Maths
>
GCSE
>
Rates of Change
>
How do you...
2 years ago
·
215 Replies
·
10565 views
Vickie Shanahan
215 Answers
University of Leeds Graduate student ready to teach all that is Maths!
The rate of change measures how a quantity changes over time or across space. It's often represented as the slope of a line connecting two points on a graph.
I'm available for 1:1 private online tuition!
Click here to view my profile and arrange a free introduction.Rate of change generally refers to how something changes with respect to something else. For example, velocity is the rate of change of distance with respect to time, and acceleration is the rate of change of velocity with respect to time.
The average rate of change represents the average rate at which something changes from one point to another.
So you need to set up the equation like this:
Rate of change of {x} = (change in x) divided by time taken for the change to happen.
E.g. Rate of change of distance is acceleration.
a = d2 - d1 / t
This is an easy thing to find out. If you have a straight line on a X-Y graph, the formula you would use is y=mx+c. The rate of change is m in this formula is is how steep the line is . To calculate m for this formula you choose two separate points on the line (taking note of their X-Y coordinates). Then you take the difference between the y coordinates then take the difference between the x coordinates. Then you take these two numbers and divide the difference between the y coordinates by the difference between the x coordinates. This will give you the steepness of the line which is m in the formula of a straight line.
The rate of change of a quantity is found using calculus, specifically by finding the derivative of the function that describes the quantity with respect to the variable of interest.
For a function y=f(x):
Take the variable that is changing over a period of time, making note of the first time point and second time point. Subtract this variable at the first time point from the variable at the second time point. Then, take this value and divide it by the difference in time between the two points to get the rate of change.
Rate of change = change in y/change in x
Ready to make your educational journey truly inspiring
3 reviews
When we discuss how objects move, we start with displacement, which indicates an object's position over time. However, just knowing the position isn't always enough—we need to understand how quickly this position changes. This is where velocity comes in. Velocity is the rate of change of displacement with respect to time, telling us how fast an object moves and in what direction. On a graph of position versus time, the slope of the curve at any given point represents the object's velocity. A steeper slope means a higher velocity, while a flatter slope indicates a lower velocity.
Acceleration takes this concept a step further by measuring how velocity changes over time. If an object speeds up, slows down, or changes direction, its velocity is changing, meaning it experiences acceleration. On a graph of velocity versus time, the slope of the curve at any point represents the object's acceleration. A steeper slope here means a greater change in velocity, while a flatter slope means a smaller change. Just as velocity is the rate of change of displacement, acceleration is the rate of change of velocity.
Differentiation is the mathematical tool we use to find these rates of change. It allows us to determine the slope of a curve at any point on a graph. For a displacement-time graph, differentiation helps us find the velocity, the rate at which displacement changes. For a velocity-time graph, differentiation helps us find the acceleration, the rate at which velocity changes. When approaching problems about rates of change, it's crucial to identify the variables, interpret the graph, determine what rate of change you need, and analyze the slope accordingly.
I'm available for 1:1 private online tuition!
Click here to view my profile and arrange a free introduction.Rate of change is a value we can find on a graph. It is simply how quickly the y component changes relative to the x component. To work this out between points (x1,y1) and (x2, y2), we can divide the change in 2 y values by the change in 2 corresponding x values as such -> (y2 - y1)/(x2-x1)
Experienced maths tutor, A level, GCSE. Flexible availability
The rate of change of a function is its first derivative so if y=f(x) then the rate of change is given by dy/dx=f’(x).
I'm available for 1:1 private online tuition!
Click here to view my profile and arrange a free introduction.First calculate the change , i.e. B-A, where A is the original figure, and B is the figure after the change. The divide the change by A and multiply by 100->((B-A)/A)*100=X%
Achieve top GCSE grades with expert tutoring from Imperial College
3 reviews
It is simply a total concerned amount divided by the total time. For example, if you want to find out rate of change of distance. You consider total distance covered by the vehicle and divide it by the total time it took for that change.
Rate of change of position = total covered distance / total taken time.
I'm available for 1:1 private online tuition!
Click here to view my profile and arrange a free introduction.Experienced tutor helping students go from zero to hero!
1 reviews
Use the formula (new-old)/old and multiply by 100 to get a percentage
I'm available for 1:1 private online tuition!
Click here to view my profile and arrange a free introduction.To find the rate of change of something you calculate how much the “something” has changed by and then divide it by the number of seconds that have passed.
The rate of change tells us how one thing changes compared to another. For example, if you're looking at how far a car travels over time, the rate of change would be its speed—how many meters the car moves every second.
First we need to know how much each of these things changes. You do this by subtracting the starting value from the ending value. For example, if a car moves from 10 meters to 30 meters in 4 seconds, the change in distance is 20 meters, and the change in time is 4 seconds.
Then you divide the change in distance by the change in time to get the rate of change. In this case, the car is moving at 5 meters per second. This means every second, the car travels 5 meters.
Hope this helps :)
Think you can help?
Get started with a free online introductions with an experienced and qualified online tutor on Sherpa.
Find a GCSE Maths Tutor