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






2. 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






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






4. 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






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. Multiply the exponents






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






8. 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






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






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






11. Part = Percent x Whole






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






13. 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






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






15. 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






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






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






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






19. 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






20. 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






21. 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






22. 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






23. The whole # left over after division






24. 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






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






26. 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)






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






28. 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






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






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






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






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






33. 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






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






35. 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






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






37. To solve a proportion - cross multiply






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






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






40. pr^2






41. 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






42. 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






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






44. Factor out the perfect squares






45. Volume of a Cylinder = pr^2h






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






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






48. 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






49. Probability= Favorable Outcomes/Total Possible Outcomes






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