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






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






4. 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






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






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






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






8. 2pr






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






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






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






12. Subtract the smallest from the largest and add 1






13. Add the exponents and keep the same base






14. 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






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






16. 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






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






18. 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






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






20. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






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






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






23. 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






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






25. 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






26. Factor out the perfect squares






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






28. 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






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






30. 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






31. Volume of a Cylinder = pr^2h






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. 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






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






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






36. Combine like terms






37. 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






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






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






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






41. 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






42. 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






43. Probability= Favorable Outcomes/Total Possible Outcomes






44. 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






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






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






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






49. 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






50. pr^2