Note: Use Q5 and Q6 from Real life graphs online tests
Question 1
Question 1(a) [3 marks]
The diagram below shows the graph of y= 0.5x^2
Find an estimate of the gradient of the curve at x=2
Give your answer to the nearest whole number.
Answer type: Simple text
ANSWER: 2
WORKING:
Draw a tangent to the graph at the point where x=2
Then we find the gradient of the curve at this point by calculating the gradient of the tangent.
Gradient = \dfrac{\text{change in } y}{\text{change in } x} \approx \dfrac{6-0}{4-1} = 2
Question 1(b) [1 mark]
Using you answer to part (a), estimate the gradient of the curve at x = -2
Answer type: Simple text
ANSWER: -2
WORKING:
The graph is symmetrical about the y-axis. Therefore the gradient must be the negative of the gradient found in part (a), since -2 is the negative of 2
Question 2 [3 marks]
A velocity-time graph of the first 3 seconds of someone running is shown below.
Estimate the instantaneous acceleration 1 second in.
Answer type: Multiple choice (grid)
ANSWER: 2 m/s^2
Wrong answers:
3 m/s^2
1 m/s^2
1.5 m/s^2
WORKING:
The instantaneous gradient is the gradient of the tangent at a point on a curve.
Therefore the instantaneous acceleration on a velocity time graph is also the gradient of the tangent at a point on the curve.
Draw a tangent to the graph at the point where the time is 1 second
Therefore the instantaneous acceleration 1 second in is equal to,
\dfrac{\text{change in } y}{\text{change in } x} \approx \dfrac{7-2}{5-2.5} = 2 m/s^2