About Course

Cambridge OLevel Mathematics Syllabus D Crash Course

Welcome to our Cambridge OLevel Mathematics Syllabus D Crash Course! Are you gearing up to conquer the challenges of mathematics and excel in your Cambridge O-Level exam? Look no further! Our crash course is meticulously designed to simplify complex mathematical concepts, making learning engaging and effective. Led by experienced educators passionate about mathematics education, our course promises to be a fulfilling journey towards exam success.

Why Choose Our Course:

Comprehensive Learning: Our crash course covers all essential topics outlined in the Cambridge O-Level Mathematics Syllabus D. From algebra to geometry, from trigonometry to calculus, we leave no stone unturned in preparing you for exam success.
Expert Guidance: Learn from experienced instructors who are experts in the field of mathematics. Our teachers are dedicated to breaking down complex concepts into easy-to-understand explanations, ensuring you grasp every concept with confidence.
Interactive Classes: Engage in dynamic and interactive lessons designed to foster curiosity and deepen understanding. Through problem-solving sessions, interactive discussions, and collaborative projects, you’ll not only understand theoretical concepts but also gain practical skills essential for success in mathematics.
Practical Practice: Practice is key to mastering mathematics, and our crash course offers plenty of opportunities for hands-on learning. From solving mathematical problems to applying concepts in real-world scenarios, you’ll have ample practice to sharpen your skills and build confidence in your abilities.
Flexible Schedule: We understand that every student has unique commitments. That’s why our crash course offers flexible scheduling options, including weekday and weekend classes, to accommodate your busy schedule without compromising on the quality of education you receive.
Convenient Location: Our institute is conveniently located, providing easy access for students from all areas. With state-of-the-art facilities and a conducive learning environment, you’ll have everything you need to excel in mathematics.

Course Structure:

Our Cambridge O-Level Mathematics Syllabus D Crash Course is thoughtfully structured to optimize your learning experience and maximize your exam readiness. Here’s an overview of what to expect:

Duration: The crash course spans [4 weeks/months], with classes held [3 times] per week.
Content Coverage: We cover all topics included in the Cambridge O-Level Mathematics Syllabus D, focusing on core concepts and problem-solving strategies.
Class Format: Each class combines theoretical instruction with practical problem-solving exercises, ensuring you understand and apply mathematical concepts effectively.
Assessments: Throughout the course, you’ll undergo regular assessments, including quizzes, tests, and mock exams, to gauge your progress and identify areas for improvement.

Enroll Now:

Don’t let the complexities of mathematics hold you back! Enroll in our Cambridge O-Level Mathematics Syllabus D Crash Course today and embark on a journey towards mastering this essential subject. For inquiries and enrollment, contact us at [email protected] or call us at +8801327331903. Let us help you unlock your potential and achieve your goals in mathematics!

Course Focus: The course is specifically tailored to prepare students for the Cambridge O Level Mathematics Syllabus D (4024) examination.
Online Learning: The course is conducted entirely online, offering the flexibility to study from anywhere with an internet connection.
Experienced Tutor: Arif Air is an experienced mathematics tutor known for his effective teaching methods and commitment to students' success.
Comprehensive Syllabus: The course covers the entire Syllabus D, including topics in algebra, geometry, trigonometry, calculus, and statistics.
Concept Clarity: Arif Air provides clear explanations to ensure students have a strong understanding of fundamental mathematical concepts.
Problem-Solving Skills: The course emphasizes the development of strong problem-solving skills, a crucial aspect of excelling in mathematics.
Exam Preparation: Students receive guidance on effective exam preparation strategies, including time management and question-solving techniques.
Personalized Support: Arif Air offers one-on-one support to address individual questions and challenges, ensuring students receive personalized guidance.
Extensive Resources: The course provides a wealth of resources, such as textbooks, worksheets, practice papers, and mock exams, to reinforce learning.
Math Mastery Program: Advanced learners have access to the Math Mastery Program, which covers more challenging mathematical topics and problem-solving techniques.
Online Learning Tools: Students become proficient in utilizing digital resources, online lectures, and live classes for effective learning.
Flexibility: The course allows students to learn at their own pace and revisit challenging topics through recorded video lectures.
Exam Success: The primary goal is to prepare students to excel in their O Level Math exams with confidence.
Understanding and Application: Beyond rote learning, the course promotes a deep understanding of mathematics and its real-world applications.
Mathematical Confidence: Students build confidence in their mathematical abilities, enabling them to tackle complex problems with ease.
Exam Techniques: Strategies for efficient time management and effective problem-solving in exams are emphasized.
Positive Learning Environment: Arif Sir's Science Hub fosters a supportive and engaging learning environment for all students.
Testimonials: The course has a track record of success, with satisfied students sharing their positive experiences and results.
Lifelong Learning: The course aims not only to prepare for exams but also to instill a lasting love for mathematics.
Academic Excellence: "Mastering Cambridge O Level Mathematics (Syllabus D) (4024) Online" is an opportunity for students to excel academically and set a strong foundation for their future studies and careers.

