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






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






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






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






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






7. 2pr






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






9. 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






10. 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






11. The whole # left over after division






12. 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






13. 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






14. To increase: add decimal version of percent to one and times that # to the # you want to increase. Example: increase 40 by 25% Work: 1.25*40=? Answer: 50






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






16. 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






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






18. 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






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






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






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






22. Probability= Favorable Outcomes/Total Possible Outcomes






23. 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)






24. Add the exponents and keep the same base






25. 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






26. 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






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






28. Combine like terms






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






30. Part = Percent x Whole






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






32. 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






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






34. Use special triangles - pythagorean theorem - or distance formula: v(x2-x1)²+(y2-y1)²






35. 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






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






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






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






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






41. Multiply the exponents






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






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






44. 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






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






46. 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






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






48. 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






49. To solve a proportion - cross multiply






50. 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






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