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






2. 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






3. 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






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






5. Combine like terms






6. 1. turn it into ax^2 + bx + c = 0 form 2. factor 3. set both factors equal to zero 4. you get 2 solutions






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






8. 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






9. Add the exponents and keep the same base






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






11. The whole # left over after division






12. 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






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






14. 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.






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






16. Factor out the perfect squares






17. 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






18. 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






19. Probability= Favorable Outcomes/Total Possible Outcomes






20. 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






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






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






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






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






25. 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






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






27. 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






28. 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






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






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






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






32. Volume of a Cylinder = pr^2h






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






34. 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






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






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






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






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






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






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






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






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






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






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






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






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






48. pr^2






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






50. 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