MATHEMATICSAlgebra
Substitution
x=2
y=5
● Master Topic Guide Verified 11+ Curriculum
Algebraic Substitution Guide 🔢
Master substituting numbers into expressions, using BIDMAS, working out word problems, and checking answers!
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ALGEBRAIC SUBSTITUTION
Substitution means replacing a letter (variable) with a number. Then work out the value of the expression.
KEY IDEAS
- ★ Letters in algebra represent numbers.
- ★ Substitute the given value into expression.
- ★ Follow order of operations (BIDMAS).
- ★ Check your answer makes sense.
1. WHAT IS SUBSTITUTION?
An expression contains letters (variables) and numbers. We can substitute a number for the letter and then simplify to find the value.
Expression: 3a + 5
↑ 3avariable (a)
↑ 5number
2. HOW TO SUBSTITUTE
1Read expression carefully.
2Replace letter with given number.
3Simplify using BIDMAS.
4Write answer clearly.
BIDMAS ORDER
B Brackets
I Indices
D Division
M Multiply
A Addition
S Subtract
Live Substitution Playground:
a =
b =
5a + 7 ➔ 5(4) + 7 ═ 27
2b - 9 ➔ 2(3) - 9 ═ -3
3(a + b) ➔ 3(4+3) ═ 21
a² + b ➔ 4² + 3 ═ 19
3. WORKED EXAMPLES
A. One StepExample: If a = 4, find 5a + 7
5a + 7
↓ substitute a = 4
═ 5 × 4 + 7
═ 20 + 7
═ 27
Answer: 27
B. Two StepsExample: If b = 6, find 2b - 9
2b - 9
↓ substitute b = 6
═ 2 × 6 - 9
═ 12 - 9
═ 3
Answer: 3
C. With BracketsExample: If c = 5, find 3(c + 2)
3(c + 2)
↓ substitute c = 5
═ 3(5 + 2)
═ 3(7)
═ 21
Answer: 21
D. More Than One OperationExample: If d = 8, find 2d² - d + 3
2d² - d + 3
↓ substitute d = 8
═ 2(8²) - 8 + 3
═ 2(64) - 8 + 3
═ 128 - 8 + 3
═ 123
Answer: 123
4. YOUR TURN - TRY THESE!
Substitute the given value and calculate:
1) If a = 3, find 4a + 5:
2) If b = 7, find 3b - 4:
3) If c = 2, find 5(c + 3):
4) If d = 4, find d² + 2d - 1:
5) If e = 6, find 3e² - 2e + 5:
5. WORD PROBLEMS
1) The perimeter of a rectangle is given by P = 2l + 2w. If l = 12 cm and w = 7 cm, what is the perimeter?
P ═ 2(12) + 2(7) ═ 24 + 14 ═ 38 cm
2) The total cost of n notebooks at £2.50 each and a pen costing £1.20 is given by C = 2.50n + 1.20. If n = 8, what is the total cost?
C ═ 2.50(8) + 1.20 ═ 20.00 + 1.20 ═ £21.20
6. TOP TIPS
- ★ Always substitute carefully.
- ★ Work in order (BIDMAS).
- ★ Use brackets when needed.
- ★ Check your answer makes sense!
7. CHECK YOUR UNDERSTANDING
If a = 5, then 2a + 3 = 13
If b = 4, then b² - 6 = 10
If c = 3, then 2(c + 4) = 14
If d = 6, then 3d - 2d = 18
8. REMEMBER 🧠
"Substitution is a key skill in algebra. Practice makes perfect!"
Swap letter ➔ Calculate BIDMAS ➔ Verify!
🚀 Ready to Test Your Skill?
Take our graded 11+ Algebraic Substitution assessment now!