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






2. Use units to keep things straight (make sure you use 1 unit for each thing) Example: use just inches in your cross multiplication - not inches and feet






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






4. The whole # left over after division






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






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






7. 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






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






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






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






11. Factor out the perfect squares






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






13. Combine like terms






14. 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






15. 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






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






17. 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






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






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






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






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






22. pr^2






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






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






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






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






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






28. 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






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






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






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






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






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






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






35. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






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






37. Probability= Favorable Outcomes/Total Possible Outcomes






38. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






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






40. 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






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






42. 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






43. 2pr






44. 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






45. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






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






47. 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)






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






49. 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






50. Subtract the smallest from the largest and add 1