Course Content

Chapter-1. Number

Lesson-1.1.1- natural numbers, integers (positive, zero and negative), prime numbers

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Lesson-1.1.2- Square numbers • Cube numbers • Common factors • Common multiples

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Lesson-1.1.3- Rational and irrational numbers • reciprocals.

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Lesson-1.1.4- Understand and use set language, notation and Venn diagrams to describe sets and represent relationships between sets.

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Lesson-1.1.5- Calculate with the following: • squares • square roots • cubes • cube roots • other powers and roots of numbers.

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Lesson-1.1.6- Use the language and notation of the following in appropriate contexts: • proper fractions • improper fractions • mixed numbers • decimals • percentages.

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Lesson-1.1.7- Recognize equivalence and convert between these forms. Includes converting between recurring decimals and fractions and vice versa, e.g. write 0 1. 7 o as a fraction.

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Lesson-1.1.8- Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾ and ⩽.

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Lesson-1.1.9- Use the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets. Includes: • negative numbers • improper fractions • mixed numbers • practical situations, e.g. temperature changes.

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Lesson-1.1.10- Understand and use indices (positive, zero, negative and fractional).

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Lesson-1.1.11- Understand and use the rules of indices.

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Lesson-1.1.12- Use the standard form A × 10n where n is a positive or negative integer and 1 ⩽ A < 10.

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Lesson-1.1.13- Convert numbers into and out of standard form. Calculate with values in standard form.

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Lesson-1.1.14- Round values to a specified degree of accuracy. Includes decimal places and significant figures. e.g. Write 5764 correct to the nearest thousand.

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Lesson-1.1.15- Make estimates for calculations involving numbers, quantities and measurements.

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Lesson-1.1.16- Round answers to a reasonable degree of accuracy in the context of a given problem.

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Lesson-1.1.17- Give upper and lower bounds for data rounded to a specified accuracy. e.g. write down the upper bound of a length measured correct to the nearest metre.

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Lesson-1.1.18- Find upper and lower bounds of the results of calculations which have used data rounded to a specified accuracy.

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Lesson-1.1.19- Understand and use ratio and proportion to: • give ratios in their simplest form • divide a quantity in a given ratio • use proportional reasoning and ratios in context.

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Lesson-1.1.20- Use common measures of rate. e.g. calculate with: • hourly rates of pay • exchange rates between currencies • flow rates • fuel consumption.

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Lesson-1.1.21- Apply other measures of rate. e.g. calculate with: • pressure • density • population density. Required formulas will be given in the question.

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Lesson-1.1.22- Solve problems involving average speed. Knowledge of speed/distance/time formula is required. e.g. A cyclist travels 45km in 3 hours 45 minutes. What is their average speed? The notation used for rates will be in the form, e.g. m/s (metres per second), g/cm3 (grams per cubic centimetre).

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Lesson-1.1.23- Calculate a given percentage of a quantity. Express one quantity as a percentage of another. Calculate percentage increase or decrease.

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Lesson-1.1.24- Calculate with simple and compound interest. Problems may include repeated percentage change. Formulas are not given.

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Lesson-1.1.25- Calculate using reverse percentages. e.g. find the cost price given the selling price and the percentage profit. Percentage calculations may include: • deposit • discount • profit and loss (as an amount or a percentage) • earnings • percentages over 100%.

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Lesson-1.1.26- Use a calculator efficiently. e.g. know not to round values within a calculation and to only round the final answer.

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Lesson-1.1.27- Enter values appropriately on a calculator. e.g. enter 2 hours 30 minutes as 2.5 hours or 2° 30’ 0’’.

