Math League practice: 1/18/21 Lesson

5 Slides • 4 Questions

1

Math League practice: 1/18/21

A and B test emphasis

2

Open Ended

Determine exactly the positive solution to

3x^2=243

Type response here

3

4

Open Ended

Given that

\frac{2x^3+14x^2+12x}{4x+4}\div\left(mx+n\right)=x

determine the exact value of n

Type response here

5

6

Open Ended

The volume of a sphere whose surface area is 36π can be expressed as nπ.

Find n

Type response here

7

The surface area of a sphere is

4πr^2

So

4πr^2=36π

, so r = 3

The volume of a sphere is

\frac{4}{3}πr^3

So

\frac{4}{3}π\left(3\right)^3=36π

Thus nπ = 36π, so n = 36

8

Open Ended

In the circle pictured, minor arcs AB and BC each measure 73˚ and the measure of angle AEB = 82˚.

Determine exactly the measure of arc AD

Type response here

9

Intersecting chords BD and CA cut off arcs AB and CD, with the relationship

$m\angle AEB=\frac{1}{2}\left(m\ AB\ +\ m\ CD\right)$
82˚ = 1/2 (73 + CD)

164˚ = 73 + CD
91˚ = CD
So arc AD = 360˚ - (91˚ + 146˚) = 123˚

Math League practice: 1/18/21

A and B test emphasis

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