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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 largest factor that two or more numbers have in common.






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






3. Part = Percent x Whole






4. Add the exponents and keep the same base






5. Subtract the smallest from the largest and add 1






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






7. 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






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






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






10. 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






11. 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






12. Probability= Favorable Outcomes/Total Possible Outcomes






13. 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






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






15. Combine like terms






16. 2pr






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






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






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






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






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






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






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






24. Example: If the ratio of males to females is 1 to 2 - then what is the ratio of males to people? - work: 1/(1+2) answer: 1/3






25. 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






26. 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






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






28. 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






29. 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






30. 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






31. The whole # left over after division






32. 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






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






34. 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






35. 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






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






37. 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






38. Volume of a Cylinder = pr^2h






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






40. 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)






41. Factor out the perfect squares






42. pr^2






43. To solve a proportion - cross multiply






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






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






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






47. 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






48. 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






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






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