Formulae — O/L Mathematics

How do I practise Formulae?

2 questions with worked solutions

1. Make 'r' the subject of the formula: A = 4πr² (where r > 0).
   1. A) r = (A / 4π)²
   2. B) r = A / (4π)
   3. C) r = √(4πA)
   4. D) r = √(A / (4π))
   Check my answer

   Correct answer: D) r = √(A / (4π))

   Divide both sides by 4π: r² = A / (4π). Taking positive square root since r > 0: r = √(A / (4π)).

   Show worked solution

   Step 1: Start with A = 4πr². Step 2: Divide both sides by 4π: r² = A / (4π). Step 3: Take square root of both sides: r = ±√(A / (4π)). Step 4: Since radius r > 0, r = √(A / (4π)). Answer: r = √(A / (4π)).
   Modelled on: the O/L Mathematics examination pattern
2. Make 't' the subject of the formula v = u + at. Hence find t when v = 20, u = 5 and a = 3.
   1. A) t = v - u - a; t = 12
   2. B) t = a(v - u); t = 45
   3. C) t = (v - u) / a; t = 5
   4. D) t = (v + u) / a; t = 25/3
   Check my answer

   Correct answer: C) t = (v - u) / a; t = 5

   Subtracting u from both sides gives v - u = at, and dividing both sides by a gives t = (v - u) / a. Substituting the values, t = (20 - 5) / 3 = 5.

   Show worked solution

   Step 1: Start with v = u + at. Step 2: Subtract u from both sides: v - u = at. Step 3: Divide both sides by a: t = (v - u) / a. Step 4: Substitute v = 20, u = 5, a = 3: t = (20 - 5) / 3 = 15 / 3 = 5. Answer: t = (v - u) / a; t = 5.
   Modelled on: the O/L Mathematics examination pattern

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Where does Formulae fit in the syllabus?

Grade 10 · Term 3