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Cambridge IGCSE Mathematics practice

exam practice - 1. Estimate the slopes of curves by drawing tangent lines. 2. Utilize the derivatives of functions in the form ax^n, where 'a' is a rational constant and 'n' is a non-negative integer, including simple combinations of up to three of these functions. 3. Use differentiation to find slopes and identify stationary points (turning points). 4. Differentiate between maximum and minimum points using methods such as: • creating an accurate sketch • applying the second derivative test • examining the gradient on either side of a turning point. Note that candidates are not required to find points of inflection. - Differentiation

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2

Paper

6

Marks

Topic

Differentiation

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Paper 2Core or Extended Mathematics6 marks

Estimating Slopes and Identifying Stationary Points

Diagram Description

Curve and Tangent

A curve is shown with a tangent line drawn at point P. The tangent line passes through points (2,3) and (4,7).

  1. a

    Calculate the slope of the tangent line at point P.

    Aim for approximately 2 distinct marking points.

    [2]
  2. b

    Write down the derivative of f(x) = 5x^2 - 4x + 1.

    Aim for approximately 2 distinct marking points.

    [2]
  3. c

    Determine the stationary point(s) of f(x) and classify each as a maximum or minimum by examining the gradient on either side.

    Aim for approximately 2 distinct marking points.

    [2]

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Maths method check

  • Topic focus: Differentiation.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
  • Check the operation, notation, units, and final answer form against the question before moving on.

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Paper 2 structured question: Differentiation

Paper 2Core or Extended Mathematics6 marks

Description

Function Analysis

Consider the function f(x) = 3x^4 - 8x^3 + 6.

  1. a

    Calculate the derivative f'(x) of the function.

    Aim for approximately 2 distinct marking points.

    [2]
  2. b

    Determine the stationary points of f(x).

    Aim for approximately 2 distinct marking points.

    [2]
  3. c

    Explain which stationary point is a maximum and which is a minimum using the second derivative test.

    Aim for approximately 2 distinct marking points.

    [2]