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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. 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






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






4. 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






5. Volume of a Cylinder = pr^2h






6. Part = Percent x Whole






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






8. 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






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






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






11. Probability= Favorable Outcomes/Total Possible Outcomes






12. The whole # left over after division






13. pr^2






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






15. 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






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






17. 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






18. 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






19. Multiply the exponents






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






22. 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






23. 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






24. 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






25. 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






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






27. Factor out the perfect squares






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






29. 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






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






31. 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)






32. 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






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






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






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






36. 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.






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






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






39. 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






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






41. Combine like terms






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






43. 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






44. 2pr






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






46. Add up numbers and divide by the number of numbers - Average=(sum of terms)/(# of terms)






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






49. To solve a proportion - cross multiply






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