MathDB

2017 Algebra #9

Source:

8/20/2022

Let

f(x)=x^3+ax^2+bx

for some

a,b

. For some

c

,

f(c)

achieves a local maximum of

539

(in other words,

f(c)

is the maximum value of

f

for some open interval around

c

). In addition, at some

d

,

f(d)

achieves a local minimum of

-325

. Given that

c

and

d

are integers, compute

a+b

.

2017Algebra Test

2017 Calculus #9

Source:

9/17/2022

Compute

\int_0^4\frac{x^4-4x+4}{1+2017^{x-2}}dx.

2017Calculus Test

2017 Discrete #9

Source:

10/12/2022

Compute the number of positive integers

n\leq1330

for which

\tbinom{2n}{n}

is not divisible by

11

.

2017Discrete Math Test

2017 Geometry #9

Source:

11/19/2022

Triangle

ABC

is isosceles with

AC=BC=25

and

AB=10

. Let

O

be the orthocenter of

\triangle ABC

, the intersection of the three altitudes of

\triangle ABC

. Reflect

O

across

AB

to a point

D

, and extend

CB

and

AD

to intersect at point

E

. Compute the area of

\triangle ABE

.

2017Geometry Test

2017 Guts #9

Source:

11/25/2022

Eddy owns

5

different cats, and has

9

fish to distribute among the cats. Each cat gets at least

1

fish and at most

3

fish. If the fish are indistinguishable, how many ways can Eddy distribute the

9

fish among the

5

cats?

2017Guts Round

9

Problems(5)