MathDB

2017 Algebra #2

Source:

8/20/2022

Eric has

2

boxes of apples, with the first box containing red and yellow apples and the second box containing green apples. Eric observes that the red apples make up

\tfrac{1}{2}

of the apples in the first box. He then moves all of the red apples to the second box, and observes that the red apples now make up

\tfrac{1}{3}

of the apples in the second box. Suppose that Eric has

28

apples in total. How many red apples does Eric have?

2017Algebra Test

2017 Algebra Tiebreaker #2

Source:

9/10/2022

Let

a

and

b

be positive integers that satisfy

ab-7a-11b+13=0

. What is the minimum possible value of

a+b

?

2017Algebra Tiebreaker

2017 Calculus #2

Source:

9/17/2022

Let

f(x)=x^2

and let

g(x)=x+1

. Let

h(x)=f(g(x))

. Compute

h'(1)

.

2017Calculus Test

2017 Calculus Tiebreaker #2

Source:

9/17/2022

Let

f

be a linear function. Compute the slope of

f

if

\int_3^5f(x)dx=0\text{ and }\int_5^7f(x)dx=12.

2017Calculus Tiebreaker

2017 Discrete #2

Source:

10/12/2022

Two distinct positive factors of

144

are selected at random. What is the probability that their product is greater than

144

?

2017Discrete Math Test

2017 Discrete Tiebreaker #2

Source:

10/12/2022

Find the remainder of

7^{1010}+8^{2017}

when divided by

57

.

2017Discrete Math Tiebreaker

2017 Geometry #2

Source:

11/19/2022

An equilateral triangle

ABC

shares a side with a square

BCDE

. If the resulting pentagon has a perimeter of

20

, what is the area of the pentagon? (The triangle and square do not overlap).

2017Geometry Test

2017 Geometry Tiebreaker #2

Source:

11/19/2022

Circles

A,B,C

are externally tangent. Let

P

be the tangent point between circles

A

and

C

, and

Q

be the tangent point between circles

B

and

C

. Let

r_C

be the radius of circle

C

. If the chord connecting

P

and

Q

has length

r_C\sqrt{2}

and the radii of circles

A

and

B

are

4

and

7

, respectively, what is the radius of circle

C

?

2017Geometry Tiebreaker

2017 Guts #2

Source:

11/25/2022

Let

5

and

13

be lengths of two sides of a right triangle. Compute the sum of all possible lengths of the third side.

2017Guts Round

2

Problems(9)