Worksheet Chapter 3: Algebraic Formulae

1. The surface area S of a cylinder with a closed top and bottom is given by S = 2πrh + 2πr². (a) Express h as the subject of the formula. (b) Find the height h of a cylinder when S = 616 cm², r = 7 cm, and π = 227.

2. Which of the following correctly expresses x as the subject of y = x + 3x - 2?

3. Given the formula p = 3q - 4r, express q as the subject of the formula.

4. Given the formula T = 2π√(Lg), express L as the subject of the formula.

5. Fill in the blank: The variable that is isolated on one side of an equation with a coefficient of +1 is called the ________ of the formula.

6. Given v² = u² + 2as, calculate the value of v when u = 10, a = 2, and s = 21.

7. The total cost RM C of producing n wooden chairs is given by C = 150 + 45n. (a) State the subject of the formula and explain what 150 represents. (b) Rearrange the formula to make n the subject. (c) Calculate how many chairs can be produced with a budget of RM 1,950.

8. True or False: In the equation y = 2x² + 3, changing the subject to x yields x = √(y - 32).

9. True or False: If A = πr², then doubling the radius r will double the area A.

10. Express m in terms of k and n given that k = √(3m - n).