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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 solve a proportion - cross multiply






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






3. Combine like terms






4. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






7. 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






8. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






9. 2pr






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






11. 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






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






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






14. 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






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






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






17. 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






18. 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






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






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






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






22. 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






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






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






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






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






27. 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






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






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






30. 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






31. 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






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






33. 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






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






35. pr^2






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






37. 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






38. The whole # left over after division






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






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






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






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






43. Volume of a Cylinder = pr^2h






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






45. 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






46. 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






47. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






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






49. Part = Percent x Whole






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