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






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






3. 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






4. To solve a proportion - cross multiply






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






6. 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






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






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






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






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






11. Volume of a Cylinder = pr^2h






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






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






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






15. 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






16. 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)






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






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






19. 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






20. 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






21. Add the exponents and keep the same base






22. 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






23. 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)






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






25. 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






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






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






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






29. 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






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






31. 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






32. 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






33. Subtract the smallest from the largest and add 1






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






35. 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






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






37. The whole # left over after division






38. 2pr






39. Part = Percent x Whole






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






41. Multiply the exponents






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






43. 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






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






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






46. Factor out the perfect squares






47. 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






48. 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






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






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