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






2. 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






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






4. 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






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






6. 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






7. Part = Percent x Whole






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






9. The whole # left over after division






10. 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






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






12. pr^2






13. Direct variation: equation: y=kx - where k is a nonzero constant trick: y changes directly as x does inverse variation: equation: xy=k trick: y doubles as x halves and vice-versa






14. Combine like terms






15. 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






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






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






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






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






20. 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






21. 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






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






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






24. 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






25. 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






26. 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






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






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






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






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






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






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






33. 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






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






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






36. 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






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






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






39. 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






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






41. Subtract the smallest from the largest and add 1






42. 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






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






44. Add the exponents and keep the same base






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






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. 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






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






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






50. An arc is a piece of the circumference. If n is the degree measure of the arc's central angle - then the formula is: Length of an Arc = 1 (n/360) (2pr)