Using Formulas

Introduction to Using Formulas in Algebra

Understanding the Role of Formulas

  • A formula in maths provides a rule for how to calculate a certain value.

  • Algebraic formulas allow for a straightforward way to express complex mathematical relationships and patterns.

  • They are expressions with set variables which can be filled in to give numerical solutions.

Common Formulas in Algebra

  • One of the basic formulas is the formula for the area of a rectangle which is Area = Length × Width.

  • The quadratic formula is another popular formula, which is used for finding the roots of a quadratic equation. The formula is x = [-b ± sqrt(b^2 - 4ac)] / 2a.

  • Pythagoras’ theorem is a key formula used in mathematics which relates the lengths of the sides in a right-angled triangle. It is a^2 + b^2 = c^2.

Applying Formulas in Algebra

Substitution of Variables

  • To use a formula, you need to substitute specific values into their corresponding variables.

  • Always carefully substitute to ensure accuracy, for example, when x=2 is necessary in the equation y = 2x + 3, the value of y becomes 7.

Solving for an Unknown Variable

  • A formula can also be rearranged to solve for an unknown variable. For example, in the formula Area = Length × Width, if the area and length are known, the formula can be rearranged to find the width.

  • Equation manipulation is essential in rearranging formulas. Strong understanding in the priority of operations and the inverse operations are essential in rearranging formulas.

Checking Answers

  • Always check your answers once you’ve used and solved a formula to ensure your solution is feasible and no mistakes were made during calculation.

Use the Correct Units

  • In practical problems, you always have to check and ensure your answer corresponds to the correct units as per the question. In distance, speed and time problems, for example: speed is typically in miles per hour or meters per second, distance is often in miles or meters, and time often in hours or seconds.

Understanding how to use formulas is essential in maths and provides a key stone for more advanced mathematics.