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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 or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






2. 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






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






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






5. 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






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






7. To solve a proportion - cross multiply






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






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






10. 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






11. Multiply the exponents






12. 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






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






14. The whole # left over after division






15. pr^2






16. 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






17. 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






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






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






20. 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






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






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






23. 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






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






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






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






27. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






30. 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






31. 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






32. 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)






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






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






35. 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






36. 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






37. 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






38. Combine like terms






39. 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






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






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






43. 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






44. 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






45. 2pr






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






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






49. Volume of a Cylinder = pr^2h






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