Jeopardy 2

Imaginary Numbers

100

Simplify:  i¹⁰

-1

200

Simplify: sqrt(-20)

(2sqrt5)i

300

Simplify: (3 - 2i)(3 + 2i)

13

400

Simplify: (5 + 4i)²

9 + 40i

500

Solve over the complex numbers: (x - 7)² = - 100

x = 7 +/- 10i

Unit Circle

100

cos90^o

0

200

sin270^o + tan225^o

0

300

Solve over [0, 2π):  tan²x - 3=0

x = π/3, 2π/3, 4π3, 5π/3

400

Evaluate f(π/3), given f(x) = 4sin(x - π/6) + 1

3

500

Solve over [0^o, 360^o):  cscx = secx

x = 45^o, 225^o

Derivatives

100

d/dx( 3x² + 2x - 1)

6x + 2

200

The slope of the line tangent to y= 3x² + 2x - 1 at x = 2

14

300

Find y', if y = sinx + e^x

y' = cosx + e^x

400

Differentiate:  (5x - 3)²

10(5x - 3) or 50x - 30

500

Differentiate:  2x^.sinx

2^.sinx + 2x^.cosx or 2(sinx + xcosx)

Area

100

Area of a triangle with base 10 and height 9

45

200

Area of a semi-circle whose radius is 8

32π

300

Area of a trapezoid with bases 6 and 10, with a height of 7. 

56

400

Given a circle with diameter 6, find the area of the sector formed by a 120^o angle. 

3π

500

The area of the region between the line y = (1/2)x - 3, the x-axis, and the line x = 10. 

4

Name the Mathematician

100

He and his students constructed the proof, so this person gets credit for this famous theorem, even though it had been used previously by Babylonians and Indians. This mathematician believed that numbers had personalities like perfect or incomplete, masculine or feminine, beautiful or ugly.

Pythagoras

200

The father of geometry

Euclid

300

His work on ‘binomial coefficients’ guided Newton to discover the binomial theorem.

Pascal

400

He introduced many notations and symbols, including Σ, e for the natural log base, a, b and c for the sides of a triangle and A, B, and C for the opposite angles, f(x), i for √−1, and he popularized the use of the symbol π. His identity (e^iπ + 1 = 0) is called, "the most beautiful equation".

Euler

500

These TWO mathematicians independently invented and described calculus in Europe in the 17th century.

Leibniz and Newton