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






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






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






4. 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






5. 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)






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






7. To solve a proportion - cross multiply






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






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






10. Volume of a Cylinder = pr^2h






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






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






13. Add the exponents and keep the same base






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






15. 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






16. 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






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






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






19. pr^2






20. 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






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






22. 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






23. Part = Percent x Whole






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






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






26. 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)






27. 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






28. 2pr






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






30. 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






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






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






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






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






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






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






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






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. 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.






40. 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






41. 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






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






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






44. 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






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






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






47. 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






48. 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






49. Subtract the smallest from the largest and add 1






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