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






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






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






4. 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






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






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






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






8. 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






9. 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






10. 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






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






13. 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






14. 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






15. Factor out the perfect squares






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






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






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






19. Multiply the exponents






20. The whole # left over after division






21. To solve a proportion - cross multiply






22. 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






23. Notation: f(x) read: 'f of x' evaluation: if you want to evaluate the function for f(4) - replace x with 4 everywhere in the equation






24. 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






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






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






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






28. 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






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






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






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






32. Add the exponents and keep the same base






33. 2pr






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






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






36. 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






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






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






39. 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






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






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






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






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






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






45. Combine like terms






46. 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






47. Subtract the smallest from the largest and add 1






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






49. 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






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