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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. 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






2. 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






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






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






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






6. 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






7. 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






8. 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






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






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






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






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






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






14. Volume of a Cylinder = pr^2h






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






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






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






18. Combine like terms






19. The whole # left over after division






20. pr^2






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






22. 2pr






23. 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






24. 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






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






26. 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






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






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






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






30. Add the exponents and keep the same base






31. 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






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






33. 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






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






35. 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






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






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






38. 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






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






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






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






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






43. Subtract the smallest from the largest and add 1






44. 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






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






46. 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






47. Factor out the perfect squares






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






50. Divisible by 3 if: sum of it's digits is divisible by 3 - divisible by 9 if: sum of digits is divisible by 9