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Countdown to Exams - Day 75 - Estimating gradients, Area under a curve

Countdown to Exams - Day 75 - Estimating gradients, Area under a curve

In today's blog, we attempt to tackle two fairly complex topics in the GCSE course. Firstly, we look at Estimating gradients.Calculating the average gradient from beginning to end does not give a good representation of what is happening in the graph. What can be done is to break the graph down into smaller sections and the average gradient of those are calculated to give a better idea of what is happening. Another method is to find the gradient at specific points on the graph, this involves constructing a series of tangents by eye and calculating the gradient at each point. This is where an estimate comes in because each tangent may vary slightly.

Secondly, we take a look at the area under a curve. The area under a velocity-time graph (most common question) will give you the distance that the object/particle has travelled. You will have to break the graph up into equal widths to give you a triangle and a series of trapezia. Calculate the area of each shape and that will tell the distance travelled.

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Countdown to Exams - Day 56 - Area and Circumference (Circles)

Countdown to Exams - Day 56 - Area and Circumference (Circles)

In today's countdown, we focus on the topic of area and circumference of circles. As with all area formulae, you will need to memorise these for the area and circumference of a circle.  Make sure you are dealing with the element of the circle (diameter or radius) before you substitute into the formula. Always double check your calculations to see if your answer is reasonable (circumference is about three times the length of the diameter).

When calculating sector areas and arc lengths remember to work out the proportion of the circle you are dealing with (amount of degrees given over 360). Then it is a case of using the original formulae to calculate your answer.

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Countdown to Exams - Day 54 - Advanced areas

Countdown to Exams - Day 54 - Advanced areas

In today's countdown, we take a look at the more Advanced areas that you will come across. We start off with a Parallelogram which is base times height (perpendicular). Just imagine a 'tilted' rectangle. The formula for the trapezium is more complex but just follow the three steps of 1) Add the parallel sides, 2)Halve it, 3)Multiply by height (perpendicular). You might be required to use this formula to find the area under a graph as well as just a shape.

We finish off with the sine rule to find the area of a triangle when you have two sides and the included angle (no height). All area formulae need to be memorised so make sure you can recall them all.

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Countdown to Exams - Day 53 - Perimeter and Area

Countdown to Exams - Day 53 - Perimeter and Area

Today our focus is on Perimeter and Area. The Perimeter of a shape is the distance around a shape and will require you to add up all of the side lengths together. You may have to deal with numbers and algebraic terms so make sure you are confident in collecting like terms. You also need to be aware of the properties of shapes so you can fill in missing lengths because they are equal etc.

Area is the space inside a 2D-shape. It is normally calculated by multiplying two lengths together (a horizontal and a vertical length).

You must take care of the units you have been given in the question and convert them all to the same if required. You are not given any formula for an area so make sure memorise them all.

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