Math Jeopardy - AJS

Conics

100

Identify the Conic:

x² + y² = 16

Circle

200

Find Center + Radius:

(x - 3)² + (y + 2)² = 25

Center: (3, -2)

Radius: 5

300

Identify the Conic:

x²/9 + y²/4 = 1

Ellipse

400

Find the Vertex of:

(y + 1)² = 8(x - 2)

(2, -1)

500

Find the asymptotes of:

x²/16 - y²/9 = 1

y = +- 3/4 x

Triginometry

100

What does SOH CAH TOA stand for?

Sin = opposite/hypotenuse

Cos = adjacent/hypotenuse

Tan = opposite/adjacent

200

Convert 120 degrees to radians

2pi/3

300

Find: 

Cos (pi/6)

squareroot 3/2

400

Solve [0, 2pi]

Cos x = 1/2

x = pi/3 , 5pi/3

500

Solve:

2cos²(x) - 3sin(x) = 0

x = pi/6 and 5pi/6

Algebra

100

What is the equation for arithmetic sequence?

a_n = a₁ + (n - 1)d

200

What is the explicit formula for geometric sequence?

a_n = a₁ * r^n-1

300

Simplify:

x² - 9/x + 3

x - 3

400

Solve:

2x² - 8 = 0

x = +- 2

500

Find all roots:

x³ + 8 = 0

-2, 1 + i squareroot 3, 1 - i squareroot 3

Functions

100

Find f(2):

f(x) = 3x + 1

7

200

Describe the transformation from y = x² to y = (x+2)²

Shift left 2 units

300

Find the inverse of:

f(x) = 2x - 5

f^-1(x) = x+5 / 2

400

Find: (f o g)(x)

If: f(x) = x², g(x) = x + 1

(x + 1)²

500

Does f(x) = x² have an inverse over all real numbers?

No

Sequences/Limts

100

Find the next term: 

2, 5, 8, 11, ...

14

200

Find the common difference:

7, 11, 15, 19,...

4

300

Find the 5th term:

a_n = 3n + 2

17

400

Evaluate:

lim (2x + 1)

x->3

7

500

Evaluate:

lim (x² + 4x)

x->2

12