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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. Add the exponents and keep the same base






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






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. 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






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






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






7. 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






8. Multiply the exponents






9. To divide fractions - invert the second one and multiply






10. 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)






11. pr^2






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






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






15. 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






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






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






18. 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






19. 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






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






21. To solve a proportion - cross multiply






22. 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






23. 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






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






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






26. 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.






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






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






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






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






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






32. The whole # left over after division






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






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






35. 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






36. 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






37. 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






38. 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






39. 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)






40. Probability= Favorable Outcomes/Total Possible Outcomes






41. Part = Percent x Whole






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






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






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






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






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. Factor out the perfect squares






48. 2pr






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






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