Polar Coordinates and Parametric Equations: Precalculus Math Quiz – PDF Download
Ten multiple-choice questions on polar points, conversions, polar graphs and parametric equations. Choose the best answer, then read the explanation to learn the typical mistake. Each question has exactly one correct option.
PrecalculusCommon Core: N-CN.B.4 · F-IF.C.7
🎯 Polar Coordinates and Parametric Equations – Precalculus math quiz
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Question 1
What are the polar coordinates of point P, using \(r> 0\) and \(0^{\circ}\le\theta< 360^{\circ}\)?
Point P on a polar grid.
A\((3,45^{\circ})\)
B\((3,225^{\circ})\)
C\((135,3)\)
D\((3,135^{\circ})\)
Question 2
What is the \(x\)-coordinate of the polar point \(\left(10,\frac{\pi}{3}\right)\)?
A\(5\sqrt{3}\)
B\(10\)
C\(5\)
D\(\frac{10}{\sqrt{3}}\)
Question 3
Which polar pair equals the rectangular point \((-1,1)\)?
A\(\left(\sqrt{2},\frac{3\pi}{4}\right)\)
B\(\left(\sqrt{2},\frac{\pi}{4}\right)\)
C\(\left(\sqrt{2},\frac{5\pi}{4}\right)\)
D\(\left(2,\frac{3\pi}{4}\right)\)
Question 4
Which rectangular equation matches \(r=4\cos\theta\)?
A\((x-2)^{2}+y^{2}=4\)
B\(x^{2}+y^{2}=4\)
C\((x-4)^{2}+y^{2}=16\)
D\(x^{2}+(y-2)^{2}=4\)
Question 5
Which equation has the graph shown, a rose with petals of length 4 and one petal pointing straight up?
A rose with five petals.
A\(r=4\cos 5\theta\)
B\(r=4\sin 5\theta\)
C\(r=4\sin 10\theta\)
D\(r=5\sin 4\theta\)
Question 6
What type of graph is \(r=2+2\sin\theta\)?
Acardioid
Bcircle
Crose with two petals
Dlimaçon with an inner loop
Question 7
Eliminate the parameter from \(x=t+2\), \(y=t^{2}\).
A\(y=x^{2}-2\)
B\(y=(x-2)^{2}\)
C\(y=(x+2)^{2}\)
D\(y=x^{2}+2\)
Question 8
An object moves along \(x=4\cos t\), \(y=2\sin t\), as shown. Where is it at \(t=\frac{\pi}{2}\)?
The path of the object; the arrow shows its direction.
A\((4,0)\)
B\((0,2)\)
C\((0,4)\)
D\((0,0)\)
Question 9
What is the distance between the polar points \((3,0)\) and \(\left(4,\frac{\pi}{2}\right)\)?
A\(7\)
B\(1\)
C\(12\)
D\(5\)
Question 10
A ball follows \(x=10t\), \(y=64t-16t^{2}\) (feet, seconds). When does it land?
A\(t=2\text{ s}\)
B\(t=8\text{ s}\)
C\(t=4\text{ s}\)
D\(t=6.4\text{ s}\)
🎉 Quiz complete!
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Remember:
Polar to rectangular: \(x=r\cos\theta\), \(y=r\sin\theta\); rectangular to polar: \(r^{2}=x^{2}+y^{2}\), \(\tan\theta=\frac{y}{x}\).
Every point has infinitely many polar names: \((r,\theta)=(r,\theta+2\pi k)=(-r,\theta+\pi)\).
A rose \(r=a\cos n\theta\) has \(n\) petals for odd \(n\) and \(2n\) petals for even \(n\).
A limaçon \(r=a+b\cos\theta\) has an inner loop when \(a< b\) and is a cardioid when \(a=b\).
To eliminate the parameter, solve one equation for \(t\) and substitute into the other.
