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SAT Math: Concepts And Tricks

Subjects : sat, math
Instructions:
  • Answer 50 questions in 20 minutes. 1 minute extra for reading the instructions.
  • 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. 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)






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






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






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






5. 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






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






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






8. 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






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






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






11. 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






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






13. Add the exponents and keep the same base






14. 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






15. Combine like terms






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






17. 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






18. Subtract the smallest from the largest and add 1






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






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






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






22. 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)






23. To add a positive and negative integer first ignore the signs and find the positive difference between the two integers - attatch the sign of the original with higher absolute value - to subtract negative integers simply change it into an addition pr






24. To solve a proportion - cross multiply






25. Volume of a Cylinder = pr^2h






26. To predict whether the sum - difference - or product will be even or odd - just take simple numbers such as 1 and 2 and see what happens; there are rules like 'odd times even is odd' - but there's no need to memorize them






27. 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






28. 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






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






30. 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






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






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






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






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






35. Factor out the perfect squares






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






37. 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






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






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






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






41. 2pr






42. 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






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






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






45. 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






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






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






48. 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






49. Multiply the exponents






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