MathDB

BMT Algebra #3 - Degree 2021 Polynomial

Source:

10/11/2020

The graph of the degree

2021

polynomial

P(x)

, which has real coefficients and leading coefficient

1

, meets the

x

-axis at the points

(1,0),\, (2,0),\,(3,0),\dots,\, (2020,0)

and nowhere else. The mean of all possible values of

P(2021)

can be written in the form

a!/b

, where

a

and

b

are positive integers and

a

is as small as possible. Compute

a+b

.

Bmtalgebrapolynomial

BMT 2020 Fall - Geometry 3

Source:

12/30/2021

Right triangular prism

ABCDEF

with triangular faces

\vartriangle ABC

and

\vartriangle DEF

and edges

\overline{AD}

,

\overline{BE}

, and

\overline{CF}

has

\angle ABC = 90^o

and

\angle EAB = \angle CAB = 60^o

. Given that

AE = 2

, the volume of

ABCDEF

can be written in the form

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Compute

m + n

. https://cdn.artofproblemsolving.com/attachments/4/7/25fbe2ce2df50270b48cc503a8af4e0c013025.png

geometry

shortest path for an ant on surface of cube 2020 BMT Team 3

Source:

1/7/2022

An ant is at one corner of a unit cube. If the ant must travel on the box’s surface, the shortest distance the ant must crawl to reach the opposite corner of the cube can be written in the form

\sqrt{a}

, where

a

is a positive integer. Compute

a

.

geometry3D geometrycube

2020 BMT Individual 3

Source:

1/9/2022

At Zoom University, people’s faces appear as circles on a rectangular screen. The radius of one’s face is directly proportional to the square root of the area of the screen it is displayed on. Haydn’s face has a radius of

2

on a computer screen with area

36

. What is the radius of his face on a

16 \times 9

computer screen?

algebrageometry

2020 BMT Discrete #3

Source:

3/10/2024

Compute the remainder when

98!

is divided by

101

.

number theory

3

Problems(5)