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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. Expressed A?B (' A union B ') - is the set of all members contained in either A or B or both.






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






3. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






6. 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






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






8. 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






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






10. 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






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






12. This is the key to solving most fraction and percent word problems. Part is usually associated with the word is/are and whole is associated with the word of. Example: 'half of the boys are blonds' whole: all of the boys part: blonds






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






14. Add the exponents and keep the same base






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






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






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






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






19. 2pr






20. 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






21. 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






22. 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






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






24. 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






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






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






27. 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






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






30. 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






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. 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






33. 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






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






35. Combine like terms






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






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






38. 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






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






40. 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.






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






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






43. 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






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






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






46. 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






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






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






49. Part = Percent x Whole






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