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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 multiply fractions - multiply the numerators and multiply the denominators






2. 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






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






4. 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






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






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






7. 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






8. A sector is a piece of the area of a circle. If n is the degree measure of the sector's central angle then the formula is: Area of a Sector = (n/360) (pr^2)






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






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






11. 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






12. 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






13. To solve a proportion - cross multiply






14. 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






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






16. 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






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






18. 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






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






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






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






22. 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






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






24. 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






25. 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






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






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






28. 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






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






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






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






32. Add the exponents and keep the same base






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






34. Factor out the perfect squares






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






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






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






38. 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






39. pr^2






40. Part = Percent x Whole






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






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






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






44. 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






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






46. 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






47. Combine like terms






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






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






50. 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