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Lesson-1.1.28- 3 Interpret the calculator display appropriately. e.g. in money 4.8 means $4.80; in time 3.25 means 3 hours 15 minutes.

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Lesson-1.1.29- Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units. Calculate times in terms of the 24-hour and 12-hour clock. 3 Read clocks and timetables.

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Lesson-1.1.30- Calculate with money. Convert from one currency to another.

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Lesson-1.1.31- Use exponential growth and decay. e.g. depreciation, population change. Knowledge of e is not required.

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Lesson-1.1.32- Understand and use surds, including simplifying expressions.

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Lesson-1.1.33- Rationalize the denominator.

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Chapter-2. Algebra and graphs

Lesson-2.1.1- Know that letters can be used to represent generalized numbers.

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Lesson-2.1.2- Substitute numbers into expressions and formulas.

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Lesson-2.1.3- Simplify expressions by collecting like terms. Simplify means give the answer in its simplest form, e.g. 2a^2 + 3ab – 1 + 5a^2 – 9ab + 4 = 7a^2 – 6ab + 3.

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Lesson-2.1.4- Expand products of algebraic expressions. e.g. expand 3x(2x – 4y), (3x + y)(x – 4y). Includes products of more than two brackets, e.g. expand (x – 2)(x + 3)(2x + 1).

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Lesson-2.1.5- Factorize by extracting common factors. Factorise means factorise fully, e.g. 9x^2 + 15xy = 3x(3x + 5y).

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Lesson-2.1.6- Factorise expressions of the form: • ax + bx + kay + kby • a^2 x^2 − b^2 y^2 • a^2 + 2ab + b2 • ax^2 + bx + c • ax^3 + bx2 + cx .

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Lesson-2.1.7- Manipulate algebraic fractions.

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Lesson-2.1.8- Factorize and simplify rational expressions.

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Lesson-2.1.9- Understand and use indices (positive, zero, negative and fractional). e.g. solve: • 32^x = 2 , 5^(x + 1) = 25^x .

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Lesson-2.1.10- Understand and use the rules of indices.

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Lesson-2.1.11- Construct expressions, equations and formulas. e.g. write an expression for the product of two consecutive even numbers. Includes constructing simultaneous equations.

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Lesson-2.1.12- Solve linear equations in one unknown. Examples include: • 3x + 4 = 10 , 5 – 2x = 3(x + 7).

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Lesson-2.1.13- Solve simultaneous linear equations in two unknowns.

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Lesson-2.1.14- Solve quadratic equations by factorization, completing the square and by use of the quadratic formula. Includes writing a quadratic expression in completed square form. Candidates may be expected to give solutions in surd form. The quadratic formula is given in the List of formulas.

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Lesson-2.1.15- Change the subject of formulas. e.g. change the subject of a formula where: • the subject appears twice • there is a power or root of the subject.

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Lesson-2.1.16- Represent and interpret inequalities, including on a number line. When representing and interpreting inequalities on a number line: • open circles should be used to represent strict inequalities () • closed circles should be used to represent inclusive inequalities (⩽, ⩾) e.g. – 3 ⩽ x < 1

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Lesson-2.1.17- Construct, solve and interpret linear inequalities. Examples include: • 3x < 2x + 4 • –3 ⩽ 3x – 2 < 7 .

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Lesson-2.1.18- Represent and interpret linear inequalities in two variables graphically. The following conventions should be used: • broken lines should be used to represent strict inequalities () • solid lines should be used to represent inclusive inequalities (⩽, ⩾) • shading should be used to represent unwanted regions (unless otherwise directed in the question).

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Lesson-2.1.19- List inequalities that define a given region. Linear programming problems are not included.

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Lesson-2.1.19- Continue a given number sequence or pattern. Subscript notation may be used, e.g. Tn is the nth term of sequence T

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Lesson-2.1.20 -Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences. Includes linear, quadratic, cubic and exponential sequences and simple combinations of these.

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Lesson-2.1.21- Find and use the nth term of sequences.

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Lesson-2.1.22- Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities. Includes linear, square, square root, cube and cube root proportion. Knowledge of proportional symbol (∞) is required.

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Lesson-2.1.23- Use and interpret graphs in practical situations including travel graphs and conversion graphs. Includes estimation and interpretation of the gradient of a tangent at a point.

