Polar coordinates and curve sketching

Polar coordinates and curve sketching Quiz

Spec 7.1 · Edexcel International A Level Further Maths: Quiz

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  1. 1. What are the Cartesian coordinates of the point with polar coordinates (4,π3)\left(4,\frac{\pi}{3}\right)?

    • A. (23,2)\left(2\sqrt3,2\right)
    • B. (2,23)\left(2,2\sqrt3\right)
    • C. (4,3)\left(4,\sqrt3\right)
    • D. (2,2)(2,2)

  2. 2. What is the polar equation of the circle x2+y2=6xx^2+y^2=6x?

    • A. r=3r=3
    • B. r=6r=6
    • C. r=6sin⁡θr=6\sin\theta
    • D. r=6cos⁡θr=6\cos\theta

  3. 3. What is the name of the curve r=a(1+cos⁡θ)r=a(1+\cos\theta)?

    • A. a cardioid
    • B. a circle
    • C. an Archimedean spiral
    • D. a lemniscate

  4. 4. For which values of θ\theta does r2=a2cos⁡2θr^2=a^2\cos2\theta exist, for 0≤θ<2π0\le\theta<2\pi?

    • A. 0≤θ≤π20\le\theta\le\frac{\pi}{2} only
    • B. 0≤θ≤π0\le\theta\le\pi
    • C. 0≤θ≤π40\le\theta\le\frac{\pi}{4}, 3π4≤θ≤5π4\frac{3\pi}{4}\le\theta\le\frac{5\pi}{4} and 7π4≤θ<2π\frac{7\pi}{4}\le\theta<2\pi
    • D. all values of θ\theta

  5. 5. A tangent to r=f(θ)r=f(\theta) is parallel to the initial line when:

    • A. drdθ=0\frac{dr}{d\theta}=0
    • B. ddθ(rsin⁡θ)=0\frac{d}{d\theta}(r\sin\theta)=0
    • C. ddθ(rcos⁡θ)=0\frac{d}{d\theta}(r\cos\theta)=0
    • D. rsin⁡θ=0r\sin\theta=0

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