GCSE Secondary Maths Age 13-17 - Ratio, Proportion & Rates of Change: Direct and Inverse Proportion - Explained

The video tutorial explains how to solve a problem involving both direct and inverse proportions. It begins by defining direct and inverse proportions, then demonstrates how to set up equations for each type. The tutorial walks through finding the constants of proportionality and combining the equations to express Y in terms of X. The final answer is simplified, and the marking scheme for the problem is discussed. The tutorial emphasizes understanding the rules of proportions and careful problem-solving.

What does 'directly proportional' imply in terms of mathematical operations?

• Division

• Multiplication

• Subtraction

• Addition

If D is directly proportional to X^2, and D = 24 when X = 2, what is the constant of proportionality?

• 3

• 4

• 6

• 5

In an inverse proportion, if Y is inversely proportional to D^2, and Y = 4 when D = 10, what is the constant of proportionality?

• 100

• 200

• 300

• 400

What operation is used to combine the direct and inverse proportion equations to eliminate D?

• Division

• Multiplication

• Substitution

• Addition

What is the final formula for Y in terms of X after simplification?

• Y = 100 / 8 * X^3

• Y = 100 / 9 * X^4

• Y = 100 / 8 * X^4

• Y = 100 / 9 * X^3

How many marks are allocated for setting up the direct proportion equation?

• 4 marks

• 3 marks

• 2 marks

• 1 mark

What is a key step in solving combined direct and inverse proportion problems?

• Using only inverse proportion

• Ignoring the constants

• Finding the constants of proportionality

• Using only direct proportion