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Lesson-2.1.24- Draw graphs from given data.

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Lesson-2.1.25- Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration.

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Lesson-2.1.26- Calculate distance travelled as area under a speed–time graph. Areas will involve linear sections only.

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Lesson-2.1.27- Construct tables of values, and draw, recognize and interpret graphs for functions

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Lesson-2.1.28- Solve associated equations graphically, including finding and interpreting roots by graphical methods. e.g. finding the intersection of a line and a curve.

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Lesson-2.1.29- Draw and interpret graphs representing exponential growth and decay problems.

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Lesson-2.1.30 -Estimate gradients of curves by drawing tangents.

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Lesson-2.1.31- Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic

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Lesson-2.1.32- Recognize, sketch and interpret graphs of the following functions: (c) cubic (d) reciprocal (e) exponential.

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Lesson-2.1.33- Understand functions, domain and range, and use function notation.

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Lesson-2.1.34- Understand and find inverse functions f^–1(x).

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Lesson-2.1.35- Form composite functions as defined by gf(x) = g(f(x)).

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Chapter-3. Coordinate Geometry

Lesson-3.1.1- Use and interpret Cartesian coordinates in two dimensions.

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Lesson-3.1.2- Draw straight-line graphs for linear equations. Examples include: • y = –2x + 5 • y = 7 – 4x • 3x + 2y = 5 .

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Lesson-3.1.3- Find the gradient of a straight line. Calculate the gradient of a straight line from the coordinates of two points on it.

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Lesson-3.1.4- Calculate the length of a line segment. Find the coordinates of the midpoint of a line segment.

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Lesson-3.1.5- Interpret and obtain the equation of a straight-line graph. Questions may: • use and request lines in different forms, e.g. ax + by = c y = mx + c x = k • involve finding the equation when the graph is given • ask for the gradient or y-intercept of a graph from an equation, e.g. find the gradient and y-intercept of the graph with equation 5x + 4y = 8. Candidates are expected to give equations of a line in a fully simplified form.

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Lesson-3.1.6- Find the gradient and equation of a straight line parallel to a given line. e.g. Find the equation of the line parallel to y = 4x – 1 that passes through (1, –3).

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Lesson-3.1.7- Find the gradient and equation of a straight line perpendicular to a given line. Examples include: • Find the gradient of a line perpendicular to 2y = 3x + 1 . • Find the equation of the perpendicular bisector of the line joining the points (–3, 8) and (9, –2).

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Chapter-4. Geometry

Lesson-4.1.1- Use and interpret the following geometrical terms: • point • vertex • line • plane • parallel • perpendicular • perpendicular bisector • bearing • right angle • acute, obtuse and reflex angles • interior and exterior angles • similar • congruent • scale factor.

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Lesson-4.1.2- Use and interpret the vocabulary of: • triangles • special quadrilaterals • polygons • nets • solids. Includes the following terms. Triangles: • equilateral • isosceles • scalene • right-angled. Quadrilaterals: • square • rectangle • kite • rhombus • parallelogram • trapezium. Polygons: • regular and irregular polygons • pentagon • hexagon • octagon • decagon. Solids: • cube • cuboid • prism • cylinder • pyramid • cone • sphere • hemisphere • frustum • face • surface • edge

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Lesson-4.1.3- Use and interpret the vocabulary of a circle. Includes the following terms: • centre • radius (plural radii) • diameter • circumference • semicircle • chord • tangent • major and minor arc • sector • segment.

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Lesson-4.1.4- Measure and draw lines and angles. A ruler should be used for all straight edges. Constructions of perpendicular bisectors and angle bisectors are not required.

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Lesson-4.1.5- Construct a triangle, given the lengths of all sides, using a ruler and pair of compasses only. e.g. construct a rhombus by drawing two triangles. Construction arcs must be shown.

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Lesson-4.1.6- Draw, use and interpret nets. Examples include: • draw nets of cubes, cuboids, prisms and pyramids • use measurements from nets to calculate volumes and surface areas.

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Lesson-4.1.7- Draw and interpret scale drawings. A ruler must be used for all straight edges.

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Lesson-4.1.8- Use and interpret three-figure bearings. Bearings are measured clockwise from north (000° to 360°), e.g. Find the bearing of A from B if the bearing of B from A is 025°. Includes an understanding of the terms north, east, south and west, e.g. point D is due east of point C.

