The derivative as a gradient and rate of change

The derivative as a gradient and rate of change Quiz

Spec 4.1 · Edexcel International A Level Maths: Quiz

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  1. 1. Find the gradient of the chord joining the points with x=1x=1 and x=3x=3 on y=x2y=x^2.

    • A. 22
    • B. 44
    • C. 66
    • D. 88

  2. 2. Which expression defines f′(x)f'(x)?

    • A. lim⁡h→0f(x)+hh\lim_{h\to0}\frac{f(x)+h}{h}
    • B. lim⁡h→0(f(x+h)−f(x))\lim_{h\to0}\left(f(x+h)-f(x)\right)
    • C. lim⁡h→0f(x+h)f(x)\lim_{h\to0}\frac{f(x+h)}{f(x)}
    • D. lim⁡h→0f(x+h)−f(x)h\lim_{h\to0}\frac{f(x+h)-f(x)}{h}

  3. 3. A particle's distance ss metres at time tt seconds has dsdt=−3\frac{\mathrm{d}s}{\mathrm{d}t}=-3 at t=2t=2. What does this mean?

    • A. ss is decreasing at 33 m s−1^{-1}
    • B. ss is increasing at 33 m s−1^{-1}
    • C. ss is −3-3 m
    • D. ss is decreasing at 33 m s−2^{-2}

  4. 4. For f(x)=x3f(x)=x^3, f′′(x)=6xf''(x)=6x. What is the rate of change of the gradient at x=2x=2?

    • A. 33
    • B. 66
    • C. 1212
    • D. 12x12x

  5. 5. If f′(a)=0f'(a)=0, which statement is true?

    • A. The curve is rising at x=ax=a
    • B. The tangent at x=ax=a is horizontal
    • C. The curve crosses the xx-axis at x=ax=a
    • D. The curve is falling at x=ax=a

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