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Difference between revisions of "2017 UNM-PNM Statewide High School Mathematics Contest II Problems"

(Created page with "UNM - PNM STATEWIDE MATHEMATICS CONTEST XLIX. February 4, 2017. Second Round. Three Hours ==Problem 1== What are the last two digits of <math>2017^{2017}</math>? 2017 UNM...")
 
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==Problem 2==
 
==Problem 2==
  
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Suppose <math>A, R, S</math>, and <math>T</math> all denote distinct digits from <math>1-9</math>. If <math>\sqrt{STARS} = SAT</math>, what are <math>A, R, S</math>, and <math>T</math>?  
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Suppose <math>A, R, S</math>, and <math>T</math> all denote distinct digits from <math>1</math> to <math>9</math>. If <math>\sqrt{STARS} = SAT</math>, what are <math>A, R, S</math>, and <math>T</math>?  
  
 
[[2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 2|Solution]]
 
[[2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 2|Solution]]

Revision as of 02:49, 15 January 2019

UNM - PNM STATEWIDE MATHEMATICS CONTEST XLIX. February 4, 2017. Second Round. Three Hours

Problem 1

What are the last two digits of $2017^{2017}$?

Solution

Problem 2

Suppose $A, R, S$, and $T$ all denote distinct digits from $1$ to $9$. If $\sqrt{STARS} = SAT$, what are $A, R, S$, and $T$?

Solution

Problem 3

Let $f(x) =\frac{x}{ x−1}$ (Error compiling LaTeX. Unknown error_msg) and $g(x) =\frac{x}{3x−1}$ (Error compiling LaTeX. Unknown error_msg).

(a) Determine $f\circ g(x)$ and $g\circ f(x)$.

(b) Denote $\underbracket{h\circ h\circ \cdot \circ h}_text{n times} := h^n$. Determine all the functions in the set $S = \{H | H = (g\circ f)n\circ g$ or $H = (f\circ g)n\circ f$ for some $n$ a whole number$\}$.

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Problem 8

Solution

Problem 9

Solution

Problem 10

Solution

See Also

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