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Skills available for Singapore secondary 4 maths curriculum

Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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S3-4.A Algebra

S3-4.G Geometry and Trigonometry

S3-4.C Calculus

  • S3-4.C1 Differentiation and 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, sinx, cosx, tanx, e to the x power, and 1nx, 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 xn for any rational n, sinx, cosx, sec²x and e to the x power, together with constant multiples, sums and differences

    • S3-4.C1.13 Integration of (ax + b)n for any rational n, sin(ax+b), cos(ax+b) and e (ax +b)

    • 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 lines(s) (excluding area of region between 2 curves)

    • S3-4.C1.17 Finding areas of regions below the x-axis

    • S3-4.C1.18 Application of differentiation and integration to problems involving displacement, velocity and acceleration of particle moving in a straight line

    • 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 = x&sup4;) and instead, use the first derivative test.

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

    • S3-4.C1.f Explain what d/dx (f(x)), integral f(x)dx and integral b and a 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.

    • S3-4.C1.h Model the motion of a particle in a straight line, using displacement, velocity and acceleration as vectors (e.g. velocity in the positive direction of x-axis is positive), and explain the physical meanings of ds/dt and dv/dt, and their signs in relation to the motion.