About Course

Cambridge OLevel Additional Mathematics Crash Course

Welcome to our Cambridge OLevel Additional Mathematics Crash Course! Are you eager to enhance your proficiency in Additional Mathematics and ace the Cambridge O-Level exam? Look no further! Our intensive crash course is meticulously designed to equip you with the essential knowledge and skills needed to excel in this challenging subject. Led by experienced educators and tailored to your exam needs, this crash course is your pathway to success in Additional Mathematics.

Why Choose Our Course:

At Arif Sir Science Hub, we recognize the unique demands of the Cambridge O-Level Additional Mathematics exam. Our crash course is designed to address those demands head-on, offering a range of benefits:

Comprehensive Coverage: Despite its condensed format, our crash course covers all vital topics from the Cambridge O-Level Additional Mathematics syllabus. From algebraic manipulation to trigonometry, calculus to vectors, we ensure you’re fully equipped to tackle every aspect of the exam.
Expert Instruction: Learn from seasoned instructors who possess a deep understanding of the Cambridge O-Level Additional Mathematics exam. Our instructors are passionate about mathematics and committed to helping you succeed. They’ll guide you through the course material, provide clear explanations, and offer invaluable tips and strategies for exam success.
Interactive Learning: Engage in dynamic lessons that make learning Additional Mathematics engaging and enjoyable. Our crash course incorporates a variety of teaching methods, including lectures, interactive discussions, visual aids, and problem-solving sessions. You’ll have the opportunity to ask questions, participate in group activities, and collaborate with your peers.
Practice and Feedback: Reinforce your learning with ample practice exercises and assessments. Our crash course includes regular quizzes, tests, and mock exams to help you assess your progress and identify areas for improvement. You’ll receive personalized feedback from your instructors, enabling you to track your growth and focus your study efforts effectively.
Flexible Schedule: Our crash course is designed to fit into your busy schedule. We offer flexible scheduling options, including weekday and weekend classes, so you can choose the time that works best for you. Whether you’re a student with multiple subjects or a working professional with limited free time, our crash course can accommodate your needs.
Convenient Location: Our institute is conveniently located, making it easy for you to attend classes without having to travel far. We provide a comfortable and conducive learning environment where you can focus on your studies and maximize your learning potential.

Course Structure:

Our Cambridge O-Level Additional Mathematics Crash Course is an intensive program designed to cover the entire syllabus efficiently. Here’s an overview of the course structure:

Duration: The crash course spans [X weeks/months], with classes held [X times] per week.
Class Duration: Each class is [X hours] long, providing ample time for in-depth instruction and practice.
Content Coverage: The course covers all topics included in the Cambridge O-Level Additional Mathematics syllabus, with a focus on key concepts, theories, and problem-solving strategies.
Assessments: Throughout the course, you’ll have the opportunity to complete quizzes, tests, and mock exams to assess your progress and readiness for the real exam.

Enroll Now:

Don’t let time constraints hold you back from achieving your academic goals in Additional Mathematics. Enroll in our crash course today and take the first step towards exam success! For inquiries and enrollment, contact us at [email protected] or call us at +8801327331903. Let us help you unlock your potential in Additional Mathematics and excel on your Cambridge O-Level exam!

Comprehensive Understanding: Grasp a comprehensive understanding of the Cambridge O Level Additional Mathematics curriculum.
Expert-Guided Instruction: Benefit from expert-guided instruction by Arif Sir, renowned for his expertise in the subject.
Advanced Mathematical Concepts: Master advanced mathematical concepts, including functions, quadratic equations, logarithms, and calculus.
Problem-Solving Skills: Develop sharp problem-solving skills crucial for tackling complex mathematical challenges.
Precise Graphical Analysis: Learn to conduct precise graphical analyses, interpreting and drawing conclusions from graphs.
Application of Mathematics: Apply mathematical theories to real-world scenarios, enhancing your critical thinking abilities.
Thorough Curriculum Coverage: Explore the comprehensive curriculum aligned with Cambridge O Level Additional Mathematics requirements.
Interactive Learning Experience: Engage in interactive learning experiences, including video lessons, practice exercises, and quizzes.
Language Flexibility: Choose your preferred language – Bangla or English – for seamless comprehension.
Personalized Guidance: Receive personalized mentorship from Arif Sir, addressing your questions and providing clarifications.
Enhanced Exam Readiness: Prepare effectively for exams using specialized materials, past paper solutions, and exam strategies.
Holistic Skill Development: Develop a holistic skill set encompassing logical reasoning, critical analysis, and mathematical techniques.
Global Learning Community: Interact with fellow students globally, exchanging insights and broadening your perspectives.
Offline Coaching Advantage: If preferred, join our exclusive offline coaching batch in Dhanmondi, Lalmatia, Dhaka, for in-person guidance.

