, complete a practice SAT 

test that gives additional information, and have a look at the evaluation 

that is produced and look at the areas where you excelled, and the 

areas where struggle was apparent. 

Your "critical" math skills will be in the areas where you have made the 

most wrong answers on your practice SAT test. Those will be the math 

skills that will best help your score in the shortest period of time, if 

you manage to practice and better these skills.  This is the area in 

which you can maximize your score increase potential. 

To master your critical math skills, there are certain steps you may 

take: 

• Find some practice SAT tests and work specifically on the questions that test your critical math skills, practicing the new skills that you have learned in through your review. 
• Use textbooks for increased detail, assistance, and question examples for the areas in which you are struggling the most. 
• Practice, practice, practice! 

The best way to get to learn your math skills is to rehearse them with 

as many new sample questions as you can get your hands on.  The 

questions you do, the more you will become familiar and comfortable 

with that type of question, so that you can move on and concentrate 

on other areas for perfection. 

Mathematical Reasoning 

There are two different mathematics sections in the PSAT, each 

containing a different kind of question.  These are: 

• Standard Multiple-Choice
• Hand-calculated responses (with Grid-ins) 

Within each section, the questions become increasingly difficult as you 

proceed. Therefore, the first few questions will always be much easier 

to solve than the last few questions will be. 

To give you an idea as to the types of questions presented, please 

consider the following examples: 

Standard Multiple-Choice 

Standard multiple-choice questions are made up of either word 

problems, algebraic manipulations, or geometry.  Here is a sample of a 

word problem: 

If one-sixth of all female students at Princeton like chips, and one- 

third of Princeton's male students have nachos.  Therefore, what 

fraction of the entire student population likes chips? 

A. 1/9 

B. 1/3 

C. 5/18 

D. 10/18 

E. It cannot be determined from the given information 

(Note: The answer would be E, this type of question acquaints you with the fact that all question in the SAT do not necessarily have an answer to them!) 

Hand-calculated responses (with Grid-ins) 

These questions are similar to the Standard Multiple Choice Questions. 

The difference is that you acquire the answer and enter it directly on 

the grid.  These problems are not difficult to solve, and as you become 

familiar with them, they do become easier.  Basically all you need to 

know is how to enter your answers onto the grid. 

Here are the rules for grid-ins.  Each column represents a digit from your 

answer, and each column has a specific purpose.

Also, as both decimals and fractions are acceptable, you don't have to 

worry about the format of your answer.  For example, the scoring 

machine will accept both 0.5 and ½, so feel free to enter whichever 

format is most comfortable to you. 

However, the grid machine doesn't understand mixed numbers, so if 

your answer is 2 ½ then you'll either have to mark it as 5/2 or 2.5. 

As the grid does not accept negative answers, you know that none of 

the answers will be negatives. 

So should your answers be: 

1) 5/16 and  2) 5.6 

You will properly mark them in in the following way: 

Question Types 

The test is very consistent with the type of mathematics questions that 

it uses, year after year.  The following are the types of mathematical 

questions that you are likely to encounter: 

• Arithmetic 
• Divisibility 
• Multiplication 
• Addition 
• Subtraction 
• Evens and Odds 
• Prime Numbers 
• Percents 
• Square of a Number 
• Exponents 
• Roots 
• Averages 
• Arithmetic 

Arithmetic skills refer to the questions that can be solved by using 

addition, subtraction, multiplication and/or division. 

Since calculators are permitted in the test, the questions will obviously 

not be purely arithmetic - they're not out to measure your ability with 

a calculator.  So in this style of question, you'll need to recall your 

order of operations.  A good trick to recall your order of operations is 

 "Please Excuse My Dear Aunt Sally" before you say "huh?" recognize 

the first letters in this phrase: 

• Work within Parenthesis 
• Simplify Exponents 
• Multiplication and Division 
• Addition and Subtraction 

The majority of arithmetic questions will require you to take multiple 

steps, and will likely test other skills as well, instead of being purely 

arithmetic.  Often, the questions will be presented in the form of word 

problems, where you will need to decide when to add, subtract, 

multiply and divide. 

For example: 

How many egg cartons are needed to hold 300 eggs, if each carton 

can hold one dozen (1 dozen = 12) 

A. 15 

B. 18 

C. 22 

D. 25 

E. 28 

Note:  the answer is 25 

Divisibility 

The factors of integer X are the integers by which X can be divided 

without leaving a remainder.  Thus, X is divisible by its factors. 

For example: 

The number 10 is divisible by both 5 and 2.  10 can be divided by both 

of these integers without leaving a remainder. 

To review the rules of divisibility, have a look at the following: 

font-size: 1