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






2. 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






3. Combine like terms






4. Multiply the exponents






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






6. 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)






7. 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






8. 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






9. Add the exponents and keep the same base






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






11. pr^2






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






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






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






15. 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






16. 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






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






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






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






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






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






22. 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






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






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






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






26. 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






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






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






29. 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






30. 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






31. 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






32. Volume of a Cylinder = pr^2h






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






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






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






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






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






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






39. The whole # left over after division






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






41. 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






42. 2pr






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






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






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






46. Subtract the smallest from the largest and add 1






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






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






49. 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






50. 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