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






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






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






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






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






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






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






10. 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






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






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






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






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






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






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






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






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






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






20. Growth pattern in which the individuals in a population reproduce at a constant rate; j-curve graph-- logarithmic - FORMULA: y=a(1+r)^ EXPLANATION: a = initial amount before measuring growth/decay r = growth/decay rate (often a percent) x = number of






21. Subtract the smallest from the largest and add 1






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






24. 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






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






26. 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






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






28. 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






29. 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






30. Combine like terms






31. 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)






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






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. 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






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






36. 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






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






38. 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






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






40. Factor out the perfect squares






41. To multiply fractions - multiply the numerators and multiply the denominators






42. Add the exponents and keep the same base






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






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






45. (average of the x coordinates - average of the y coordinates)






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






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. The whole # left over after division






49. 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






50. Area of Triangle = 1/2 (base)(height) - the height is the perpendicular distance between the side that's chosen as the base and the opposite vertex