<p>Here is my guess at the scoring guidelines:</p>
<p>1a:
+1 for speed
+1 for acceleration vector</p>
<p>1b:
- 1 for Dy/dx at t = 3 </p>
<p>1c:
+1 for x position
+1 for y position</p>
<p>1d:
+1 integral
+1 answer</p>
<h2>+2 more points somewhere </h2>
<p>2a:
+1 for value at t = 3.5</p>
<p>2b:
+1 for trapezoidal rule
+1 for approximation
+1 for meaning</p>
<p>2c:
+1 for value
+1 for explanation</p>
<p>2d:
+1 for integral of B(t)
+1 for answer
+1 for difference</p>
<h2>+1 for units</h2>
<p>3a:
+1 for 1+k+e^2k
+1 for integral of the arclength
+1 for the limits of the arclength</p>
<p>3b:
+1 integrand
+1 answer
+1 for limits of integration</p>
<p>3c:
+1 for derivative?
+1 for substituting values in</p>
<h2>+1 for answer</h2>
<p>4a:
+1 g(-3)
+1 g(x)
+1 g(-3)</p>
<p>4b:
+1 for considering 5/2
+1 for explanation</p>
<p>4c:
+1 for identifying x = 0
+1 for explanation</p>
<p>4d:
+1 average change</p>
<h2>+1 explanation</h2>
<p>5a:
+1 for approximation</p>
<p>5b:
+1 for second derivative
+1 for under approximation and why</p>
<p>5c:
+1 separation of variables
+2 antiderivatives
+1 constant of integration
+1 uses initial condition</p>
<h2>+1 solves for y</h2>
<p>6a:
+1 for sin(x)
+1 for sin(x^2)</p>
<p>6b:
+1 for cos(x)
+3 for taylor series of f(x)</p>
<p>6c:
+1 value</p>
<p>6d:
+2 showing error bound</p>