Maths

>

GCSE

Rates of Change

Question

How do you find the rate of change?

2 years ago

ยท

205 Replies

ยท

9352 views

V

Vickie Shanahan


Get A Free Cheatsheet For Rates of Change ๐Ÿ”ฅ

Use our concise notes and diagrams to only revise what you need to know.

By submitting your email, you agree to join our mailing list. You can unsubscribe at any time.

205 Answers

M
Milton Tom

Frays of change is how much x. Ganges w time or another variable . So this can be done by working out the gradient of a graph or differentiating If it is an expression

Found this useful? Give kudos!

Y
Yunho Kwon

Linear functions have a constant rate of change which is represented as the gradient of the graph.

It is simply the change of y-values with respect to x-values i.e. (y1-y2) / (x1-x2) where (x1,y1), (x2,y2) are the coordinates

Found this useful? Give kudos!

L
Leon Cragg

the change in y-values by the change in x-values.

Found this useful? Give kudos!

K
Kai Zhang

The rate of change measures how one quantity changes relative to another. In mathematics, it is often calculated using derivatives in calculus or the difference between two points in algebra. Here are the common methods to find the rate of change:

1. Average Rate of Change (Algebraic Approach)

The average rate of change between two points on a function is calculated as the slope of the line connecting the points. This is given by: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

2. Instantaneous Rate of Change (Using Derivatives)

The instantaneous rate of change of a function at a specific point is the value of the derivative at that point.

wEE8CHEi7wD7gAAAABJRU5ErkJggg==

This gives the slope of the tangent line to the curve at x=ax = ax=a, representing how the function changes at that exact point.

gAAAAASUVORK5CYII=

Found this useful? Give kudos!

Stuart W Profile Picture
Stuart W Verified Sherpa Tutor โœ“

Experienced Physics and Mathematics tutor from beginner to degree

The Rate of change (ROC) is the increase or decrease of one value related to another value.

The speed of a car for instance is the distance covered divided by the time taken.

In mathematics this can be the gradient of a graph in general terms.

Found this useful? Give kudos!

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Abdul M Profile Picture
Abdul M Verified Sherpa Tutor โœ“

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.

Found this useful? Give kudos!

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Andrea Profile Picture
Andrea Verified Sherpa Tutor โœ“

Science & Maths tutor - A-Level, GCSE & KS3 Struggling/Higher Attainers

4 reviews

find the change in y over change in x using triangle on give graph

Found this useful? Give kudos!

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
S
Sam Morris

To find the average rate of change of a function over an interval, you can use the formula:

Average Rate of Change = (Change in Y) / (Change in X) = (ฮ”Y) / (ฮ”X)

Found this useful? Give kudos!

Emanuel Profile Picture
Emanuel Verified Sherpa Tutor โœ“

Experienced and enthusiastic Maths Tutor and Maths teacher of GCSE and

1 reviews

You would have to differentiate

Found this useful? Give kudos!

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
S
Sonya Pervez

The rate of change (ROC) is how much the value of something changes over a period of time and it is given in percentage terms.


To find this you first calculate the change in "Y" values (or the change in an outcome variable) divided by the change in "X" values (or the change in input variables).


So if my tutoring time increases from 3 hours in week 1 to 16 hours in week 2 and my income increases from ยฃ45 per week to ยฃ240 per week, Y values are my income and X values are the work hours I put in. r

To calculate the ROC I would do the following.


(240 - 45) / (16 - 3) = 195 / 13 = 15% rate of change in my earnings between week 1 and week 2.

Found this useful? Give kudos!

Dr M Profile Picture
Dr M Verified Sherpa Tutor โœ“

An experienced tutor for science subjects and competitive exams

If you take the change in Y values and divide that with the change in X-values the result will be a rate of change,

Found this useful? Give kudos!

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
Vashisht K Profile Picture
Vashisht K Verified Sherpa Tutor โœ“

5 years teaching STEM up to Degree level. Master's Graduate from KCL

40 reviews

In a graph of a value vs time, it would be the gradient. Otherwise simply divide the difference in any particular value by the time taken.

Found this useful? Give kudos!

I'm available for 1:1 private online tuition!

Click here to view my profile and arrange a free introduction.
P
Paul Hunt

This is easier to work out from a graph, the rate of change is the gradient of the line - the change in y divided by the change in x. However, you might not have time in exam conditions to draw a graph when it's not asked of you, so I would suggest picking two points of the data - ignoring outliers if there are any. Calculate the difference between them by taking them away from each other, then divide that by the difference in time between them. This will give you the rate of change.

Found this useful? Give kudos!

K
Kaustubh Joshi

Rate of change is essentially the change in the dependent variable (y axis) over the change in the independent variable (x axis). It is how much one quantity e.g velocity changes with respect to another e.g time. All you have to do is figure out the gradient at the point you are trying to find the rate of change at! This gradient is the y/x e.g acceleration.

Found this useful? Give kudos!

U
Unai Llona Carbajo

Derivatives are the best tool, but not for everyone... Considering two variables (distance and time, for example), you can also take the first and last value of both in a certain process, subtract the ones from the same variable (e.g. last and first distances of the bus from your position) and divide the subtractions of different variables. By doing this with position/distance and time, the rate of change you get is the speed of the object you're analyzing!

Found this useful? Give kudos!

Think you can help?

More Maths GCSE Questions
Sherpa Badge

Need a GCSE Maths tutor?

Get started with a free online introductions with an experienced and qualified online tutor on Sherpa.

Find a GCSE Maths Tutor