Substitution (Edexcel GCSE Maths): Revision Notes

Simple Substitution Example

If $x = 7$ and $y = 2$, and you need to find the value of $x + 5y$:

• Replace $x$ with 7: $7 + 5y$
• Replace $y$ with 2: $7 + 5 \times 2$
• Calculate: $7 + 10 = 17$

BIDMAS Example

To work out $2 \times 5^2 - (14 + 8)$:

1. Brackets first: $(14 + 8) = 22$
2. Indices next: $5^2 = 25$
3. Multiplication: $2 \times 25 = 50$
4. Subtraction: $50 - 22 = 28$

Example 1: Simple substitution with negative numbers

Work out the value of $5x + 1$ when $x = -3$

Step 1: Substitute $x = -3$ into the expression $5 \times (-3) + 1$

Step 2: Calculate multiplication first (BIDMAS) $= -15 + 1$

Step 3: Add the numbers $= -14$

Example 2: Substitution with indices

Work out the value of $5p^3$ when $p = 2$

Step 1: Substitute $p = 2$ into the expression $5 \times 2^3$

Step 2: Calculate the index first (BIDMAS) $2^3 = 8$

Step 3: Multiply $5 \times 8 = 40$

Example 3: Multiple variables

Work out the value of $3m + 4n$ when $m = 5$ and $n = -2$

Step 1: Substitute both values $3 \times 5 + 4 \times (-2)$

Step 2: Calculate multiplications first $= 15 + (-8)$

Step 3: Add the numbers $= 15 - 8 = 7$

Example 4: Expressions with brackets

Work out the value of $2x(x - 1)$ when $x = 11$

Step 1: Substitute $x = 11$ into the expression $2 \times 11 \times (11 - 1)$

Step 2: Work out the brackets first $= 2 \times 11 \times 10$

Step 3: Multiply from left to right $= 22 \times 10 = 220$