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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 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






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






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






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






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






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






7. Add the exponents and keep the same base






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






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






10. To solve a proportion - cross multiply






11. 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






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






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






14. 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






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






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






17. 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






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






19. 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






20. 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






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






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






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






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






25. 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






26. 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






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






28. 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






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






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






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






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






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






34. 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






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






36. Combine like terms






37. 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






38. The whole # left over after division






39. 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






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






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. To divide fractions - invert the second one and multiply






43. Part = Percent x Whole






44. 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






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






46. 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






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






48. 2pr






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






50. 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.