Formulae (AQA GCSE Maths): Revision Notes

Worked Example: Calculating Cooking Time

Let's look at a practical formula for calculating cooking time:

Formula: Cooking time = Weight in kg × 30 + 45

Problem: Find the cooking time for a 7kg turkey

Solution: Step 1: Substitute the weight Cooking time = 7 × 30 + 45

Step 2: Follow BIDMAS - multiply first = 210 + 45

Step 3: Then add = 255 minutes

Step 4: Convert to hours and minutes 255 ÷ 60 = 4 hours and 15 minutes

Worked Example: Physics Distance Calculation

Physics often uses formulae to calculate distance, speed, and time. Here's a distance formula:

Formula: $D = ut - 5t^2$

Given: u = 20 and t = 3

Solution following BIDMAS: Step 1: Indices first $t^2 = 3^2 = 9$

Step 2: Multiplication next $20 \times 3 = 60$ and $5 \times 9 = 45$

Step 3: Subtraction last $D = 60 - 45 = 15$

Therefore, D = 15

Worked Example: Trapezium Area Formula

Formula: $A = \frac{1}{2}(a + b)h$

Given: h = 4.5, a = 6.5, and b = 9.5

Key steps:

• Substitute all values before calculating
• Follow the order of operations carefully
• Work through brackets first, then multiply

$A = \frac{1}{2}(6.5 + 9.5) \times 4.5 = \frac{1}{2} \times 16 \times 4.5 = 36$

Worked Example: Quadratic Formula Component

Formula: $D = b^2 - 4ac$

Given: a = 2, b = 5, and c = -3

Solution: Step 1: Calculate the index first $b^2 = 5^2 = 25$

Step 2: Then multiplication $4 \times 2 \times (-3) = -24$

Step 3: Finally subtraction $D = 25 - (-24) = 25 + 24 = 49$