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Substitution and Formulas Worksheet

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Substitution and Formulas Worksheet worksheet preview

Substitution and Formulas Worksheet

Mathematical formulas and equations illustration

📚 Understanding Substitution and Formulas

What is substitution? Substitution means replacing letters (variables) in a formula with numbers.

Example 1: If y = 3x + 5 and x = 4

Substitute x = 4: y = 3(4) + 5 = 12 + 5 = 17

Example 2: Area of rectangle: A = l × w

If length = 8m and width = 5m: A = 8 × 5 = 40m²

Example 3: Converting temperature: F = (9 × C) ÷ 5 + 32

If C = 20°C: F = (9 × 20) ÷ 5 + 32 = 180 ÷ 5 + 32 = 36 + 32 = 68°F

1. If y = 2x + 7 and x = 3, what is the value of y?

10

13

14

17

2. Using the formula A = l × w, find the area when l = 6cm and w = 4cm.

10cm²

20cm²

24cm²

26cm²

✏️ Substitution Practice

3. If p = 4q - 3 and q = 5, find p. Show your working:
4. Substitute a = 2 and b = 7 into the expression 3a + 2b:
5. The formula for the perimeter of a rectangle is P = 2l + 2w. Find P when l = 9m and w = 4m:
6. If y = x² + 4 and x = 3, calculate y:
7. The cost formula is C = 5n + 10, where n is the number of items. Find the cost when n = 8:

🎯 Real-World Applications

8. The formula to convert miles to kilometres is K = 1.6M, where M is miles. How many kilometres is 15 miles?
9. A mobile phone tariff costs £12 per month plus £0.15 per text. The formula is C = 12 + 0.15t. Find the cost for 80 texts:
10. The area of a triangle is A = ½bh, where b is base and h is height. Find the area when b = 10cm and h = 6cm:
11. Challenge: If s = ut + ½at² and u = 5, t = 4, a = 2, find s:

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