Lesson video

Hello, my name is Mr Clasper and today we are going to be applying skills from previous lessons on upper and lower bounds.

Write down the error intervals for A and B.

So for each of these numbers, we need to find our lower and upper bounds and write these as an error interval with inequality notation.

So let's have a look at A we have a number line with 24.

2 as a midpoint, and either side is 24.

1 and 24.

3.

Our lower bound and upper bound will be the midpoints.

And therefore my error interval will be 24.

15 is less than or equal to A which is less than 24.

25.

If I look at B, I've got 27 as a midpoint, and 26 and 28 on either side.

And my midpoints are my bounds.

Therefore, my inequality or error interval will be 26.

5 is less than or equal to B which is less than 27.

5.

Let's have a look at this example, work out the upper bound of B minus A now remember the upper bound needs to give us the largest possible difference between B and A.

Therefore, I'm going to have to calculate my upper bound for B.

Subtract my lower bound for A as this will give us the largest possible difference.

Therefore my upper bound is 3.

35.

Working out the lower bound for B minus A, we need to find the smallest possible difference between the two numbers.

Therefore, I'm going to calculate my lower bound for B subtract my upper bound for A.

This gives me a lower bound of 2.

25.

Work out the upper bound of B divided by A.

To find the upper bound, we're going to need to take the largest possible value for B and divide it by the smallest possible value for A or we're going to need the upper bound of B and divide this by the lower bound of A.

In this case, we would get an upper bound of 1.

138716.

Similarly, with our lower bound we're going to need to use the smallest possible value for B and divide this by the largest possible value for A.

Therefore, I'm going to calculate the lower bound of B divided by the upper bound of A.

This gives us a lower bound of 1.

09278.

Here are some questions for you to try.

Pause the video to complete your task and click resume once you're finished.

And here are your solutions.

So for question one, the error interval would be found by finding your upper and lower bounds.

And for question two, if you think about this carefully, we need the least possible area.

So this means we're going to multiply the lower bound of the length by the lower bound of the length as it's a square.

And to find the least possible perimeter, we're going to calculate with the lower bound of the length and multiply this by four as we have four sides.

And here's your last question.

Pause the video to complete your task and click resume once you're finished.

And here are your solutions.

So remember, just take care with this question.

The first step will be to find the upper and lower bound of A and the upper and lower bound of B, and then consider each question carefully as you work through them.

And that brings us to the end of our lesson.

So by now you should be able to combine lots of skills incorporating upper and lower bounds.

Why not try our exit quiz to show off your new skills.

I'll hopefully see you soon.