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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. Volume of a Cylinder = pr^2h






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






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






4. 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






5. 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






6. 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






7. 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






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






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






10. 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






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






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






13. 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






14. 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






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






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






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






18. 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






19. 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






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






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






22. 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.






23. 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






24. 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






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






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






27. Factor out the perfect squares






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






29. 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






30. The whole # left over after division






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






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






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






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






35. pr^2






36. 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






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






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






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






40. 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






41. 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






42. 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






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






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






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






46. 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






47. 2pr






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






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






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