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






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






3. Add the exponents and keep the same base






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






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






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






7. pr^2






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






9. 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






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






11. 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






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






13. 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






14. 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






15. Subtract the smallest from the largest and add 1






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






17. 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






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






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






20. 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






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






22. Volume of a Cylinder = pr^2h






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






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






25. Multiply the exponents






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






27. 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






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






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






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






31. 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)






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






33. Factor out the perfect squares






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






35. Combine like terms






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






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






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






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






40. 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






41. 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






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






43. 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






44. Probability= Favorable Outcomes/Total Possible Outcomes






45. The whole # left over after division






46. 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






47. 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






48. 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.






49. 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






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