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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. 2pr






2. Add the exponents and keep the same base






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






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






5. 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






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






7. 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






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






9. 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






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






11. To solve a proportion - cross multiply






12. To combine like terms - keep the variable part unchanged while adding or subtracting the coefficients - Example: 2a+3a=? work: (2+3)a answer: 5a






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






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






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






17. The whole # left over after division






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






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






21. Factor out the perfect squares






22. 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






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






24. 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






25. 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






26. The sum of the measures of the interior angles of a polygon = (n - 2) × 180 - where n is the number of sides






27. 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






28. 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






29. 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






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






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






32. 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






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






34. 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






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. Multiply the exponents






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






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






39. Probability= Favorable Outcomes/Total Possible Outcomes






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






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. 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






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






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






45. 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






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. 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






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






49. 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






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