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






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






3. Add the exponents and keep the same base






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






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






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






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






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






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






10. 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






11. 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






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






13. 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






14. 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)






15. Volume of a Cylinder = pr^2h






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






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






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






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






20. 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)






21. 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






22. Part = Percent x Whole






23. Factor out the perfect squares






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






25. 2pr






26. 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






27. 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






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






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






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






31. 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






32. 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






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






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






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






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






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






39. If there are m ways one event can happen and n ways a second event can happen - then there are m × n ways for the 2 events to happen






40. Multiply the exponents






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






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






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






45. 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






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






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






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






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