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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 find the reciprocal of a fraction switch the numerator and the denominator






2. 2pr






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






4. 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






5. The whole # left over after division






6. Part = Percent x Whole






7. 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






8. 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.






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






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






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






12. Add the exponents and keep the same base






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






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






15. 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






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






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






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






19. 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






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






21. Combine like terms






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






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






24. 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






25. Subtract the smallest from the largest and add 1






26. Multiply the exponents






27. 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






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






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






30. 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






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






32. 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






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






34. 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






35. 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






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






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






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






39. 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)






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






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






42. 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






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






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






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






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






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






48. 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






49. pr^2






50. 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