Course Content

Chapter-1. Functions

Lesson-1.1.1- understand the terms: function, domain, range (image set), one-one function, inverse function and composition of functions.

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Lesson-1.1.2- use the notation f(x) = sin x, f: x ↦ lg x, (x > 0), f –1(x) and f 2 (x) [= f(f(x))]

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Lesson-1.1.3- understand the relationship between y = f(x) and y = |f(x)|, where f(x) may be linear, quadratic or trigonometric.

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Lesson-1.1.4- explain in words why a given function is a function or why it does not have an inverse.

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Lesson-1.1.5- find the inverse of a one-one function and form composite functions.

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Lesson-1.1.6- use sketch graphs to show the relationship between a function and its inverse.

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Chapter-2. Quadratic Functions

Chapter-3. Equations, Inequalities and Graphs

Chapter-4. Indices and Surds

Chapter-5. Factors of Polynomials

Chapter-6. Simultaneous Equations

Chapter-7. Logarithmic and Exponential Functions

Chapter-8. Straight line Graphs

Chapter-9. Circular Measure

Chapter-10. Trigonometry

Chapter-11. Permutations and Combinations

Chapter-12. Series

Chapter-13. Vectors in Two Dimensions

Chapter-14. Differentiation and Integration

Lesson-14.1.1- understand the idea of a derived function

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Lesson-14.1.2- differentiate products and quotients of functions

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Lesson-14.1.3- apply differentiation to gradients, tangents and normals, stationary points, connected rates of change, small increments and approximations and practical maxima and minima problems.

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Lesson-14.1.4- use the first and second derivative tests to discriminate between maxima and minima.

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Lesson-14.1.5- understand integration as the reverse process of differentiation.

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Lesson-14.1.6- evaluate definite integrals and apply integration to the evaluation of plane areas.

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Lesson-14.1.7- apply differentiation and integration to kinematics problems that involve displacement, velocity and acceleration of a particle moving in a straight line with variable or constant acceleration, and the use of x–t and v–t graphs.

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About Course

Cambridge OLevel Additional Mathematics Crash Course

What Will You Learn?

Course Content

Chapter-1. Functions

Lesson-1.1.1- understand the terms: function, domain, range (image set), one-one function, inverse function and composition of functions.

Lesson-1.1.2- use the notation f(x) = sin x, f: x ↦ lg x, (x > 0), f –1(x) and f 2 (x) [= f(f(x))]

Lesson-1.1.3- understand the relationship between y = f(x) and y = |f(x)|, where f(x) may be linear, quadratic or trigonometric.

Lesson-1.1.4- explain in words why a given function is a function or why it does not have an inverse.

Lesson-1.1.5- find the inverse of a one-one function and form composite functions.

Lesson-1.1.6- use sketch graphs to show the relationship between a function and its inverse.

Chapter-2. Quadratic Functions

Lesson-2.1.1- find the maximum or minimum value of the quadratic function f : x ↦ ax 2 + bx + c by any method.

Lesson-2.1.2- use the maximum or minimum value of f(x) to sketch the graph or determine the range for a given domain.

Lesson-2.1.3- know the conditions for f(x) = 0 to have: (i) two real roots, (ii) two equal roots, (iii) no real roots.

Lesson- 2.1.4- know the conditions for f(x) = 0 to have: and the related conditions for a given line to (i) intersect a given curve, (ii) be a tangent to a given curve, (iii) not intersect a given curve.

Lesson-2.1.5- solve quadratic equations for real roots and find the solution set for quadratic inequalities.

Chapter-3. Equations, Inequalities and Graphs

Lesson-3.1.1- solve graphically or algebraically equations of the type |ax + b| = c (c ⩾ 0) and |ax + b| = |cx + d

Lesson-3.1.2- solve graphically or algebraically inequalities of the type |ax + b| > c (c ⩾ 0), |ax + b| ⩽ c (c > 0) and |ax + b| ⩽ |cx + d|

Lesson-3.1.3- use substitution to form and solve a quadratic equation in order to solve a related equation.

