Math Team Jeopardy

Algebra

100

Solve for x:

2x + 3 = 9

x = 3

200

Solve for the quadratic equation:

x² - 5x + 6

x = 2 and x = 3

300

Find the discriminant of x²-6x+11 = 0

What is -8

400

Given the geometric sequence where the first term is 3 and the fourth term is 24, find the common ratio.

Common ratio: 2

500

Solve for x:

log₂(x-1) + log₂(x+1) = 3

x = 3

Extraneous: x = -3

Pre-Calculus

100

Evaluate:

sin(45)

sqrt(2)/2

200

Find the equation of the line that passes through the points (2,3) and (4,7).

y = 2x - 1

300

Simplify the complex number: 

(3 + 2i)(4 - 5i)

22 - 7i

400

Find the domain:

f(x) = sqrt(5-x)

x is less than or equal to 5

500

Determine the polar coordinates of the point with Cartesian coordinates (-4, 4/sqrt(3)) where r is positive and 0 ≤ θ < 2pi.

(8(sqrt3)/3, 5pi/6)

Differential Calculus

100

The operation used to find the instantaneous rate of change or the slope of a tangent line to a curve.

What is differentiation? (or What is a derivative?)

200

Formula for the rate of change of x with respect to y.

What is dx/dy?

300

Solve y=4x⁵+2x³+4x² with respect to x.

*Find d⁴y/dx⁴

What is 480x?

400

The slope of chord formula.

*Hint not y₂-y_1/x_2-x₁

What is f(x+∆x)-F(x)/∆x?

500

Contributors to Differential Calculus.

Who are Augustin Louis Cauchy (1789–1857), Bernhard Riemann (1826–1866), and Karl Weierstrass (1815–1897)?

Calculus AB

100

Find the limit as x approches 0:

sin(x)/x

limit = 1

200

Evaluate the integral from 0 to 3:

(2x + 1)dx

12

300

Use implicit differentiation to find dy/dx:

x² + xy + y² = 7

dy/dx = (-2x-y)/(x+2y)

400

Find the derivative:

f(x) = e^2xsin(x)

f'(x) = 2e^2xsin(x) + e^2xcos(x)

500

Determine the area of the region bounded by y = x² and y = 4x - x².

8/3

Calculus BC

100

Find the derivative of the vector valued function:

r(t) = <t², sin(t), e^t>

r'(t) = <2t, cos(t), e^t>

200

Find the integral of the vector valued function with the initial condition <1,2,1>:

r(t) = <2t, cos(t), e^t>

r'(t) = <t² + 1, sin(t) + 2, e^t + 1>

300

Solve the integral using integration by parts:

(xe^x)dx

xe^x - e^x + C

400

Find the arc length of the curve given the parametric equations x = 3t² and y = 2t³ from t = 0 to t = 1.

7sqrt(14) - 4

500

Evaluate the improper integral with bounds from 1 to infinity:

(ln(x)/x²)dx

-1