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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. 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






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






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






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






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. 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






7. Integers are whole numbers; they include negtavie whole numbers and zero - Rational numbers can be expressed as a ratio of two integers - irration numbers are real numbers that cant be expressed precisely as a fraction or decimal.






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






9. 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






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






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






12. Multiply the exponents






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






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






15. 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






16. Factor out the perfect squares






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






18. 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






19. To solve a proportion - cross multiply






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






21. Add the exponents and keep the same base






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






23. 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






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






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






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






27. 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






28. Probability= Favorable Outcomes/Total Possible Outcomes






29. 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






30. 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






31. 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






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






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






34. pr^2






35. 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






36. 2pr






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






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






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






40. 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






41. Volume of a Cylinder = pr^2h






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






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






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






45. 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






46. Part = Percent x Whole






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






48. The whole # left over after division






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






50. Surface Area = 2lw + 2wh + 2lh