June Crash Course for Secondary & JC Students | Future Achievers Hub

Trigonometry is one of the most important yet most misunderstood chapters in Additional Mathematics. It integrates graphical understanding, algebraic manipulation, and real-world modelling – and it’s a consistent feature in both Paper 1 and Paper 2 of the O-Level exam.

In this 2.5-hour A-Math crash course, your child will:

• Learn how to confidently use all six trigonometric functions and identities, including advanced forms such as angle addition and double-angle formulae.
• Understand how to transform and sketch sine, cosine, and tangent graphs, with proper attention to amplitude, period, and phase shift.
• Simplify trigonometric expressions and solve equations using proven techniques to reduce careless mistakes.
• Convert expressions like acos⁡θ+bsin⁡θ into Rcos⁡(θ±α) form – a commonly tested skill with wide applications.
• Practise applying trigonometric identities in structured questions and real-world modelling scenarios.

All materials are designed by our team of ex-MOE tutors, ensuring that students are exposed to a diverse range of question types and exam-standard thinking processes.

If your child struggles with trig graphs, identities, or solving trigonometric equations, this session will help them build confidence and competence, just in time for their O-Level preparation.

Coordinate geometry and circles form a key part of the O-Level Additional Mathematics curriculum, combining geometric reasoning with algebraic manipulation and graph interpretation. These topics demand precision and clear understanding – yet many students struggle with applying concepts to novel exam questions.

In this intensive 2.5-hour A-Math crash course, your child will:

• Learn to determine if lines are parallel or perpendicular based on gradient relationships
• Master techniques to find the midpoint, area of rectilinear shapes, and use these in structured geometry problems
• Work confidently with the equation of a circle in both standard and expanded forms
• Transform non-linear equations (e.g. y=axⁿ, y=kbˣ) into linear form to interpret and extract constants from straight-line graphs – a skill often tested in data analysis questions

With targeted practice curated by our team of ex-MOE tutors, your child will build clarity and exam fluency, turning these graph-heavy questions into a scoring opportunity.

This session focuses on real techniques that help students avoid careless errors and master the thinking process required to succeed in Additional Math.

Differentiation is a cornerstone of O-Level Additional Mathematics, and one that many students find conceptually challenging. From applying advanced rules to solving real-world problems involving tangents and rates of change, this chapter plays a crucial role in both Papers 1 and 2.

In this 2.5-hour intensive crash course, students will:

• Learn how to apply product, quotient, and chain rules with clarity across algebraic, trigonometric, and exponential functions.
• Understand how to find and interpret stationary points, and apply the second derivative test to classify them as maxima, minima, or points of inflexion.
• Apply differentiation to solve structured problems involving tangents and normals, gradient at a point, rates of change, and motion in a straight line – all of which are heavily tested.

The crash course will include targeted teaching of concepts that many students find challenging and sharing of key exam answering strategies, followed by hands-on application practice, where students attempt exam-style questions specially curated by our team of experienced ex-MOE tutors.

These questions are designed to reflect current assessment trends and common pitfalls, helping students learn the exact phrasing and technique required to score the greatest number of marks in their examinations.

Integration is more than just reversing differentiation – it’s the mathematical engine behind calculating areas, interpreting motion, and making sense of graphs. Yet many students struggle to apply integration meaningfully in exam contexts, especially when dealing with definite integrals and real-world scenarios.

In this 2.5-hour crash course, students will:

• Learn to integrate a range of functions, including powers, trigonometric functions like sin⁡x, cos⁡x, and exponentials like eˣ, as well as composite forms like (ax+b)ⁿ.
• Understand the conceptual difference between definite and indefinite integrals, and apply integration to calculate areas under curves, regions below the x-axis, and between functions.
• Tackle structured problems involving displacement, velocity, and acceleration, reinforcing the link between calculus and real-world physics.

