CSEC Maths - Changing the subject of the formula

Summary

In this tutorial, the presenter walks through the essential mathematical process of changing the subject of a formula. Key steps include isolating variables by applying operations such as addition, subtraction, multiplication, division, and cross-multiplication. The video also explores how to handle equations with fractions and square roots, as well as more complex expressions. Emphasis is placed on understanding the rationale behind each operation and practicing various examples to build confidence in solving equations. The tutorial is designed to help learners master this foundational math skill.

Takeaways

• 🔢 Changing the subject of a formula means rearranging the equation to express one variable in terms of others.
• ➖ To isolate a variable, perform the same operation on both sides of the equation (e.g., subtracting or adding).
• ✖️ In equations like y + 2 = x, subtract 2 from both sides to make y the subject (y = x - 2).
• ➕ For equations like y - 5 = x, add 5 to both sides to get y = x + 5.
• ⚖️ When variables appear on both sides, ensure they are moved to one side by performing inverse operations (e.g., 2x = 6 - y → add y to both sides).
• ➗ When a variable is multiplied by a constant, divide both sides by that constant to isolate the variable (e.g., 5y = 10 → y = 10 / 5).
• 🧮 Cross-multiply when fractions are involved to make the variable the subject (e.g., y/2 = 6 → y = 12).
• √ To remove square roots, square both sides of the equation (e.g., x = √(y - 2) → x² = y - 2).
• 📏 Complex formulas, such as those with multiple terms or constants, require careful steps of applying inverse operations (e.g., L = t²G / 4π²).
• 🔑 Practice and familiarity with these methods help make changing the subject of the formula second nature.

Q & A

What does it mean to change the subject of a formula?

Changing the subject of a formula means to manipulate the equation so that the variable of interest is isolated on one side of the equation, typically the left side, and expressed in terms of the other variables or constants.

How do you make 'y' the subject of the formula y + 2 = x?

To make 'y' the subject of the formula y + 2 = x, you need to subtract 2 from both sides of the equation, resulting in y = x - 2.

What is the rule for performing operations on both sides of an equation?

The rule is that whatever operation you perform on one side of the equation, you must perform the same operation on the other side to maintain equality.

How do you handle a negative sign when changing the subject of a formula?

When changing the subject of a formula and encountering a negative sign, you can move the term to the other side of the equation, which converts the negative sign to a positive.

What is cross-multiplication and when is it used?

Cross-multiplication is a technique used when you have a fraction set equal to another fraction. You multiply the numerator of the first fraction by the denominator of the second fraction and set it equal to the product of the denominator of the first fraction and the numerator of the second fraction.

How do you deal with an equation that has square roots when changing the subject?

When dealing with square roots in an equation, you square both sides of the equation to eliminate the square root sign, then proceed with isolating the variable of interest.

What is the distributive law and how does it apply to equations with brackets?

The distributive law states that a(b + c) = ab + ac. In equations with brackets, you apply the distributive law to remove the brackets by multiplying each term inside the brackets by the term outside.

Can you provide an example of how to change the subject of a formula involving fractions?

An example from the script is y/2 = 6. To change the subject, you can write 6 as 6/1, then cross-multiply to get y * 1 = 2 * 6, resulting in y = 12.

How do you handle equations with multiple terms involving the variable when changing the subject?

First, combine like terms involving the variable on one side of the equation. Then, perform operations to isolate the variable, such as adding or subtracting terms and dividing by coefficients.

What is the final step after making the variable of interest the subject of the formula?

The final step is to ensure the variable is isolated on one side of the equation, typically the left side, and expressed in terms of the other variables or constants.