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






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






3. 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






4. Combine like terms






5. 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






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






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






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






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






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






11. 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






12. 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






13. 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






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






15. Probability= Favorable Outcomes/Total Possible Outcomes






16. 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






17. Volume of a Cylinder = pr^2h






18. 2pr






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






20. Part = Percent x Whole






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






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






23. Subtract the smallest from the largest and add 1






24. 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






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






26. Add the exponents and keep the same base






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






28. 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






29. 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






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






31. 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






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






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






34. To find the y-intercept: put the equation into slope-intercept form (b is the y-intercept): y=mx+b or plug x=0 and solve for y - To find the x-intercept: plug y=0 and solve for x






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






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






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






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






39. 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






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






41. 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






42. 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






43. 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)






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






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






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






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






48. 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.






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






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