Direct Proportion: Finding The Relationship Between Variables

Introduction

Welcome back to another Secondary Math blog post on the topic of Direct Proportion!

In this blog post, we will be answering a Direct Proportion question from the 2018 Zhonghua Secondary School (ZHSS) S2E SA1 Examination Paper.

Keep on reading to learn how to approach questions about the relationship between two variables.

Alternatively, you can watch our explainer video on this question here.

Let’s Take A Look At This Direct Proportion Question

Source: Zhonghua Secondary School — 2018 S2E SA1 Examination Paper [Q11]

Thought Process

🧐 What Is The Formula For A Direct Proportion Question? 🧐

The formula is y = kx, where k is a constant. Remember that for direct proportion questions, the only two variables are y and x.

However, you will notice that in the question, there is no y or x because they are replaced by A and h.

How can we form our equation then?

We are going to replace y with A, and x with h. Meanwhile, k will remain the same.

But the question says that A is directly proportional, not to h. It is directly proportional to the square root of h.

So our equation should be:

💭 Remember This When Writing The Equation 💭

Write down “where k is a constant.” This is important because k is not a variable, k always has to be a constant.

Next, the question says that given that A = 10 and h = 225, what is the relationship between A and h?

Whenever the question asks about the relationship of the two variables, which are A and h in this question, what it wants you to do is to write down the equation that involves A and h as the variables.

So in the final stage, when we come up with our equation, we only want to see A and h as the variables. Any other coefficients should be in numbers.

Therefore, we do not want k in our equation because we only want A and h to be our variables. This means that we need to look for the value of k.

Since the question gave us the values of A and h, we can substitute these values to form the equation:

Let us now solve the equation!

Because k is a constant, it will always be 2/3.

From here, we can now come up with our equation with only A and h as our variables:

Suggested Answer

Conclusion

I hope that after reading this blog post, you learned how to approach Direct Proportion questions better and faster!

To summarise the key learning points:

• When faced with any questions about Direct Proportion, remember that the formula is y = kx, where k is a constant. Write this on your question paper first!
• When you are asked to find the relationship between two variables, which are A and h in this question, it wants you to write down the equation with only A and h as variables. Other coefficients should be in numbers.

Stay tuned for more Secondary Math blog posts!