Lesson-3.1.4- sketch the graphs of cubic polynomials and their moduli, when given in factorised form y = k(x – a)(x – b)(x – c).

Lesson-3.1.5- solve cubic inequalities in the form k(x – a)(x – b)(x – c) ⩽ d graphically.

Chapter-4. Indices and Surds

Lesson-4.1.1- perform simple operations with indices and with surds, including rationalising the denominator.

Chapter-5. Factors of Polynomials

Lesson-5.1.1- know and use the remainder and factor theorems.

Lesson-5.1.2- find factors of polynomials.

Lesson-5.1.3- solve cubic equations

Chapter-6. Simultaneous Equations

Lesson-6.1.1- solve simple simultaneous equations in two unknowns by elimination or substitution.

Chapter-7. Logarithmic and Exponential Functions

Lesson-7.1.1- know simple properties and graphs of the logarithmic and exponential functions including l nx and e x (series expansions are not required) and graphs of ke nx + a and k ln(ax + b) where n, k, a and b are integers.

Lesson-7.1.2- know and use the laws of logarithms (including change of base of logarithms).

Lesson-7.1.3- solve equations of the form ax = b

Chapter-8. Straight line Graphs

Lesson-8.1.1- interpret the equation of a straight line graph in the form y = mx + c

Lesson-8.1.2- transform given relationships, including y = axn and y = Abx , to straight line form and hence determine unknown constants by calculating the gradient or intercept of the transformed graph.

Lesson-8.1.3- solve questions involving mid-point and length of a line.

Lesson-8.1.4- know and use the condition for two lines to be parallel or perpendicular, including finding the equation of perpendicular bisectors.

Chapter-9. Circular Measure

Lesson-9.1.1- solve problems involving the arc length and sector area of a circle, including knowledge and use of radian measure.

Chapter-10. Trigonometry

Lesson-10.1.1- know the six trigonometric functions of angles of any magnitude (sine, cosine, tangent, secant, cosecant, cotangent).

Lesson-10.1.2- understand amplitude and periodicity and the relationship between graphs of related trigonometric functions, e.g. sin x and sin 2x

Lesson-10.1.3- draw and use the graphs of y = a sin bx + c y = a cos bx + c y = a tan bx + c where a is a positive integer, b is a simple fraction or integer (fractions will have a denominator of 2, 3, 4, 6 or 8 only), and c is an integer.

Lesson-10.1.4- solve simple trigonometric equations involving the six trigonometric functions and the above relationships (not including general solution of trigonometric equations)

Lesson-10.1.5- prove simple trigonometric identities

Chapter-11. Permutations and Combinations

Lesson-11.1.1- recognise and distinguish between a permutation case and a combination case.

Lesson-11.1.2- know and use the notation n! (with 0! = 1), and the expressions for permutations and combinations of n items taken r at a time.

Lesson-11.1.3- answer simple problems on arrangement and selection (cases with repetition of objects, or with objects arranged in a circle, or involving both permutations and combinations, are excluded).

Chapter-12. Series

Lesson-12.1.1- use the Binomial Theorem for expansion of (a + b) n for positive integer n.

Lesson-12.1.2- recognise arithmetic and geometric progressions

Lesson-12.1.3- use the condition for the convergence of a geometric progression, and the formula for the sum to infinity of a convergent geometric progression.

Chapter-13. Vectors in Two Dimensions

Lesson-13.1.1- know and use position vectors and unit vectors.

Lesson-13.1.2- find the magnitude of a vector; add and subtract vectors and multiply vectors by scalars.

Lesson-13.1.3- compose and resolve velocities

Chapter-14. Differentiation and Integration

Lesson-14.1.1- understand the idea of a derived function

Lesson-14.1.2- differentiate products and quotients of functions

Lesson-14.1.3- apply differentiation to gradients, tangents and normals, stationary points, connected rates of change, small increments and approximations and practical maxima and minima problems.

Lesson-14.1.4- use the first and second derivative tests to discriminate between maxima and minima.

Lesson-14.1.5- understand integration as the reverse process of differentiation.

Lesson-14.1.6- evaluate definite integrals and apply integration to the evaluation of plane areas.

Lesson-14.1.7- apply differentiation and integration to kinematics problems that involve displacement, velocity and acceleration of a particle moving in a straight line with variable or constant acceleration, and the use of x–t and v–t graphs.

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