Why Jeopardy?
This is the main reason Jeopardy increases student participation during review sessions.
Why is fun/engaging?
This is the limit of (4x+2)/x as x approaches infinity.
What is 4?
This is the method of finding the area under a curve using antiderivatives.
What is integration? (or the fundamental theorem of calculus)
This coordinate system is best for problems with circular symmetry.
What is the Polar Coordinate System?
This type of matrix has 1s on the diagonal and 0s elsewhere.
What is the identity matrix?
This learning benefit occurs when students explain answers to each other during team Jeopardy games.
What is peer teaching or collaborative learning?
The derivative of x²+3x is this expression.
What is 2x + 3?
The integral of 1/x dx is this.
What is ln|x| + C?
The vector ⟨1, 2, 3⟩ has this magnitude.
What is sqrt(14)?
To add two matrices, they must have this in common.
What are the same dimensions (same number of rows and columns)?
Using Jeopardy helps students self-assess by organizing questions in this way.
What is by topic and difficulty level?
These rules allow you to find the derivative of f(x) * g(h(x)).
What are the product and chain rules?
You are rotating the region between two functions around the y-axis using cylindrical shells. This is the format of the integral you would need to set up to solve the problem.
What is ∫ 2π(radius)(height) dx?
You are given the series ∑ from n=1-infinity of the equation 1/n2. This test helps you determine if the series converges.
What is the p-series test?
When multiplying an m*n matrix by an n*p matrix, the result is this size.
What is m*p?
Playing Jeopardy in workshops helps reinforce this type of memory, critical for test-taking.
What is recall?
This is the derivative of -cos(2x).
What is 2sin(2x)dx?
A cylindrical tank with a height of 10 meters and a radius of 2 meters is full of water. This is the unevaluated integral for the work required to pump all the water to the top of the tank? Use 1000 kg/m³ for the density of water and 9.8 m/s² for gravity.
What is W = (definite integral from 0-10) ∫ (1000 * 9.8 * π(2)2 * y) dy?
This equation represents a plane in 3D space, with a normal vector n=⟨3,−2,4⟩ passing through the point (1, 2, 3). What is the equation of the plane?
What is 3(x - 1) - 2(y - 2) + 4(z - 3) = 0?
This first-order linear differential equation has the form dy/dx + P(x)y = Q(x). The general method for solving it involves finding this function.
What is the integrating factor?
Jeopardy can help reduce this common test-prep emotion by adding a game-based environment.
What is anxiety?
Air is being pumped into a spherical balloon so that its volume increases at a rate of 100 cm³/sec. This is how fast the radius is increasing when the radius is 5 cm.
What is 1/π cm/sec?
Choose the best method to evaluate ∫x⋅ln(x) dx. Then set up (but do not evaluate) the integral using that method.
What is Integration by Parts with the new expression ln(x)·(x²⁄2) − ∫ (x²⁄2)·(1⁄x) dx?
This is the radius of convergence of the series ∑ from n=1 - infinity (2x−3)n/n2.
What is 1/2?
Given matrices
A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]],
this is the product AB.
What is the matrix [[2, 1], [4, 3]]?