Add to make Perfect Squares
Question What must be added to each of the following expressions to obtain a perfect square? [Q1] a^2…
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If you double 18, then double again, and again… how often will you get a square number?
Answer You are essentially getting the number X which is of the form below : X = 2^a…
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Algebra: Solve an equation
Question Solve for x. (x-2)^2 = (√x) + 2 Answer (x-2)^2 = (√x) + 2 x^2 – 4x…
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A Remainder Problem: “How to find the remainder of 3^7 divided by 7 using modulo arithmetic?”
Answer Here is a short way. Fermat’s little theorem says that if p is a prime and b…
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A Number Theory Question: “If abcd x 4 = dcba what are the values of a b c and d?”
Answer Let us reason out completely and not just “guess” at an answer. We use base 10. abcd…
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Counting Problem: “How many dots in the n-th rectangle?”
Question •• 1st rectangle ••• ••• 2nd rectangle •••• •••• •••• 3rd rectangle ••••• ••••• ••••• ••••• 4th…
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Solve for x and y which are both real numbers? Given that 4x+3y(i-1)-12(1-i)=9-2x(1+i)+(1-2y)i
Answer 4x+3y(i-1)-12(1-i)=9-2x(1+i)+(1-2y)i Separate the ‘real’ and ‘complex’ part as follows: (4x – 3y -12) + (3y + 12)i…
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Math Patterns: “Can you find the rule for this sequence?”
Question 10, 22, 36, 55, … Answer One answer is (n^3 – 4n^2 + 29n – 6) /…
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Sequences
Question Find in terms of n, the n th term of the sequence: 1/3 , 2/5 , 3/7,…
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Maxima Problems: “Find two possible real numbers whose product is a maximum, and the sum is 110 ?”
Answer I’ll show you a couple of ways. Let the two numbers be p and q respectively. We…