JC A-Level H2 Mathematics Syllabus

Explore the JC A-Level H2 Mathematics syllabus with AO Studies. This syllabus plays a pivotal role in your academic journey. In this comprehensive overview, we’ll delve into its intricacies, highlighting how mastering this subject not only enhances your academic skills but also equips you with essential problem-solving skills and analytical thinking, ensuring you’re well-prepared to excel.

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Advanced Level Higher 2 Mathematics (Syllabus 9758)

The JC A-Level H2 Mathematics syllabus (Syllabus 9758) is designed to provide students with a robust foundation in mathematical concepts and problem-solving skills. Here’s a breakdown of the topics and subtopics you will encounter:

1. Functions and graphs

Understanding the fundamental concepts of functions and their graphical representations. 

1.1 Functions

An in-depth exploration of functions, including domains, ranges, and their applications in mathematics, as well as finding inverse and composite functions and understanding the relationship between inverse functions.

1.2 Graphs and transformations

Analysing graphs, investigating the impact of transformations on graphical representations, and utilising a graphic calculator for solving problems. Also, covering the sketching of hyperbola, ellipse, and parametric curves.

1.3 Equations and inequalities

Solving equations and inequalities, including quadratic equations and systems of linear inequalities, and addressing the formulation of systems of linear equations.

2. Sequences and series

Investigating sequences and series, including concepts of arithmetic progression and geometric progression.

2.1 Sequences and series

An in-depth study of sequences and series, including convergence and divergence, finite and infinite sequences, concepts of arithmetic and geometric progression, the usage of summation notation, and conditions for convergence of an infinite series.

3. Vectors

Introduction to vectors and vector algebra, with a focus on two and three dimensions, as well as understanding of position and direction vectors.

3.1 Basic properties of vectors in two and three dimensions 

Exploring vector properties, operations, and applications in both two and three dimensions, and comprehending concepts such as collinearity, unit vectors, and the understanding ratio theorem.

3.2 Scalar and vector products in vectors 

Understanding scalar and vector products of vectors and their geometrical significance.

3.3 Three-dimensional vector geometry

Extending vector concepts to three-dimensional space and geometry, and exploring the relationships between two lines; two planes; and a line with a plane.

4. Introduction to Complex numbers

Introduction to complex numbers and their algebraic properties.

4.1 Complex numbers expressed in Cartesian form 

Extension of the number system from real numbers to complex numbers, exploring the solution of equations involving complex roots, and understanding conditions for conjugate roots.

4.2 Complex numbers expressed in polar and trigonometric form

Representing complex numbers in polar form for various applications in engineering, physics, and mathematical analysis. Expressing complex numbers in trigonometric and exponential forms, and solving simultaneous equations involving complex numbers.

5. Calculus

Comprehensive study of calculus, including differentiation, integration, and their applications.

H4 5.1 Differentiation

In-depth examination of differentiation techniques and their role in calculus, including differentiating simple functions from first principles, differentiating functions defined implicitly or parametrically, and determining equations of normals and tangents for functions defined implicitly or parametrically.

5.2 Maclaurin series

Derivation of the initial terms of the Maclaurin Series, and understanding the concepts of approximations. 

5.3 Integration techniques 

Exploration of integration techniques including methods like integration by parts and substitution, finding the area of regions bounded by curves defined parametrically or implicitly, and calculating the volume of revolution about the x or y-axis.

5.4 Definite integrals 

In-depth study of definite integrals and their applications.

5.5 Differential equations 

Formulating differential equations from a problem situation, interpreting a differential equation solution in context of the problem, and solving differential equations, including first-order and second-order differential equations.

6. Probability and Statistics

Introduction to probability theory and statistical analysis.

6.1 Probability and Permutations & Combinations

An exploration of probability, including conditional probability and probability distributions, as well as delving into the arrangement of objects in a line or circle, including scenarios involving repetition. Understanding concepts of mutually exclusive or independent events, along with the utilisation of outcome tables, Venn diagrams, tree diagrams, permutation, and combinations techniques for calculating probabilities.

6.2 Discrete random variables

Analysis of discrete random variables and concepts of permutation and combinations .

6.3 Normal distribution 

Understanding the normal distribution and its applications in statistics, including the concepts of binomial distribution B(n,p) as an example of the discrete probability distribution model, as well as the usage of mean and variance of binomial distribution, understanding mode of binomial distribution, standardising a normal distribution, and solving problems involving E(aX+bY) and Var(aX+bY) where X and Y are independent events.

6.4 Sampling

Concepts of population and sample, understanding and usage Central Limit Theorem. 

6.5 Hypothesis testing 

An in-depth exploration of hypothesis testing, covering null and alternative hypotheses, test statistics, critical regions, level of significance, p-value, and the important concepts of 1 and 2 tail tests.

6.6 Correlation and Linear regression 

Analysing correlation and performing linear regression analysis in statistics.

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