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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 15 minutes.
  • If you are not ready to take this test, you can study here.
  • Match each statement with the correct term.
  • Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Combine equations in such a way that one of the variables cancel out






2. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






3. The largest factor that two or more numbers have in common.






4. Average the smallest and largest numbers Example: What is the average of integers 13 through 77? Work: (13+77)/2 Answer: 45






5. The length of one side of a triangle must be greater than the difference and less than the sum of the lengths of the other two sides






6. Part = Percent x Whole






7. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






8. Change in y/ change in x rise/run






9. To solve an inequality do whatever is necessary to both sides to isolate the variable. When you multiply or divide both sides by a negative number you must reverse the sign






10. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)






11. Subtract the smallest from the largest and add 1






12. Divisible by 2 if: last digit is even - divisible by 4 if: last two digits form a multiple of 4






13. To reduce a fraction to lowest terms - factor out and cancel all factors the numerator and denominator have in common






14. Volume of a Cylinder = pr^2h






15. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






16. A rectangle is a four-sided figure with four right angles opposite sides are equal - diagonals are equal; Area of Rectangle = length x width






17. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






18. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9






19. When a line is tangent to a circle the radius of the circles perpendicular to the line at the point of contact






20. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






21. Add the exponents and keep the same base






22. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






23. To add or subtract fraction - first find a common denominator - then add or subtract the numerators






24. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






25. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






26. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






27. Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional






28. 2pr






29. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides






30. Negative exponent: put number under 1 in a fraction and work out the exponent Rational exponent: square root it- 1. make the root of the problem whatever the denominator of the exponent is 2. the exponent under your root sign is the numerator of the






31. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






32. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






33. you can add/subtract when the part under the radical is the same






34. Parentheses - Exponents -Multiplication and Division(reversible) - Addition and Subtraction (reversible)






35. To divide fractions - invert the second one and multiply






36. The median is the value that falls in the middle of the set - the mode is the value that appears most often






37. To find the reciprocal of a fraction switch the numerator and the denominator






38. To solve a proportion - cross multiply






39. For all right triangles: a^2+b^2=c^2






40. A decimal with a sequence of digits that repeats itself indefinitely; to find a particular digit in the repetition - use the example: if there are 3 digits that repeat - every 3rd digit is the same. If you want the 31st digit - then the 30th digit is






41. Multiply the exponents






42. To evaluate an algebraic expression - plug in the given values for the unknowns and calculate according to PEMDAS






43. A square is a rectangle with four equal sides; Area of Square = side*side






44. To convert a mixed number to an improper fraction - multiply the whole number by the denominator - then add the numerator over the same denominator - to convert an improper fraction to a mixed number - divide the denominator into the numerator to get






45. 1. Re-express them with common denominators 2. Convert them to decimals






46. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






47. Factor out the perfect squares






48. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)






49. The whole # left over after division






50. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






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