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Using Formulae0%

Measurement & Geometry · Topic 3 of 9

Using Formulae

Video coming soon3 worked examples

Theory

The Golden Rule: The most critical step when using any formula is checking the units before you substitute your numbers. Questions frequently give you a measurement in centimetres when the formula explicitly requires metres. If you plug the raw numbers in without converting first, you will lose the majority of the marks.

1. Given Formulae

In the exam, you will often be asked to calculate a quantity based on two related pieces of information. For these questions, you will be given the specific formula in the text of the question (e.g., calculating Density or Body Mass Index). You do not need to memorise these specific scientific formulae; you simply need to substitute the correct numbers into them.

2. Formula Triangles & Rearranging

Many of the formulae you will be given involve three variables (e.g., $\text{Density} = \frac{\text{Volume}}{\text{Mass}}$ ).

You can use a "formula triangle" to help you rearrange the equation.

Put the isolated variable (e.g., Mass) at the top of the triangle, and the other two (Density and Volume) at the bottom.
Cover up the value you are trying to find: if the remaining two are next to each other, you multiply. If one is above the other, you divide.

3. Unit Consistency

You must ensure the units of the numbers you are substituting match the units required by the formula. For example, if a formula calculates density in grams per cubic centimetre (g/cm³), your mass must be in grams and your volume must be in cubic centimetres before you calculate.

4. BODMAS in Formulae

When using formulae like $\text{BMI} = \frac{\text{Mass}}{\text{Height}^2}$ , you must remember your order of operations. The height must be squared before you divide the mass by it.

⚠️ Common Examiner Traps

The "Unit Mismatch" Trap: This is the most common trick in formula questions. For example, giving a patient's height in centimetres (e.g., 182 cm) but asking you to use a BMI formula that requires the height to be in metres. You must convert 182 cm to 1.82 m before substituting it in.
The "Wrong Subject" Trap: A question gives you the Density and the Mass, but asks you to calculate the Volume. Candidates often just divide the first number by the second number blindly. Use your formula triangle to ensure you are doing the correct operation!
The "Forgotten Square" Trap: In formulae with indices (like $\text{Height}^2$ ), candidates frequently forget to actually square the number on their calculator, dividing only by the base height.

Worked examples

Example 1

A medical clinic uses the following formula to calculate Body Mass Index (BMI):

\text{BMI} = \frac{\text{Mass}}{\text{Height}^2}

(where Mass is in kilograms and Height is in metres).

A patient’s mass is 84 kilograms and their height is 165 centimetres. Calculate the BMI of the patient. Give your answer to 1 decimal place. (3 marks)

Step 1: Check the units. The mass is in kg (correct), but the height is in cm. Convert the height to metres.

165 \text{ cm} \div 100 = 1.65 \text{ m}

Step 2: Substitute the values into the formula and apply BODMAS (square the height first).

\text{Height}^2 = 1.65^2 = 2.7225

Step 3: Divide the mass by the squared height.

84 \div 2.7225 = 30.85399...

Step 4: Round to 1 decimal place.

\text{BMI} = 30.9

Example 2

The density of an object can be calculated using the formula below.

\text{Density} = \frac{\text{Mass}}{\text{Volume}}

A solid metal rectangular block has dimensions 5 cm by 4 cm by 12 cm. The mass of the block is 1.68 kilograms. Calculate the density of the metal block. Give your answer in grams per cubic centimetre. (4 marks)

Step 1: Calculate the volume of the block.

V = 5 \times 4 \times 12 = 240 \text{ cm}^3

Step 2: Check the required units for the final answer. It requires grams, but the mass given is in kilograms. Convert the mass.

1.68 \text{ kg} \times 1000 = 1680 \text{ grams}

Step 3: Substitute the compatible values into the formula.

\text{Density} = \frac{1680}{240}

Final Answer:

\text{Density} = 7 \text{ g/cm}^3

Example 3

The pressure exerted by an object on the ground can be calculated using the formula:

\text{Pressure} = \frac{\text{Force}}{\text{Area}}

A heavy crate exerts a pressure of 45 N/m² over a ground area of 3.2 m². Calculate the total force applied by the crate. (2 marks)

Step 1: Rearrange the formula to make Force the subject. Using a formula triangle, because Pressure and Area are on the bottom, we multiply them to find the Force on top.

\text{Force} = \text{Pressure} \times \text{Area}

Step 2: Substitute the values (the units already match).

\text{Force} = 45 \times 3.2

Final Answer:

\text{Force} = 144 \text{ N}

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8 Using Formulae questions with answers and video solutions