MathDB

BMT 2022 Fall Algebra P6

Source:

5/5/2023

The degree-

6

polynomial

f

satisfies

f(7) - f(1) = 1, f(8) - f(2) = 16, f(9) - f(3) = 81, f(10) - f(4) = 256

and

f(11) - f(5) = 625.

Compute

f(15) - f(-3).

algebrafunctions

BMT 2022 Fall Discrete P6

Source:

5/6/2023

Bayus has eight slips of paper, which are labeled 1

, 2, 4, 8, 16, 32, 64,

and

128.

Uniformly at random, he draws three slips with replacement; suppose the three slips he draws are labeled

a, b,

and

c.

What is the probability that Bayus can form a quadratic polynomial with coefficients

a, b,

and

c,

in some order, with

2

distinct real roots?

DiscreteDiscrete Math

BMT 2022 Geometry #6 / General #24

Source:

8/12/2023

Triangle

\vartriangle BMT

has

BM = 4

,

BT = 6

, and

MT = 8

. Point

A

lies on line

\overleftrightarrow{BM}

and point

Y

lies on line

\overleftrightarrow{BT}

such that

\overline{AY}

is parallel to

\overline{MT}

and the center of the circle inscribed in triangle

\vartriangle BAY

lies on

\overline{MT}

. Compute

AY

.

geometry

BMT 2022 Guts #6

Source:

8/31/2023

Equilateral triangle

ABC

has side length

20

. Let

PQRS

be a square such that

A

is the midpoint of

\overline{RS}

and

Q

is the midpoint of

\overline{BC}

. Compute the area of

PQRS

.

geometry

6

Problems(4)