What sets this crash course apart is its exam-focused design. Students will not only revise concepts but also attempt specially curated exam-style questions developed by our team of ex-MOE tutors, who ensure each question mimics real O-Level difficulty and phrasing.

They will also walk away, equipped with key exam strategies that will empower them to score the maximum number of marks effectively in examinations.

Exponential and logarithmic functions are a common stumbling block for students, not because they haven’t memorised the laws, but because they don’t fully understand when or how to apply them in real questions. These concepts form the foundation for algebraic problem-solving and real-world modelling, yet students often lose marks due to unclear working or misapplied formulas.

This crash course isn’t just about going through the motions – it’s about helping students think critically, apply concepts correctly, and score confidently in exams.

In this 2.5-hour crash course, your child will:

• Master the use of exponential and logarithmic functions, including laws of logs, switching between forms, and base changes
• Practise solving equations involving ex, ln⁡x, and base-10 or base-a logs
• Apply these skills to real-world modelling scenarios, such as exponential growth and decay
• Understand how to break down expressions and structure answers to meet exam requirements

During the session, students will attempt exam-style questions curated by ex-MOE tutors and be guided through step-by-step answering techniques to avoid common pitfalls and show proper working. This structured approach ensures students don’t just memorise – they develop the reasoning needed to perform under exam conditions.

By the end of the session, your child will walk away with a stronger grasp of this abstract chapter – and the confidence to turn it into a scoring strength.

Polynomials, partial fractions, and the binomial theorem are essential components of the O-Level Additional Math syllabus. They frequently appear in both Paper 1 and Paper 2, yet many students struggle to apply the correct strategies when faced with unusual question formats or complex expressions.

In this 2.5-hour crash course, your child will:

• Learn how to factor, divide, and expand polynomials using the remainder and factor theorems
• Practise breaking down partial fractions with repeated and quadratic terms in the denominator
• Understand and apply the binomial expansion formula using nCr notation, and find specific terms from the expansion efficiently

Throughout the session, students will attempt exam-standard questions curated by our ex-MOE tutors, with guided walkthroughs to teach them answering strategies and techniques that improve clarity, step-by-step logic, and scoring potential. The session focuses not only on solving, but on showing the examiner exactly what they want to see.

By the end, your child will gain confidence in tackling multi-step algebra problems and apply these foundational tools with precision across other A-Math topics.

Many students struggle with geometry questions because they lack a clear approach to identifying congruent or similar figures and applying circle theorems accurately – especially under exam pressure. This crash course session focuses on equipping your child with the tools to spot geometric relationships and apply properties with confidence.

In this 2.5-hour crash course, your child will:

• Understand how to determine congruence and similarity between triangles and polygons
• Apply key rules related to scale drawings, area and volume ratios, and angle bisectors
• Master circle theorems, including tangents, chord properties, angles at the centre and circumference, and symmetry relationships
• Practise a range of exam-style questions, with guided solutions and answering techniques curated by ex-MOE tutors

This session is hands-on and application-focused, helping students move beyond memorisation to real understanding, so they can tackle geometry questions with clarity and structure.

Students will also learn key exam answering techniques to avoid careless mistakes and pick up proven strategies to maximise marks in questions involving angle properties, ratios, and geometric reasoning.

Many students struggle with algebra-heavy topics due to weak foundational understanding or a lack of exposure to application-based questions. This session brings together the most essential topics that appear frequently in examinations – from solving equations to interpreting graphs.

In this 2.5-hour crash course, your child will:

• Solve and sketch quadratic equations and functions, identify turning points, and analyse symmetry
• Tackle linear inequalities, including representing solutions on number lines
• Strengthen understanding of indices and standard form, key areas where students often make careless mistakes
• Apply coordinate geometry concepts to find gradients, line equations, and solve geometric problems
• Practise a variety of exam-style questions, carefully selected by ex-MOE tutors to reinforce key concepts and highlight common traps

This session is structured for hands-on learning, equipping students with techniques for answering accurately and presenting work clearly—skills essential for scoring in exams.

