2018 UNCO Math Contest II Answer Key

1) $666$

2) $150$

3) $B=3$

4) $149$

5) $\frac{8}{5}$

6) $C; p(x) = 2x^3-2x + 3$

7) $\frac{7}{18}$

8) $r(x) = -x^2-3$

9) a) $G(3) = 5, G(4) = 8, G(5) = 13$

b) $G(n) = G(n 1) + G(n 2); G(0) = 1 and G(1) = 2$

c) $G(n + 1) = G(n) + G(n 1)$ .

10) a) $P(6) = 10$

b) $P(n) = Q(n-1) + Q(n-2) (n>=4); Q(n) = Q(n-1) + Q(n-3) (n>=4)$

c) $P(n) = P(n-1) + P(n-3) (n>=7)$

d) $P(11) = 74; P(13) = 158$

11) $7$ (Other acceptable answers are $41, 239, 1393, 8119$ , and, in general, anything generated by the formula in part b. The answer students are most likely to give is $7$

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2018 UNCO Math Contest II Answer Key