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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. 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






2. To solve a proportion - cross multiply






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






4. Volume of a Cylinder = pr^2h






5. 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






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






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






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






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






10. 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






11. 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






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






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






14. Factor out the perfect squares






15. pr^2






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






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






18. 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






19. 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






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






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






22. 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






23. 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






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






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






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






28. 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






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






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






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






32. 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






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






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






35. 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






36. 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






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






38. Add the exponents and keep the same base






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






40. The whole # left over after division






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






42. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






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






44. 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






45. 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






46. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






50. 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