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






2. 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)






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






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






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






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






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






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






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






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






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






12. 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






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






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






16. Volume of a Cylinder = pr^2h






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






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






19. 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






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






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






22. Factor out the perfect squares






23. To solve a proportion - cross multiply






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






25. 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






26. 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






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






28. Add the exponents and keep the same base






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






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






31. 2pr






32. 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






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






34. Part = Percent x Whole






35. 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






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






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






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






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






40. The whole # left over after division






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






42. 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






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






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






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






46. 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






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






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






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






50. 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