2017 UNM-PNM Statewide High School Mathematics Contest II Problems

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

Problem 1

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

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 $f(x)=\frac{x}{x-1}$ and $g(x)=\frac{x}{3x-1}$ .

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

(b) Denote $\underbrace{h\circ h\circ \cdot \circ h}_\text{n times} := h^n$ . 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

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2017 UNM-PNM Statewide High School Mathematics Contest II Problems

Contents

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

See Also