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NSC / Matric Differential Calculus — practice questions

Explore 6 free Differential Calculus questions in NSC / Matric Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Differential Calculus questions and exercises with answers

Showing questions 1–6 of 6.

Which two related branches make up calculus?Read the answer and worked solution →When does the limit of a function at a point exist?Read the answer and worked solution →What does the derivative of a function give at a chosen point on its graph?Read the answer and worked solution →Why are the turning points of a cubic graph called local maximum and local minimum points?Read the answer and worked solution →Find the x coordinates of the stationary points of f(x) = x^3 minus 3x^2 minus 9x plus 5.Read the answer and worked solution →The curve f(x) = x^2 plus 2x is taken at the point where x = 1. What is the equation of the tangent to the curve there?Read the answer and worked solution →

Worked practice questions

Which two related branches make up calculus?

  1. Algebraic and numerical
  2. Analytical and Euclidean
  3. Discrete and continuous
  4. Differential and integral
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Correct answer: D. Differential and integral

1. Calculus grew out of algebra and geometry and rests on the idea of a limit. 2. It is made up of two related branches, differential calculus and integral calculus. 3. Grade 12 work covers only the differential branch. 4. That branch is used for rates of change and for optimisation problems. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 6: Differential calculus_

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When does the limit of a function at a point exist?

  1. Both sides approach one value
  2. The function is defined there
  3. The graph has no sharp corner
  4. The function is always rising
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Correct answer: A. Both sides approach one value

1. A limit asks what value a function heads towards as the input creeps up on a chosen point. 2. The input can creep up from the left or from the right, and the two need not agree. 3. The limit exists only when the function heads for the same value from both sides. 4. If the two sides head for different values, the limit at that point does not exist. 5. A function can have a limit at a point where it is not even defined, so being defined there is not the test. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 6: Differential calculus_

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What does the derivative of a function give at a chosen point on its graph?

  1. The gradient of the secant
  2. The gradient of the tangent
  3. The area under the curve
  4. The height of the curve
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Correct answer: B. The gradient of the tangent

1. The average gradient between two points on a curve is the gradient of the secant joining them. 2. Slide the second point closer and closer to the first and the secant turns towards the tangent. 3. The limit of that process gives the gradient of the tangent at the single point. 4. That limit is exactly what the derivative calculates. 5. The secant needs two points, so it cannot be what a derivative at one point returns. _Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 6: Differential calculus_

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