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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 solve a proportion - cross multiply






2. Subtract the smallest from the largest and add 1






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






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






5. 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






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






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






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






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






10. 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






11. 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






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






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






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






15. 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






16. 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






17. The whole # left over after division






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






19. 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






20. Probability= Favorable Outcomes/Total Possible Outcomes






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






22. 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






23. 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






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






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






26. 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






27. Volume of a Cylinder = pr^2h






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






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






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






31. 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)






32. Combine like terms






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






34. 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






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






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






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






38. 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






39. Part = Percent x Whole






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






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






42. A parallelogram has two pairs of parallel sides - opposite sides are equal - opposite angles are equal - consecutive angles add up to 180 degrees; Area of Parallelogram = base x height






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






44. 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






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






46. 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






47. 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)






48. Add the exponents and keep the same base






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