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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. 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






2. 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






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






4. 2pr






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






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






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






8. 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






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






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






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






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






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






14. Factor out the perfect squares






15. 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






16. To divide fractions - invert the second one and multiply






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






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






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






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






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






22. 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






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






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






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






26. Part = Percent x Whole






27. 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






28. 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






29. Volume of a Cylinder = pr^2h






30. Multiply the exponents






31. 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.






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






33. 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






34. 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






35. 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






36. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






40. 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






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






42. The whole # left over after division






43. 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






44. pr^2






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






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






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






48. 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






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






50. 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