problem solving in math
TRANSCRIPT
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PROBLEM SOLVINGYeah, this is for real.
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RULES 1. Be attentive. 2. Compute.3. CP's/calculators are not allowed.4. Listen.5. Enjoy.
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GEORGE POLYA'S PROBLEM SOLVING TECHNIQUES Understand the problem.Device a plan. Carry out the plan.Look back.
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PATTERNSNEED FOR DIAGRAMNEED FOR SIMPLER PROBLEM
TRUE TO ONE, TRUE TO ALL
BASIC TECHNIQUES (eg
fractions)
WORK BACKWARDS
BUILD CONJECTURES
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WHAT IS THE PATTERN? -2 1 11 41 61 30-3 1 9 23 15 0-5 1 6 5 0 1 1 0
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WHAT IS THE PATTERN?
x, y, 2x, 5y, 4x, 9y, 8x, 13y, 16x, 17y, 32x, 21y
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WHAT IS THE PATTERN?
10, 21, 31, 52, 83, 135, 218, 353, 571, 924
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EXERCISE I If A is the first two-digit term of a series and adding B (any two-digit number) to the first term to determine the next, what
must be the sum of the first ten terms?
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1. A2. B3. A + B4. A + 2B5. 2A + 3B6. 3A + 5B
7. 5A + 8B 8. 8A + 13B9. 13A + 21B10. 21A + 34B SUM = 55A + 88B = 11(5A +
8B)
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1. A = 322. B = 15 3. A + B4. A + 2B5. 2A + 3B6. 3A + 5B
7. 5A + 8B 8. 8A + 13B9. 13A + 21B10. 21A + 34B
EXERCISE II
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1. 322. 15 3. 474. 625. 1096. 171
7. 2808. 4519. 73110. 1182
Find the SUM in 10 seconds.
SUM = 3080
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EXERCISE IIIDivide 987 654 321 by 5 WITHOUT using calculator. The usual way of long division IS NOT ALLOWED.
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EXERCISE IV (BY GROUP)Find the area of a triangle whose vertices are at (-1,4), (1,2) and (3,6). Show your illustration and complete solution.
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EXERCISE V (BY GROUP)What is the product when (x + y) raised to 6 is expanded using binomial theorem? Show all pertinent solutions.
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DISCUSSIONWhat is Binomial Theorem?
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EXERCISE V.5 (FOLLOW UP)What is the numerical coefficient of the third to the last term of the binomial expansion of
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EXERCISE VI (BY GROUP) If another square is drawn inside a square whose vertices of the smaller touch the sides of the small, what is the difference of their areas?
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EXERCISE VIIA, B and C have no common factor greater than 1. Alog200 5 + Blog200 2 = C, find A, B, and C.
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EXERCISE VIII (BY PAIR)Six digit numbers will be selected from the numbers 1,2,3,4,….10. If the second to the smallest digit is 3, how many arrangements are possible?
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EXERCISE IX (BY GROUP)Show all ways to find the area of the figure without actual measurements.
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EXERCISE XSimplify .
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EXERCISE XIWhat is the value of k in
+ 2kx – 15 = 0 if the sum of the roots is -2?
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EXERCISE XII
Solve for n in = and • = .
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EXERCISE XIII (BY GROUP) How big is the
area of the black region compared to that of the
orange square?
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EXERCISE IXWhat is the sum of the
sequence 1, , ………..?
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EXERCISE XXEvaluate
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THANK YOU!