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






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






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






4. To solve a proportion - cross multiply






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






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






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






8. Subtract the smallest from the largest and add 1






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






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






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






12. Part = Percent x Whole






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






14. 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






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






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






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






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






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






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






21. pr^2






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






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






24. Combine like terms






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






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






27. 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






28. 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






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. Probability= Favorable Outcomes/Total Possible Outcomes






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






32. 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






33. Volume of a Cylinder = pr^2h






34. 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






35. 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






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






37. 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






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






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






40. 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






41. 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)






42. The whole # left over after division






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






44. 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






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






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






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






48. 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






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






50. Add the exponents and keep the same base