We will also cover key exam strategies for solving equations efficiently, choosing the correct graphing approach, and managing common traps in inequalities, indices, and coordinates – helping your child gain clarity, speed, and precision.

Chemical bonding is one of the most conceptually dense chapters in the A-Level H2 Chemistry syllabus. It forms the basis for understanding molecular structure, polarity, physical properties, and intermolecular interactions—all of which are critical for both foundational learning and long-answer questions in the examinations.

In this 2.5-hour crash course, your child will:

Deepen their understanding of ionic, covalent, metallic, and dative bonding, including orbital overlap and the nature of σ and π bonds

• Use Valence Shell Electron Pair Repulsion (VSEPR) theory to accurately deduce and explain molecular shapes and bond angles
• Analyse electronegativity, bond polarity, and the overall polarity of molecules
• Master key concepts related to intermolecular forces, such as hydrogen bonding, dipole interactions, including their implications on physical properties
• Interpret and explain bond energy, bond length, and how they influence reactivity

Beyond conceptual mastery, students will attempt exam-style questions curated by ex-MOE tutors, and receive guided instruction on how to structure high-quality responses, justify reasoning using chemical principles, and avoid common pitfalls that cost marks.

By the end of the session, your child will not only be able to recall bonding concepts – they’ll be able to apply them flexibly and confidently in data-based and explanatory contexts across the A-Level Chemistry syllabus.

Atomic structure and redox reactions are two of the most foundational and frequently tested areas in the A-Level H2 Chemistry syllabus. This integrated session is designed to equip students with both conceptual depth and application skills needed to tackle structured and data-based exam questions confidently.

In this 2.5-hour crash course, your child will:

• Build a strong understanding of atomic substructure, including orbitals, quantum levels, and electronic configurations of atoms and ions
• Analyse and interpret ionisation energy data, and use it to deduce electron arrangement and periodic trends – a common structured question format in the examinations
• Learn key exam answering techniques to solve atomic structure questions effectively and efficiently
• Practise techniques for constructing oxidation and reduction half-equations, and confidently combine them for redox reactions in both acidic and basic medium
• Apply mole concepts in electron-transfer calculations – crucial for quantitative redox questions in practical and theory-based assessments

The session includes carefully curated exam-style questions by our team of ex-MOE tutors, allowing students to practise applying these concepts under timed, exam-aligned conditions. Tutors will also guide students through step-by-step answering techniques, helping them structure their work for full marks and avoid common errors.

By the end of the session, your child will not only grasp the “why” behind atomic and redox principles but also develop the ability to confidently apply them across various JC-level question formats.

Acid-base chemistry is a core pillar of the A-Level H2 Chemistry syllabus – and one that many students struggle with due to its abstract theories, quantitative calculations, and application-heavy questions. This chapter spans both foundational theory (Arrhenius, Brønsted-Lowry, Lewis) and higher-level equilibrium concepts essential to perform well in the examinations.

In this 2.5-hour crash course, students will:

• Develop a strong conceptual grasp of acid-base theories
• Apply quantitative skills to pH and pKa/pKb/Kw calculations, including weak acid/base systems
• Gain clarity on buffer solutions – both in terms of biological relevance (e.g., blood pH regulation) and exam-based calculation and explanation
• Analyse pH titration curves and learn how to select suitable indicators for different titration pairs
• Learn the step-by-step approach to solving any acid-base question that is posed to the student

Students will not only revise key concepts but also practise with exam-style questions curated by ex-MOE tutors, focusing on common pitfalls and high-frequency question types. They will be taught how to structure full-mark answers, interpret equilibrium data, and manage multi-step pH calculations under timed conditions.

By the end of the session, your child will walk away with greater confidence, deeper conceptual understanding, and a clear strategy to tackle this high-weighted topic in the A-Level exams.

