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






3. 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






4. 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






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






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






7. Factor out the perfect squares






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






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






10. pr^2






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






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






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






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






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






16. 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






17. 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






18. 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)






19. 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






20. 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






21. The whole # left over after division






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






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






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






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






27. 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






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






29. 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






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






31. Subtract the smallest from the largest and add 1






32. 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






33. 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






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






35. 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






36. 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






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






38. 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






39. Add the exponents and keep the same base






40. 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






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






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






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






44. Volume of a Cylinder = pr^2h






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






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






47. The absolute value of a number is the distance of the number from zero - since absolute value is distance it is always positive






48. Probability= Favorable Outcomes/Total Possible Outcomes






49. 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






50. 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