Functions and graphs

• Use graphing calculator (GC) to sketch various functions and label necessary points.
• Determine its domain and range from the graph.
• Determine the equations of asymptotes using algebraic methods.
• Use proper notations in functions and graphs.
• Find inverse functions, composite functions and state their necessary conditions.
• Establish graphical relationship between a function and its inverse.
• Sketch the effects of transformations on graph by identifying the correct sequence of transformation.
• Formulate a system of linear equations or inequalities from the situation given (for example optimisation problems) and solve them graphically and algebraically.

Sequence and series

• Master the concepts of sequence and series for finite and infinite cases and its conditions for convergence with the use of appropriate notation.
• Form suitable equation for the n^th term and sum of terms given a sequence or pattern by using formula in arithmetic progression, geometric progression or method of difference.
• Relate the concept to real life situation such as financial maths

Vectors

• Comprehend important terms used in vectors such as position vectors, unit vectors and length of projection.
• Calculate and interpret geometrically vectors’ magnitude, direction, dot product, cross product, angle, length of projection, perpendicular distance and foot of perpendicular.
• Use ratio theorem in geometrical application questions.
• Interpret given information to form vector, cartesian and parametric equations of lines and planes.
• Describe geometrical and algebraic relationships between lines and planes.

Complex numbers

• Interchange of cartesian form and polar form of complex number.
• Solve complex roots of quadratic equations with real coefficients by making use of conjugate roots properties.
• Basic operations of complex numbers and solving using algebraic method.
• Represent complex numbers in the Argand diagram.
• Link the concepts to electrical circuits.

Calculus

• Sketch y = f′(x) from y = f(x) or vice versa.
• Differentiate functions defined implicitly or parametrically.
• Findstationary points and their nature algebraically and graphically.
• Find equations of tangents and normals to curves.
• Solve rates of change problems given real-life problems by using chain rule.
• Manipulate the standard series expansionformula given in MF26to solve questions related to Maclaurin series and state the range of values of x for which it converges.
• Apply differentiation repeatedly to find the terms in Maclaurin expansion.
• Substitute appropriate value of x in order to use Maclaurin series for approximation.
• Integrate functions using formulae, substitution and by parts methods.
• Identify the appropriate functions and limits when using definite integral to find area bounded by curves and volume of revolution about the x-axis or y-axis.
• Master the use of GC wherever possible to find an approximate value of a definite integral and differentiation of function at given point.
• Form differential equations from a real-life scenario such as population growth, radioactive decay, heating and cooling problems.
• Solve general solutions and particular solutions of differential equations using integration.
• Explain the importance of the solution based on the context of the question.

Permutation, combination and probability

• Use concepts of permutation and combination to find the arrangements of objects in a line or in a circle, including cases involving repetition and restriction.
• Comprehend the terms mutually exclusive events and independent events.
• Use tables of outcomes, Venn diagrams, tree diagrams, permutations and combinations techniques to calculate probabilities including conditional probabilities.

Discrete and continuous distribution

• Comprehend the concept of discrete random variable, tabulate its probability distribution and calculate its expectation and variance.
• Find the mean and variance of binomial distributionand represent it as B(n, p).
• State the necessary conditions where binomial distribution is a suitable model.
• Represent normal distribution as an example of a continuous probability model with mean, µ and variance, σ².
• Standardise normal distribution and use the symmetry of the normal curve and its properties to find its unknown parameters
• Solve problems involving the use of the distribution aX + bY + c where X and Y are independent.
• Know the differences between population, random and non-random samples, sample mean and sample variance.
• Use Central Limit Theorem to treat sample means as having normal distribution when the sample size is sufficiently large.
• Calculate unbiased estimates of the population mean and variance from a sample.
• Master the use of GC to find the required probability and parameters for various distribution.

Hypothesis testing

• Comprehend the concepts of null hypothesis, alternative hypotheses, test statistic, critical region, critical value, level of significance and p-value.
• Write the proper steps in conducting hypothesis testing.
• Interpretthe results of a hypothesis test in the context of the problem such as standardised testing, market research and clinical research.

Correlation and Linear regression

• With the help of GC, use scatter diagram and product moment correlation coefficient to determine if there is alinear relationship between two variables.
• Calculate the product moment correlation coefficient using its formula and discuss its significance in the context of the question.
• Use GC to find theequation of the regression line using the given information.
• Estimate the values of x or y in practical situations using the appropriate regression line.
• Determine if interpolation and extrapolation can be applied to approximate given values in the situation given.
• Transform given graph to achieve linearity.

• To be exposed on different types of problem-solving questions and link it to other related disciplines like sciences and engineering.
• Develop proper thinking and reasoning skills to solve mathematical problems.
• Identify and apply the relevant mathematical concepts and skills in various problems, including unfamiliar contexts.
• Link concepts from different topics together to solve given problems.
• Apply the concepts correctly by having a clear thought process and showing all necessary steps.
• Master the use of GC and to solve the questions more efficiently.
• Solve the mathematical problems and explain its significance in the context of the problems.