Algebra Study Guide

Changing the subject of a formula means rearranging an equation to isolate a different variable. This involves performing inverse operations on both sides of the equation until the desired variable is by itself on one side. For higher methods, this often includes dealing with more complex structures like square roots, squares, fractions where the subject is in the denominator, and sometimes expressions where the subject appears multiple times, requiring factorisation. The core principle remains to undo operations in reverse order of operations (BIDMAS/PEMDAS). For instance, if the subject is multiplied and then has a number added, you first subtract the number then divide. When the subject is part of a fraction, multiplying by the denominator is usually the first step to clear the fraction. If the subject appears in multiple terms, collect those terms on one side and then factorise to isolate it. Remember that whatever operation you perform on one side of the equation, you must perform the exact same operation on the other side to maintain equality. Careful attention to signs and the order of operations is crucial for success.

The circumference and area of a circle are two fundamental measurements that describe its properties. The circumference is the distance around the edge of the circle, similar to the perimeter of other shapes. The area is the amount of surface enclosed within the circle. Both of these measurements are directly related to the circle's radius (the distance from the centre to any point on the circumference) or its diameter (the distance across the circle through the centre, which is twice the radius). The mathematical constant pi (π) plays a crucial role in these formulas. Pi is an irrational number, approximately 3.14159, representing the ratio of a circle's circumference to its diameter. We use specific formulas to calculate these values. For circumference, there are two primary formulas: C = 2πr (where 'r' is the radius) or C = πd (where 'd' is the diameter). These are equivalent because d = 2r. For the area of a circle, the formula is A = πr². It's important to remember these formulas as they are not typically provided in examinations and are widely used in various mathematical and real-world applications.