There are only 6 arithmetic operations tested on the SAT: Addition Subtraction Multiplication Division Exponents Square roots Remember PEMDAS

Apply the distributive law * wherever possible…often this is enough to find ETS’ answer. * If you’re multiplying the sum of two numbers by a third number, you can multiply each number in your sum individually.

A fraction is just another way of expressing division. You will need to know how to add, subtract, multiply and divide fractions. Before you multiply two fractions, for example, see if you can reduce either or both fractions.

What about the calculator? If you know how to do fractions on it, use it to help you with fraction related questions. Be sure to practice both ways…just in case…know how to do them with pencil and paper too.

A decimal is just another way to express a fraction. Use your calculator to add, subtract, multiply and divide decimals.

Exponents are shorthand for expressing numbers that are the product of the same factor multiplied over and over again.

- To multiply two exponential expressions with the same base, add the exponents. - To divide two exponential expressions with the same base, subtract the exponents. - To raise one exponential expression to another power, multiply the exponents.

To remember the exponent rules, think MADSPM. MultiplyAdd DivideSubtract PowerMultiply

 When you raise a positive number greater than 1 to a power greater than 1, the result is larger.  When you raise a positive fraction less than 1 to an exponent greater than 1, the result is smaller.

A negative number raised to an even power becomes positive. A negative number raised to an odd power remains negative.

 When you’re asked for the square root of any number, you’re being asked for the positive root only.

Here are the only rules regarding square roots that you need for the SAT:

 One part of the math section will contain 10 questions called “Student produced responses.” We call ’em grid-ins.  Why?  Because your answer sheet has little grids in which you write your answers.  Here are a few tips for using the grids…

 Write the numbers in the boxes at the top of the grid before filling in the ovals below.  Be careful to correctly fill in the ovals  Always begin writing your answer in the far left box at the top of the grid.

 If the answer has a fraction or decimal, you can grid it in either way – no need to convert  There is no need to round decimals  If you have a long or repeating decimal (as in ) be sure to fill up all the spaces in the grid.  There is no need to reduce fractions

 The ETS scoring machine does not recognize mixed numbers so…  Convert mixed numbers to decimals or fractions before gridding in.  Some grid-in questions will have more than one correct answer. It doesn’t matter which one you choose.  There is no guessing penalty on grid-in questions.

 Negatives, , square roots and % cannot be gridded in.  Grid-ins are in easy, medium, hard order.  In each group of 10, the first third is easy, the second third is medium and the last third is hard.  Remember, Joe Bloggs applies to grid-ins too.

Ratios Percentages Decimals Averages, Medians, & Modes Probability Permutations

A ratio can be expressed as a fraction, but ratios are not fractions A ratio compares parts to parts; a fraction compares a part to the whole Use a ratio box to solve ratio questions.

There are half as many girls in Mr. Radcliff’s class as there are boys. There 8 girls in the class. How many students are there in the class?

Direct proportion is x 1 /y 1 = x 2/ y 2. Indirect proportion is x 1 y 1 = x 2 y 2

Percentage is just a convenient way of expressing a fraction whose bottom is 100. To convert a percentage to a fraction, put the percentage over 100 and reduce.

To convert a fraction to a percentage, use your calculator to DIVIDE the TOP NUMBER of the fraction BY the BOTTOM NUMBER. Next multiply the result by 100.

To convert a percentage to a decimal, move the decimal point two places to the left.

To convert a decimal to a percentage, move the decimal point two places to the right.

Gotta find a series of percentages? Remember: Each successive increase or decrease is performed on the result of the previous one.

Need to find the percent of increase or decrease? Use % change = difference/original X 100

To find the mean or average of several values, add up the values and divide by the number there are.

Use the average pie to solve problems involving averages. The key to most average problems is finding the total.

The median of a group of numbers is the one in the middle of the group when the group is arranged from smallest to largest:

If there is an even number of numbers, the median is the average of the two middle numbers:

The mode of a group of numbers is the number that appears most often:

Probability is expressed as a fraction Probability of x = number of outcomes that are x total number of possible outcomes

To find permutations or possible orders of objects, use factorials. A factorial is the whole series of integers counting down from the given numbers, all multiplied together.