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






2. Combine like terms






3. 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






4. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






5. 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






6. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






7. Subtract the smallest from the largest and add 1






8. Volume of a Cylinder = pr^2h






9. To find the prime factorization of an integer just keep breaking it up into factors until all the factors are prime






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






11. 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






12. 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.






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






14. 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






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






16. # associated with of on top - # associated with to on bottom Example: ratio of 20 oranges to 12 apples? Work: 20/12 Answer: 5/3






17. The whole # left over after division






18. 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






19. To solve a proportion - cross multiply






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






21. Domain: all possible values of x for a function range: all possible outputs of a function






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






23. Part = Percent x Whole






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






25. When two lines intersect - adjacent angles (angles next to each other) are supplementary (=180) and vertical angles are equal






26. All acute angles are = all obtuse angles are = any obtuse angle+any acute angle= 180






27. Factor can be divisible (factor of 12 and 8 is 4). Multiple is a multiple (multiple of 12 and 8 is 24).






28. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






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






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






31. Multiply the exponents






32. 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






33. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






34. 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






35. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






36. pr^2






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






38. Combine equations in such a way that one of the variables cancel out






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






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






41. The intersection of the sets of A and B - written AnB - is the set of elements that are in both A and B.






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






43. 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






44. Surface Area = 2lw + 2wh + 2lh






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






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






47. Use this example: Example: after a 5% increase - the population was 59 -346. What was the population before the increase? Work: 1.05x=59 -346 Answer: 56 -520






48. Volume of a Rectangular Solid = lwh; Volume of a Cube= (L)^3






49. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive






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