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  1. AP Pre Calculus
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Functions Involving Parameters, Vectors, and Matrices

Question 1
college-boardPre-CalculusAPExam Style
1 mark

If a circle has parametric equations x=5cos(theta)x = 5 \\cos(\\theta)x=5cos(theta) and y=5sin(theta)y = 5 \\sin(\\theta)y=5sin(theta), what is its radius?

Question 2
college-boardPre-CalculusAPExam Style
1 mark

When evaluating functions for continuity at a point c, which condition must NOT be met to conclude that there's a discontinuity at c?

Question 3
college-boardPre-CalculusAPExam Style
1 mark

If the parametric equations x=cos⁡(t)x = \cos(t)x=cos(t) and y=sin⁡(t)y = \sin(t)y=sin(t) define a circle, for what value of ttt will the point on the circle be at its farthest from the line y=xy = xy=x?

Question 4
college-boardPre-CalculusAPExam Style
1 mark

If a particle moves along the path described by parametric equations x=(10−sint)x = (10 - \\sin t)x=(10−sint), y=(5cost)y = (5 \\cos t)y=(5cost), at what time(s) during 0leqt<6pi0 \\leq t < 6\\pi0leqt<6pi does its velocity have both positive components?

Question 5
college-boardPre-CalculusAPExam Style
1 mark

Which of the following equations represents a line tangent to the circle defined by parametric equations x(t)=rcos(t)x(t) = r \\cos(t)x(t)=rcos(t), y(t)=rsin(t)y(t) = r \\sin(t)y(t)=rsin(t), where ttt is measured in radians?

Question 6
college-boardPre-CalculusAPExam Style
1 mark

What is the parametric equation for a circle with radius 5 centered at the origin?

Question 7
college-boardPre-CalculusAPExam Style
1 mark

Which set of parametric equations represents a line passing through (0,0) and (1,1)?

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Question 8
college-boardPre-CalculusAPExam Style
1 mark

How do you find the equation of the tangent line to a parameterized curve given by X=V(T)X=V(T)X=V(T) and Y=W(T)Y=W(T)Y=W(T) at a specific point?

Question 9
college-boardPre-CalculusAPExam Style
1 mark

If the parametric equations x=rcos(theta)x = r \\cos(\\theta)x=rcos(theta) and y=rsin(theta)y = r \\sin(\\theta)y=rsin(theta) describe a circle, what does theta\\thetatheta represent?

Question 10
college-boardPre-CalculusAPExam Style
1 mark

Which set of parametric equations represents a line passing through the origin with slope m?