26 SAT MATH REMINDERS, STRATEGIES, TIPS & SHORTCUTS

math image1. There are only six arithmetic operations tested on the SAT: addition, subtraction, multiplication, division, exponents, and square roots.

2. These operations must be performed in the proper order (PEMDAS), beginning with operations inside parentheses.

3. Apply the distributive law whenever possible. Very often, this is enough to find an answer.

4. A fraction is just another way of expressing division.

5. You must know how to add, subtract, multiply, and divide fractions.

6. In any problems involving large or confusing fractions, try to reduce the fractions first. Before you multiply two fractions, for example, see if it’s possible to reduce either or both of the fractions.

7. If you know how to work out fractions on your calculator, use it to help you with questions that involve fractions. If you intend to use your calculator for fractions, make sure you practice. You should also know how to work with fractions the old-fashioned way.

8. A decimal is just another way of expressing a fraction.

9. Use a calculator to add, subtract, multiply, and divide decimals.

10. A ratio can be expressed as a fraction.

11. Use a Ratio Box to solve ratio questions.

12. A percentage is just a convenient way of expressing a fraction whose bottom is 100.

13. To convert a percentage to a fraction, put the percentage over 100 and reduce.

14. To convert a fraction to a percentage, use your calculator to divide the top of the fraction by the bottom of the fraction. Then multiply the result by 100.

15. 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.

16. In problems that require you to find a series of percentage increases or decreases, remember that each successive increase or decrease is performed on the result of the previous one.

17. To find the average (or arithmetic mean) of several values, add up the values and divide the total by the number of values.

18. Use the Average Pie to solve problems involving averages. The key to most average problems is finding the total.

19. The median of a group of numbers is the number that is exactly in the middle of the group when the group is arranged from smallest to largest, as on a number line.

20. The mode of a group of numbers is the number in the group that appears most often.

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

22. To multiply two exponential expressions with the same base, add the exponents.

23. To divide two exponential expressions with the same base, subtract the exponents.

24. To raise one exponential expression to another power, multiply the exponents.

25. 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.

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

ADDITIONAL MATH TIPS:

  1. POE — Look for wrong answers and GUESS.
  2. Plug-in or Backsolve (Look at answers and see if you can plug them into the question)
  3. When your answers are listed as a sequence, start with C.
  4. Substitute for variables.
  5. Approximate / Estimate
  6. Write out all calculations.
  7. Draw — create visuals!
  8. If you have time, try a different way.
  9. Check form of answer…..Go to the answers and see what is being asked for.
  10. Every problem has a shortcut; always look for shortcuts.
  11. Diagrams are not drawn to scale; redraw to get perspective.
  12. Don’t rush through easy problems just to get to difficult.
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