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






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






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






4. 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






5. 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






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






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






8. 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






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






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






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






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






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






14. 2pr






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






16. 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






17. Probability= Favorable Outcomes/Total Possible Outcomes






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






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






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






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






22. 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






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






24. An isosceles triangle has 2 equal sides and the angles opposite the equal sides (base angles) are also equal - an equaliteral is a triangle where all 3 sides are equal - thus the angles are equal - regardless of side length the angle is always 60 deg






25. 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






26. pr^2






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






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






29. Subtract the smallest from the largest and add 1






30. 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






31. 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






32. 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






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






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






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






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. 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






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






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






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






42. Add the exponents and keep the same base






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






44. 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)






45. Volume of a Cylinder = pr^2h






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






47. 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






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






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






50. 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