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






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






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






4. 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






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






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






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






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






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






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






11. 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






12. Multiply the exponents






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






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






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






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






17. 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






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






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






22. 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)






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






25. Add the exponents and keep the same base






26. To solve a proportion - cross multiply






27. 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






28. 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






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






30. Combine like terms






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






32. Probability= Favorable Outcomes/Total Possible Outcomes






33. Part = Percent x Whole






34. 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






35. 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






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






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






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






39. 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






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






41. 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






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






43. 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






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






45. pr^2






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






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






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






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






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