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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. Multiply the exponents






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






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. Part = Percent x Whole






6. Subtract the smallest from the largest and add 1






7. 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






8. 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






9. 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






10. Add the exponents and keep the same base






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






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






13. Combine like terms






14. 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






15. 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






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






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






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






19. 2pr






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






21. 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






22. 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






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






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






25. pr^2






26. 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






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






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






29. To solve a proportion - cross multiply






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






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






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






33. 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






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






35. 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






36. 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






37. 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






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






39. The whole # left over after division






40. Factor out the perfect squares






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






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






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






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






45. 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






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






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






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






50. 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