Notation, vocabulary and manipulation: substitute numerical values into formulae and expressions, including scientific formulae

The idea

Substitution involves replacing each letter in a mathematical or scientific formula with a specific numerical value, then evaluating the expression using the correct order of operations. For example, in the kinematic formula v = u + at, if u = 3, a = 2, and t = 5, substituting these values gives v = 3 + 2 × 5 = 13. Scientific formulae, such as F = ma or v = fλ, require the exact same mathematical process. When tackling multiple-choice questions, substitute values carefully, ensure units are consistent, and evaluate step-by-step. Negative values must be placed in brackets when substituted; for instance, evaluating x² when x = −4 yields (−4)² = 16, whereas omitting brackets might lead to an incorrect −16.

What earns the marks

• Replace each letter in the expression or formula with its given numerical value, using brackets for negative values.
• Apply the correct order of operations (BIDMAS/BODMAS), ensuring indices are calculated before multiplication and division.
• Evaluate scientific formulae such as F = ma or v = fλ accurately by substituting the given quantities.
• Keep units consistent throughout the calculation and interpret the final numerical result in its correct context.
• Check the computed value against the multiple-choice options, ensuring no sign errors were made.

Common mistakes and how to put them right

• Substituting a negative number without brackets, so x² with x = −4 is wrongly evaluated as −16.

  Put it right by writing (−4)² = 16.

• Applying operations in the wrong order, for example adding before multiplying.

  Put it right: Strictly following the order of operations.

• Treating a coefficient as an added term, for example reading 3y as 3 + y.

  Put it right by treating 3y as 3 × y.

Exam tips

• Write the substitution step explicitly before calculating so you can check each value has been placed correctly.
• Use brackets around every negative value you substitute, especially when it is raised to a power.
• Re-read the formula to confirm which letter represents which quantity before substituting.