Estimating Gradients Quiz

1. What does the gradient at a point on a curve estimate?

• A. The average value of $y$
• B. The instantaneous rate of change at that point
• C. The total area under the curve
• D. The maximum value of the curve

2. A tangent to a curve at point $P$ passes through $(2, 5)$ and $(6, 17)$. What is the estimated gradient at $P$?

• A. 2
• B. 3
• C. 4
• D. 6

3. On a distance-time graph, what does the gradient at a point represent?

• A. Total distance travelled
• B. Instantaneous speed
• C. Instantaneous acceleration
• D. Average speed over the whole journey

4. A table gives coordinates $(2, 4)$, $(3, 9)$ and $(4, 16)$. Using the points either side, what is the estimated gradient at $x = 3$?

• A. 5
• B. 6
• C. 7
• D. 9

5. Why does using two well-separated points on a long tangent line, rather than two very close points on it, improve the accuracy of an estimated gradient?

• A. It changes the true gradient of the curve
• B. It reduces the relative effect of small errors in reading coordinates off the graph
• C. It makes the tangent touch the curve at more points
• D. It converts the estimate into an exact value