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






2. 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






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






4. The whole # left over after division






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






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






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






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






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






10. 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






11. 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)






12. Combine like terms






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






14. 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)






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






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






17. Multiply the exponents






18. Volume of a Cylinder = pr^2h






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






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






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






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






23. 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






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






25. 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.






26. Factor out the perfect squares






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






28. 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






29. 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






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






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






32. To multiply or divide integers - firstly ignore the sign and compute the problem - given 2 negatives make a positive - 2 positives make a positive - and one negative - and one positive make a negative attach the correct sign






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






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






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






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






37. 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






38. 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






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






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






41. Integers that have no common factor other than 1 - to determine whether two integers are relative primes break them both down to their prime factorizations






42. Add the exponents and keep the same base






43. 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






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






45. 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






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






47. 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






48. 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






49. 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






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