Gcse maths question help!

[Thisisnotmyname2022]

My daughter has had a go at this question this evening, she thought the answer was 1.5 and I agree.. however the 3 marks are given for 1, and only 1 mark given for her answer.

What have we missed?

Thank you

2.8/2 so 1.4 Did she show workings? Was there any instruction to round?

I’d have estimated 2/9 of 4 so more or less 1 ie the total time is 9 and the maximum speed is 4 and it’s an even curve so at time 2 it’s 2/9 of the maximum speed. I’m not a mathematician though and the logic might be wrong!

To estimate a gradient on a curve you need to draw a tangent to the curve at the point you're estimating and then do the gradient of that tangent.

It looks like you can drag the dots to make the blue line a gradient to the curve at the point where t=2.

So she’s saying acceleration = change of speed/change of time.

I’ll forward these messages on to her. There’s nowhere to input any working out, it’s an online platform, but the answer of 1 gives her full marks. It says estimate, so we assumed that means round to the nearest whole number.

Not a mathematician, but focusing on t=2:
The gradient is changing, at 1.8 on the x-axis, the y value is 2.6. At 2.2 on the x-axis, the y value has increased to 3.0.
The change in y compared to the change in x is 0.4/0.4 = 1.

Is the acceleration irrelevant? If it’s asking for gradient?

@Thisisnotmyname2022 it says estimate, because you can't measure it with perfect accuracy, not because it wants you to round to the nearest whole.

the gradient is the acceleration.

Makes sense, thank you.

Thats what we thought, but then figured we must be wrong 😑

We can’t figure out how the answer is 1 though.

I’ll send her this, thank you.

You need to use the blue line on the graph to make a tangent at t=2. The gradient of that line will be 1.

Thank you, I’ve passed that on to her too. Hopefully these comments will have made it click.

Forgive the poor phone edit but drawing a tangent at t=2 roughly gives a gradient of 3/3 which is 1.

as pp stated, a gradient at a specific point on the x axis on a curved graph requires a tangent to be drawn at that specific value of x (where straight line is touching the curve at that point and in same direction).

Former maths teacher here. The gradient of a speed-time graph tells you the acceleration (rate of change of speed). To find this when the graph is a curve you need to draw a tangent at the point in time of interest, and find its gradient.

If you draw a tangent to the curve at t=2, you will draw a line that by my eye will go through (2,2.8) and pass through (1,1.8) and (3,3.8). That has a gradient of 1: (3.8 - 1.8) / (3-1) = 1.

You need to draw a tangent to the curve as others have mentioned

The tangent basically measures the rate that the Y axis is changing compared to 1 of the X axis. In otherward, how much the speed changes per second. Which is acceleration.

In other subjects, especially science ones, she will need to do tangents, often to work out the rate of reaction.

e.g temp change per second

gas produced per second

And work out when the rate slowed down.

For fans of calculus (this goes a bit beyond GCSE), you can actually work out that the curve plotted in this question is speed = (9t - t^2)/5 so acceleration is (9 - 2t)/5. Put t = 2 into that and you get exactly 1.

Thanks everyone, she said it’s helped.

This is what I would do too

The gradient of the blue line is -1. The gradient of the tangent to the curve is approximately perpendicular to the blue line.
The product of gradients of perpendicular lines equals -1. Therefore the gradient of the graph at 2 is +1.

Either draw a tangent by eye at the point where t=2, or draw a smaller triangle under curve. How did you both get 1.5?

@Thisisnotmyname2022 I'm a GCSE maths tutor. This is the correct way to answer this question.

We just did 3/2… she sees now what she should have done, it’s been a while since I’ve done something like this.