5.1 Limits and the derivative Quiz

1. For $f(x)=x^{2}$, find the gradient of the chord from $x=1$ to $x=1.1$.

• A. 2
• B. 2.1
• C. 0.21
• D. 1.1

2. Values of an expression as $x\to0$ are $0.5018, 0.5002, 0.50002$ from above and $0.4983, 0.4998, 0.49998$ from below. Estimate the limit.

• A. 0
• B. 0.498
• C. 0.5
• D. The limit does not exist

3. Which notation means the rate of change of $A$ with respect to $r$?

• A. $\frac{\mathrm{d}r}{\mathrm{d}A}$
• B. $\frac{\mathrm{d}A}{\mathrm{d}r}$
• C. $A'(t)$
• D. $\frac{A}{r}$

4. The chord gradient on a curve at $x=2$ simplifies to $7-3h$. What is the gradient of the curve at $x=2$?

• A. 7
• B. 4
• C. -3
• D. 10

5. $\frac{\mathrm{d}D}{\mathrm{d}t}=-0.4$ m per minute at $t=5$, where $D$ m is the depth of water in a tank. What does this mean?

• A. The depth is 0.4 m at $t=5$.
• B. The depth is falling at 0.4 m per minute at $t=5$.
• C. The depth fell by 0.4 m in the first 5 minutes.
• D. The depth is rising at 0.4 m per minute at $t=5$.