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

Question 1
college-boardPre-CalculusAPExam Style
1 mark

A particle moves according to parametric functions defined by x(t)=atb+cx(t)=at^b+cx(t)=atb+c and y(t)=dte+fy(t)=dt^e+fy(t)=dte+f, where a,b,c,d,e,f are constants; for what values of b and e does its acceleration have constant magnitude?

Question 2
college-boardPre-CalculusAPExam Style
1 mark

If the parametric equations x(t)=3sin⁡(2t)x(t) = 3\sin(2t)x(t)=3sin(2t) and y(t)=2cos⁡(5t)y(t) = 2\cos(5t)y(t)=2cos(5t) model a particle's planar motion, what is the period of the particle’s path along the x-axis?

Question 3
college-boardPre-CalculusAPExam Style
1 mark

What is an advantage of using numerical methods to solve higher-degree equations related to parametrics?

Question 4
college-boardPre-CalculusAPExam Style
1 mark

If the position of an object is given by the parametric equations x(t)=5cos⁡(πt6)x(t)=5\cos\left(\frac{\pi t}{6}\right)x(t)=5cos(6πt​), y=5sin⁡(πt6)y=5\sin\left(\frac{\pi t}{6}\right)y=5sin(6πt​), which path does it take in the plane?

Question 5
college-boardPre-CalculusAPExam Style
1 mark

Which set describes parametric equations correctly?

Question 6
college-boardPre-CalculusAPExam Style
1 mark

What does the independent variable in parametric equations often represent?

Question 7
college-boardPre-CalculusAPExam Style
1 mark

What type of graph would represent a continuous movement along a straight line for increasing values of the parameter t?

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Question 8
college-boardPre-CalculusAPExam Style
1 mark

In parametric functions modeling planar motion, which type of symmetry indicates that if (x(t),y(t))(x(t), y(t))(x(t),y(t)) is on the path then so is (x(−t),−y(−t))(x(-t), -y(-t))(x(−t),−y(−t))?

Question 9
college-boardPre-CalculusAPExam Style
1 mark

What condition must be true about the limits lim⁡s→a−f(s)\lim_{s \to a^-} f(s)lims→a−​f(s), lim⁡s→a+f(s)\lim_{s \to a^+} f(s)lims→a+​f(s), and f(a)f(a)f(a) for the parametric curve described by x=f(s)x=f(s)x=f(s), y=g(s)y=g(s)y=g(s)?

Question 10
college-boardPre-CalculusAPExam Style
1 mark

Why might understanding continuity be important when modeling real-world planar motion with parametrics?