Organic Chemistry remains one of the most challenging components of the A-Level H2 Chemistry syllabus – not because students don’t study hard, but because they often lack the right framework and techniques to handle synthesis-based, mechanism-heavy, and data-driven questions under exam conditions.

In this 2.5-hour crash course, your child will:

• Learn a structured framework for tackling organic synthesis, drawing mechanisms, and performing structural elucidation – all common question types where many students lose marks.
• Understand how to connect concepts across different chapters, making the memorisation of reagents and conditions easier and more logical.
• Clarify how to identify different types of organic reactions using key indicators and examples – so they’ll never be unsure of what transformation is taking place.
• Get exposed to standard organic question types that often recur in predictable formats – and how to answer them precisely for full marks.

This is a highly hands-on, question-focused session. Students will receive a specially designed worksheet packed with exam-standard questions, curated by our team of ex-MOE tutors, and be guided through them with detailed, step-by-step explanations.

Rather than just going through content, this session will allow students to step into the mind of a top scorer – learning how high-performing students think, structure, and present their answers in organic questions.

We’ll also cover key exam answering techniques, including how to write answers that examiners are looking for, how to avoid common pitfalls, and how to think critically under pressure.

By the end of the session, your child will walk away not only understanding Organic Chemistry better but with the confidence and strategic know-how to score in it.

Sequences and series form a critical foundation for A-Level Math, yet many students struggle with applying formulas accurately, interpreting recursive terms, and handling convergence of infinite series – all of which are commonly tested in structured questions and graph-based applications.

In this 2.5-hour crash course, your child will:

• Master the use of formulas for the n-th term and sum to n terms in both arithmetic and geometric progressions
• Understand the principles of convergence in infinite geometric series, and apply the correct conditions and formulas
• Work confidently with recursive sequences, including graphing calculator interpretation and sequence generation
• Practise a wide range of exam-style questions curated by ex-MOE tutors, focusing on accuracy, logic, and structured thinking

The session is question-driven and strategy-focused, with students receiving targeted support in applying key formulas, structuring full-mark responses, and avoiding common pitfalls in problem-solving.

By the end of the session, your child will be equipped with the techniques and confidence needed to approach APGP questions strategically – turning this foundational topic into a scoring advantage.

Vectors are a high-weighted topic in A-Level Mathematics, combining algebraic manipulation with 3D spatial reasoning. Students often struggle with understanding the geometry behind equations of lines and planes, and applying vector operations correctly in exam scenarios.

In this 2.5-hour crash course, your child will:

• Master the addition, subtraction, and scalar multiplication of vectors, including displacement and direction vectors
• Understand the scalar and vector product, and how to apply them to find angles and perpendicularity
• Solve problems involving vector and Cartesian equations of lines and planes, including perpendicular foot, angle between lines, and collinearity
• Learn how to apply the ratio theorem and interpret vector expressions geometrically
• Attempt a variety of exam-style questions curated by ex-MOE tutors, with a focus on clear working, spatial interpretation, and logical deduction

This session is hands-on, highly application-focused, and designed to help students develop both spatial awareness and precise exam technique – turning vectors from a point of confusion into a point of strength.

Integration is one of the most heavily tested topics in the A-Level H2 Math syllabus, especially in the examinations. Students frequently struggle with complex integration techniques and applying them to calculate areas, volumes, and bounded regions accurately under time pressure.

In this 2.5-hour crash course, your child will:

• Practise a wide range of integration techniques, including substitution and integration by parts
• Learn to integrate forms of standard integrals quickly and accurately
• Apply definite integrals to find areas under curves, between curves, and regions below the x-axis
• Understand the concept of volume of revolution, and apply it to solve structured and real-world problems
• Work through exam-style questions curated by ex-MOE tutors, with guided instruction on answering techniques and step-by-step logic

This session is problem-based, helping students move beyond rote application to full understanding and accuracy, equipping them with the structure and precision to score confidently in high-weighted integration questions.