Download - Problem solving in math
PROBLEM SOLVINGYeah, this is for real.
RULES 1. Be attentive. 2. Compute.3. CP's/calculators are not allowed.4. Listen.5. Enjoy.
GEORGE POLYA'S PROBLEM SOLVING TECHNIQUES Understand the problem.Device a plan. Carry out the plan.Look back.
PATTERNSNEED FOR DIAGRAMNEED FOR SIMPLER PROBLEM
TRUE TO ONE, TRUE TO ALL
BASIC TECHNIQUES (eg
fractions)
WORK BACKWARDS
BUILD CONJECTURES
WHAT IS THE PATTERN? -2 1 11 41 61 30-3 1 9 23 15 0-5 1 6 5 0 1 1 0
WHAT IS THE PATTERN?
x, y, 2x, 5y, 4x, 9y, 8x, 13y, 16x, 17y, 32x, 21y
WHAT IS THE PATTERN?
10, 21, 31, 52, 83, 135, 218, 353, 571, 924
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?
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)
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
1. 322. 15 3. 474. 625. 1096. 171
7. 2808. 4519. 73110. 1182
Find the SUM in 10 seconds.
SUM = 3080
EXERCISE IIIDivide 987 654 321 by 5 WITHOUT using calculator. The usual way of long division IS NOT ALLOWED.
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.
EXERCISE V (BY GROUP)What is the product when (x + y) raised to 6 is expanded using binomial theorem? Show all pertinent solutions.
DISCUSSIONWhat is Binomial Theorem?
EXERCISE V.5 (FOLLOW UP)What is the numerical coefficient of the third to the last term of the binomial expansion of
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?
EXERCISE VIIA, B and C have no common factor greater than 1. Alog200 5 + Blog200 2 = C, find A, B, and C.
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?
EXERCISE IX (BY GROUP)Show all ways to find the area of the figure without actual measurements.
EXERCISE XSimplify .
EXERCISE XIWhat is the value of k in
+ 2kx – 15 = 0 if the sum of the roots is -2?
EXERCISE XII
Solve for n in = and • = .
EXERCISE XIII (BY GROUP) How big is the
area of the black region compared to that of the
orange square?
EXERCISE IXWhat is the sum of the
sequence 1, , ………..?
EXERCISE XXEvaluate
THANK YOU!