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






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






3. 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






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






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






6. 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






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






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






9. Part = Percent x Whole






10. 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






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






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






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






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






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






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






17. pr^2






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






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






20. 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






21. 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






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






24. 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






25. 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






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






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






28. Multiply te coefficients and the variables separately Example: 2a*3a Work: (23)(aa) Answer: 6a^2






29. 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






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






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






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






33. 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






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






35. 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






36. Factor out the perfect squares






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






38. 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






39. 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






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






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






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






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






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. 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






46. Add the exponents and keep the same base






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






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






49. 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)






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