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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 smallest multiple (other than zero) that two or more numbers have in common.






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






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






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






5. 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






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






7. Sum=(Average) x (Number of Terms)






8. 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)






9. Subtract the smallest from the largest and add 1






10. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






11. Multiply the exponents






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






13. 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






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






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






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






17. 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






18. pr^2






19. 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






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






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






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






23. 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






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






25. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






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






27. The 3 angles of any triangle add up to 180 degrees - an exterior angles of a triangle is equal to the sum of the remote interior angles - the 3 exterior angles add up to 360 degrees






28. Factor out the perfect squares






29. Part = Percent x Whole






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






31. Add the exponents and keep the same base






32. To find the slope of a line from an equation - put the equation into slope-intercept form (m is the slope): y=mx+b






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






34. 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






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






36. To solve a proportion - cross multiply






37. Volume of a Cylinder = pr^2h






38. Average A per B: (total A)/(total B) - Example: average speed formula - total distance/ total time - Basically: Don't just average the 2 speeds






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






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






41. 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






42. 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






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






44. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






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






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






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






48. The whole # left over after division






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






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