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Substituting Complex Formulas Worksheet

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Substituting Complex Formulas Worksheet

Mathematical formulas and variables illustration

📚 Part 1: Worked Examples

Example 1: If P = 3a² + 2b - 5, find P when a = 4 and b = 7

Solution:

P = 3a² + 2b - 5

P = 3(4)² + 2(7) - 5

P = 3(16) + 14 - 5

P = 48 + 14 - 5 = 57

Example 2: If Q = 2x(y - 3) + 4y², find Q when x = -2 and y = 5

Solution:

Q = 2x(y - 3) + 4y²

Q = 2(-2)(5 - 3) + 4(5)²

Q = -4(2) + 4(25)

Q = -8 + 100 = 92

Example 3: If R = (a + b)² - 3ab, find R when a = 6 and b = -4

Solution:

R = (a + b)² - 3ab

R = (6 + (-4))² - 3(6)(-4)

R = (2)² - 3(-24)

R = 4 + 72 = 76

✏️ Part 2: Practice Questions

1. If A = 2x² + 3y, find A when x = 3 and y = 5
2. If B = 4p - 2q², find B when p = 7 and q = -3
3. If C = 3m(n + 4), find C when m = -2 and n = 6
4. If D = (x - y)² + 2xy, find D when x = 5 and y = 3
5. If E = 2a² - 3b² + 4c, find E when a = 4, b = 2, and c = -1
6. If F = 5x(y - 2) - 3y², find F when x = -1 and y = 4

🎯 Part 3: Challenge Problems

7. The area of a rectangle is given by A = l × w. If the length is (2x + 3) and the width is (x - 1), find the area when x = 5
8. The formula for the volume of a cylinder is V = πr²h. Find V when r = 3 and h = 8 (use π = 3.14)
9. If T = 3(a + b)² - 2(a - b)², find T when a = 7 and b = 3
10. The cost of hiring a van is given by C = 25 + 0.30d, where d is the distance in miles. Find the cost when d = 120 miles

Answer: £ ___________

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