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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. Factor out the perfect squares






2. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






3. Part = Percent x Whole






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






5. 2pr






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






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






8. 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






9. 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






10. 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






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






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






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






14. 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






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






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






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






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






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






20. Probability= Favorable Outcomes/Total Possible Outcomes






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






22. 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






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






24. 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






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






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






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






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






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






30. 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






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






32. 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






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






34. 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






35. To solve a proportion - cross multiply






36. 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






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






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






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






40. Volume of a Cylinder = pr^2h






41. 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






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






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






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






45. 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






46. Start with 100 as a starting value - Example: A price rises by 10% one year and by 20% the next. What's the combined percent increase? - Say the original price is $100. Year one: $100 + (10% of 100) = 100 + 10 = 110 Year two: 110 + (20% of 110) = 110






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






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






49. 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






50. 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