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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. 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






3. Probability= Favorable Outcomes/Total Possible Outcomes






4. 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






5. 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






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






7. Combine like terms






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






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






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






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






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






13. 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






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






15. pr^2






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






17. 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






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






19. Multiplying: multiply the #s inside the root - but KEEP the ROOT sign - dividing: divide the #s inside the root - but KEEP the ROOT sign






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






21. 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






22. Subtract the smallest from the largest and add 1






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






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






26. 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






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






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






29. 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






30. 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)






31. Factor out the perfect squares






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






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






34. 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






35. Volume of a Cylinder = pr^2h






36. 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






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






38. Add the exponents and keep the same base






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






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






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






42. 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






43. 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






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






45. 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






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






47. 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






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






49. 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






50. 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