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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. 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






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






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






4. Probability= Favorable Outcomes/Total Possible Outcomes






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






6. 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






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






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






9. Part = Percent x Whole






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






11. 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






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






13. 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






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






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






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






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






18. Add the exponents and keep the same base






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






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






21. 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






22. Subtract the smallest from the largest and add 1






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






24. 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.






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






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






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






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






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






30. 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






31. To solve a proportion - cross multiply






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






33. 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






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






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






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






37. 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






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






39. 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






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






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






42. Volume of a Cylinder = pr^2h






43. Use the sum - Example: if the average of 4 #s is 7 - and the #s are 3 - 5 - 8 - and ____ - what is the fourth #? Work: sum= 4*7 =28 3+5+8=16 28-16=? Answer: 12






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






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






46. 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






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 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 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






50. 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







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