What is direct proportion ?

Direct proportion means that as one variable goes up the other goes up by the same factor .

What is inverse proportion ?

Inverse proportion means as one variable goes up the other goes down by the same factor .

How do you test whether a suggested variation model fits a table of data?

Substitute each x value from the table into the model and compare the y value it predicts with the actual one. Do this for at least three data points before deciding whether the model is a good fit.

True or False? If a variation model fits one data point, it is a good model for the data.

False. You can always choose k to make a model of any type pass exactly through a single point, so one point rules nothing out. It is the second and third points that show whether the shape of the model is right.

Two different variation models are suggested for the same data. How do you decide which is more suitable?

Work out what each model predicts at every x value in the table, and set both sets of predictions beside the actual values. Neither model has to fit perfectly: the more suitable one is simply the one whose predictions stay consistently closer to the real data.

How can a rough graph of the data help you choose a variation model?

The shape of the plotted points suggests which family to try, so a U shaped curve points towards a quadratic model. A graphic display calculator will plot the points for you, and you then test that suggested model against the numbers.

IGCSEMathsCambridge (CIE)International MathsExtendedFlashcardsAlgebra & SequencesProportion

Proportion (Cambridge (CIE) IGCSE International Maths: Extended): Flashcards

Exam code: 0607

1/20

0Still learning

Know0

FrontDirect Proportion
What is direct proportion?

Was this flashcard helpful?

Cards in this collection (20)

What is direct proportion?
Direct proportion means that as one variable goes up the other goes up by the same factor.
True or False?
If $x$ and $y$ are directly proportional, then $x : y$ will always be the same.
True.
If $x$ and $y$ are directly proportional, then $x : y$ will always be the same.
What is $k$ used to represent when working with direct proportion?
When working with direct proportion, $k$ is used to represent the constant of proportionality that connects $x$ and $y$ .
$y = k x$ when $x$ and $y$ are directly proportional.
What does it mean for $y$ to be directly proportional to the square of $x$ ?
If $y$ is directly proportional to the square of $x$ , it means that $y = k x^{2}$ .
True or False?
The graph of two directly proportional variables is a straight line.
True.
The graph of two directly proportional variables is a straight line.
True or false?
When solving a direct proportion problem, one of the first things you should do is find the value of the constant of proportionality $k$ .
True.
When solving a direct proportion problem, one of the first things you should do is find the value of the constant of proportionality $k$ .
What is inverse proportion?
Inverse proportion means as one variable goes up the other goes down by the same factor.
What is $k$ used to represent when working with inverse proportion?
When working with inverse proportion, $k$ is used to represent the constant of proportionality that connects $x$ and $y$ .
$y = \frac{k}{x}$ when $x$ and $y$ are inversely proportional.
True or False?
If $x$ is inversely proportional to $y$ , then $x : y$ will always be the same.
False.
If $x$ is inversely proportional to $y$ , then $x : \frac{1}{y}$ will always be the same.
How would you describe the relationship between $A$ and $B$ if $A = \frac{k}{B}$ ?
If $A = \frac{k}{B}$ , it means that $A$ is inversely proportional to $B$ .
What is the equation for $A$ in terms of $B$ if $A$ is inversely proportional to the square of $B$ ?
If $A$ is inversely proportional to the square of $B$ , then $A = \frac{k}{B^{2}}$ .
True or False?
The graph of two inversely proportional variables is a straight line.
False.
The graph of two inversely proportional variables is a not a straight line.
What is the formula for $y$ in terms of $x$ if $y$ is inversely proportional to the cube root of $x$ ?
If $y$ is inversely proportional to the cube root of $x$ , then $y = \frac{k}{\sqrt[3]{x}}$ .
Using laws of indices that can also be written as $y = \frac{k}{x^{\frac{1}{3}}}$ or $y = k x^{- \frac{1}{3}}$ .
Complete the names of the variation models.
A model of the form $y = k x$ is called linear, one of the form $y = k x^{2}$ is called $______$ and one of the form $y = k x^{3}$ is called $______$ as well.
The completed sentence is:
A model of the form $y = k x$ is called linear, one of the form $y = k x^{2}$ is called quadratic and one of the form $y = k x^{3}$ is called cubic as well.
Each name comes from the power of x in the equation.
How do you test whether a suggested variation model fits a table of data?
Substitute each x value from the table into the model and compare the y value it predicts with the actual one.
Do this for at least three data points before deciding whether the model is a good fit.
True or False?
If a variation model fits one data point, it is a good model for the data.
False.
You can always choose k to make a model of any type pass exactly through a single point, so one point rules nothing out.
It is the second and third points that show whether the shape of the model is right.
A model is known to be quadratic, and the data includes the point where x is 2 and y is 20. What is its equation?
Substitute into $y = k x^{2}$ to get $20 = k \times 2^{2}$ which gives $k = 5$ for this data.
The full equation of the model is therefore $y = 5 x^{2}$ throughout.
For data $x = 2, 4, 6$ with $y = 20, 80, 180$ in order, is a linear model suitable?
No, because a linear model $y = k x$ fitted to the first point gives $k = 10$ as its constant.
That model predicts $10 \times 4 = 40$ at $x = 4$ where the data says 80, so the linear shape is wrong.
Two different variation models are suggested for the same data. How do you decide which is more suitable?
Work out what each model predicts at every x value in the table, and set both sets of predictions beside the actual values.
Neither model has to fit perfectly: the more suitable one is simply the one whose predictions stay consistently closer to the real data.
How can a rough graph of the data help you choose a variation model?
The shape of the plotted points suggests which family to try, so a U shaped curve points towards a quadratic model.
A graphic display calculator will plot the points for you, and you then test that suggested model against the numbers.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:SequencesNext:Exponentials & Logarithms