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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 divide fractions - invert the second one and multiply






2. 2pr






3. 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






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






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






6. If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 or 4:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side






7. 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






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






9. 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






10. Combine like terms






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






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






13. 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






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






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






16. 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






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






18. Volume of a Cylinder = pr^2h






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






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






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






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






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






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






25. 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






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






27. 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






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






29. Part = Percent x Whole






30. 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






31. 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






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






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






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






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






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






37. 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)






38. 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






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






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






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






42. 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






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






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






45. 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






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






47. 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






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






49. 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






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