Crackin’ the Math

On hard math questions, Joe Bloggs is attracted to the quick, easy answers…

Don’t go there!

Use your knowledge of this to eliminate the answers that seem too easy.

Joe is also attracted to answers that simply repeat numbers from the question…

Don’t go there!

Scratch through those choices on hard questions.

On hard questions asking you to find the least or greatest number THAT FULFILLS CERTAIN CONDITIONS, the least or greatest number among the answer choices will NOT be the answer.

Scratch through them.

On hard problems you can almost always eliminate

the answer choice that says, “It cannot be

determined from the information given.”

Use Joe to help you eliminate answer choices and increase

your odds of getting the correct answer.

THE CALCULATOR

- You should use a calculator on the SAT.- Use one that you are familiar with. This is NOT the day to try out a new one.- You do not need a fancy calculator. - Make sure your calculator does not beep or have a typewriter style keyboard (qwerty pad)

Even if you already use a calculator all the time, practice with it the day before the test to be sure you remember how the functions

work.

Watch what you are doing as you key in numbers. Look at the display screen to be sure you tap the right key.

Hit the clear button after each problem.

A calculator can’t help you find the answer if you don’t understand the problem.

Use your calculator as a tool, not a crutch.

It can actually cost you more time if you use it for things you can really do on your own.

Set up the problem on paper first.

This will:- Eliminate the possibility of getting lost or confused- Save time since you won’t have to go back and repeat things if you forget where you are.

AVOID the memory function on your calculator…write in the test booklet (your scratch paper).

Why?

See previous page.

Remember:

Whether you are using calculator, pencil and paper…or your fingers (: >), you must always use the proper order.

PLEASE EXCUSE MY DEAR AUNT SALLY

And remember:

Put in new calculator batteries a day or two before the test!

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METIC

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

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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.

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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.

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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.

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A decimal is just another way to express a fraction.

Use your calculator to add, subtract, multiply and divide decimals.

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

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- 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.

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To remember the exponent rules, think MADSPM.

Multiply AddDivide SubtractPower Multiply

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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.

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

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

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

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Grid-ins

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…

A sample grid

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 1.3636363636) 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, p, 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.

ADVANCED ARITHMETIC•Ratios•Percentages•Decimals•Averages, Medians, & Modes•Probability•Permutations

Ratios•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?

Proportions

•Direct proportion is x1/y1 = x2/y2.

•Indirect proportion is x1y1 = x2y2

Percentage•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.

Percentage•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.

Percentage

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

Percentage

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

Percentage

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

Percentage

Need to find the percent of increase or decrease?

Use % change = difference/original X 100

Mean

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

The Average Pie

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

Median

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:

1 2 4 8 3 7 5 6 9

Median

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

1 3 5 8 4 0 5 7

Mode

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

2 1 4 6 5 8 3 9 3 4 0 2 3

Probability

Probability is expressed as a fraction

Probability of x =

number of outcomes that are xtotal number of possible

outcomes

Permutations•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.