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### 11 Cards in this Set

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 What is the best way to solve problems with unspecified amounts? Pick numbers. Example: If the length of the side of a cube decreases by two-thirds, by what percentage will the volume of the cube decrease? Solution: Pick numbers! Volume of cube = s^3 = 27 Therefore s = 3. If side decreases by 2/3 therefore 1/3*3 = 1 New volume = 1^3 = 1 Percent change = (27-1)/27 = 96.3% What is the general formula for a sequence who's terms are seperated by a constant? kn+x k is the difference between successive terms. n is the nth term. x is a real number. If the difference between successive terms is always the same, the rule wil take the form of kn+x, where k and x are real numbers and k is equal to the difference between successive terms. Example: 16, 20, 24, 28 The difference between the terms is 4 (i.e k=4). kn+x 4+x=16 x=12 Thus the formula is 4n+12 What is the general formula for a sequence who's terms are seperated by a constant of a constant? If the difference between thedifference between successive terms is always the same, the rule will take the form of an^2+bn+c, where a, b, and c are real numbers. Example: 18, 27, 38, 51 9, 11, 13 2, 2 Thus since the difference of the difference is a constant we know that the sequence will take the form an^2+bn+c Thus the first term in the sequence is a(1)^2+b(1)+c=18 Thus the second term in the sequence is a(2)^2+b(2)+c=27 Thus the third term in the sequence is a(3)^2+b(3)+c=38 Thus we have 3 equation and 3 unknown we can solve for a, b and c. a(1)^2+b(1)+c=18 a(2)^2+b(2)+c=27 a(3)^2+b(3)+c=38 Therefore a = 1, b = 6 and c = 11. Thus the formula for this sequence is n^2+6n+11. When would you use another method to determine a sequence? If the problem seems to require too much computation consider an alternative method. Example: If each number in a sequence is three more than the previous number, and the sixth number is 32, what is the 100th number? Solution: We know that S6=32 and we know that between 100th term and the 6th term there are 94 jumps of 3. Thus 94*3=282 Therefore the 100th term must be 282 units greater than the 6th term. (i.e S100=32+282 = 314) What can an absolute value be thought as? The distance from zero. Example: abs(-5) = 5 or five units from 0. What is the best way to visualize inequalities problems? Draw a number line. What is the best way to solve combined inequality problems when no real numbers are given? Line them up and use LICHLUC. List Change Line up Combine Example: Give the ur, ft is b>u? List and Change: u ab=144/cd Thus ab-2= 144/cd-2 Simplfying results in (144-cd)/cd and multiplying both numerator and denominator by "a" yields: a(144-cd)/(acd) which is D.