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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. 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






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






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






4. 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






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






6. 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






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






8. A square is a rectangle with four equal sides; Area of Square = side*side






9. 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






10. pr^2






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






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






13. 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.






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






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






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. To solve a proportion - cross multiply






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






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






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






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






23. 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






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






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






26. Multiply the exponents






27. 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






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






29. 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)






30. 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






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






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






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






34. 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






35. 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






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






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






38. 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






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






40. 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






41. Volume of a Cylinder = pr^2h






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






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






44. 2pr






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






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






47. Part = Percent x Whole






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






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






50. 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)