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Skills available for Singapore secondary 4 maths curriculum

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S3-4.A Algebra

S3-4.G Geometry and Trigonometry

S3-4.C Calculus

  • S3-4.C1 Derivative of integration

    • S3-4.C1.1 Derivative of f(x) as the gradient of the tangent to the graph of y = f(x) at a point

    • S3-4.C1.2 Derivative as rate of change

    • S3-4.C1.3 Use of standard notations f'(x), f"(x), dy/dx, d²y/dx²[= d/dx (dy/dx)]

    • S3-4.C1.4 Derivatives of xn, for any rational n, together with constant multiples, sums and differences

    • S3-4.C1.5 Derivatives of products and quotients of functions

    • S3-4.C1.6 Derivatives of composite functions

    • S3-4.C1.7 Increasing and decreasing functions

    • S3-4.C1.8 Stationary points (maximum and minimum turning points and stationary points of inflexion)

    • S3-4.C1.9 Use of second derivative test to discriminate between maxima and minima

    • S3-4.C1.10 Apply differentiation to gradients, tangents and normals, connected rates of change and maxima and minima problems

    • S3-4.C1.11 Integration as the reverse of differentiation

    • S3-4.C1.12 Integration of xn for any rational, n (excluding n = -1), together with constant multiples, sums and differences

    • S3-4.C1.13 Integration of (ax + b)n for any rational, n (excluding n = -1)

    • S3-4.C1.14 Definite integral as area under a curve

    • S3-4.C1.15 Evaluation of definite integrals

    • S3-4.C1.16 Finding the area of a region bounded by a curve and line(s)

    • S3-4.C1.a Relate the derivative of a function to the gradient of the tangent to a curve at a given point, including horizontal and vertical tangents.

    • S3-4.C1.b Distinguish between constant, average and instantaneous rate of change with reference to graphs.

    • S3-4.C1.c Relate the sign of the first derivative of a function to the behaviour of the function (increasing or decreasing), locate points on the graph where the derivative is zero, and describe the behaviour of the function before, at and after these points.

    • S3-4.C1.d Discuss cases where the second derivative test to discriminate between maxima and minima fails (e.g. y = x3, y = x4) and instead, use the first derivative test.

    • S3-4.C1.e Discuss examples of problems in real-world contexts (e.g. business and sciences), involving the use of differentiation.

    • S3-4.C1.f Explain what d/dx (f(x)),Γf(x)dx and Γ of a to b of f (x) dx represent and make connections between

      • S3-4.C1.f.1 derivative and indefinite integral;

      • S3-4.C1.f.2 definite and indefinite integrals.

    • S3-4.C1.g Relate the area bounded by a curve and the y-axis to the area under the curve. (excluding area of region between 2 curves)