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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. pr^2






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






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






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






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






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






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






8. 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






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






10. 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






11. 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)






12. 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






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






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






15. 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






16. Probability= Favorable Outcomes/Total Possible Outcomes






17. 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






18. 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






19. 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






20. 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






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






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






23. 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






24. Multiply the exponents






25. The whole # left over after division






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






27. 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






28. Combine like terms






29. 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






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






31. Add the exponents and keep the same base






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






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






34. 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






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






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






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






38. If a right triangle's leg-to-leg ratio is 5:12 - or if the leg-to-hypotenuse ratio is 5:13 or 12:13 - it's a 5-12-13 triangle






39. 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






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






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






42. Factor out the perfect squares






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






44. 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






45. 2pr






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. Part = Percent x Whole






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






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






50. 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