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Lesson-4.1.9- Calculate lengths of similar shapes. 2 Use the relationships between lengths and areas of similar shapes and lengths, surface areas and volumes of similar solids.

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Lesson-4.1.10- Solve problems and give simple explanations involving similarity. Includes showing that two triangles are similar using geometric reasons.

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Lesson-4.1.11- Recognize line symmetry and order of rotational symmetry in two dimensions. Includes properties of triangles, quadrilaterals and polygons directly related to their symmetries.

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Lesson-4.1.12- Calculate unknown angles and give simple explanations using the following geometrical properties: • sum of angles at a point = 360° • sum of angles at a point on a straight line = 180° • vertically opposite angles are equal • angle sum of a triangle = 180° and angle sum of a quadrilateral = 360°.

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Lesson-4.1.13 – Calculate unknown angles and give geometric explanations for angles formed within parallel lines: • corresponding angles are equal • alternate angles are equal • co-interior (supplementary) angles sum to 180°.

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Lesson-4.1.14- Know and use angle properties of regular and irregular polygons. Includes exterior and interior angles, and angle sum.

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Lesson-4.1.15- alculate unknown angles and give explanations using the following geometrical properties of circles: • angle in a semicircle = 90° • angle between tangent and radius = 90° • angle at the centre is twice the angle at the circumference • angles in the same segment are equal • opposite angles of a cyclic quadrilateral sum to 180° (supplementary) • alternate segment theorem.

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Lesson-4.1.16- Use the following symmetry properties of circles: • equal chords are equidistant from the centre • the perpendicular bisector of a chord passes through the Centre • tangents from an external point are equal in length.

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Chapter-5. Mensuration

Lesson-5.1.1- Use metric units of mass, length, area, volume and capacity in practical situations and convert quantities into larger or smaller units. Units include: • mm, cm, m, km • mm^2 , cm^2 , m^2 , km^2 • mm^3 , cm^3 , m^3 • ml, l • g, kg .

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Lesson-5.1.2- Carry out calculations involving the perimeter and area of a rectangle, triangle, parallelogram and trapezium. Except for the area of a triangle, formulas are not given.

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Lesson-5.1.3- Carry out calculations involving the circumference and area of a circle. Answers may be asked for in terms of π. Formulas are given in the List of formulas.

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Lesson-5.1.4- Carry out calculations involving arc length and sector area as fractions of the circumference and area of a circle. Includes minor and major sectors.

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Lesson-5.1.5- Carry out calculations and solve problems involving the surface area and volume of a: • cuboid • prism • cylinder • sphere • pyramid • cone. Answers may be asked for in terms of π. The following formulas are given in the List of formulas: • curved surface area of a cylinder • curved surface area of a cone • surface area of a sphere • volume of a prism • volume of a pyramid • volume of a cylinder • volume of a cone • volume of a sphere.

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Lesson-5.1.6- Carry out calculations and solve problems involving perimeters and areas of: • compound shapes • parts of shapes. Answers may be asked for in terms of π.

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Lesson-5.1.7- Carry out calculations and solve problems involving surface areas and volumes of: • compound solids • parts of solids. e.g. find the surface area and volume of a frustum

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Chapter-6. Trigonometry

Lesson-6.1.1- Know and use Pythagoras’ theorem.

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Lesson-6.1.2- Know and use the sine, cosine and tangent ratios for acute angles in calculations involving sides and angles of a right-angled triangle. Angles will be given in degrees and answers should be written in degrees, with decimals correct to one decimal place.

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Lesson-6.1.3- Solve problems in two dimensions using Pythagoras’ theorem and trigonometry. Knowledge of bearings may be required.

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Lesson-6.1.4- Know that the perpendicular distance from a point to a line is the shortest distance to the line.

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Lesson-6.1.5- Carry out calculations involving angles of elevation and depression.

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Lesson-6.1.6- Use the sine and cosine rules in calculations involving lengths and angles for any triangle. Includes problems involving obtuse angles and the ambiguous case.

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Lesson-6.1.7- Use the formula area of triangle = 1/2 ab sinC . The sine and cosine rules and the formula for area of a triangle are given in the List of formulas.

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Lesson-6.1.8- Carry out calculations and solve problems in three dimensions using Pythagoras’ theorem and trigonometry, including calculating the angle between a line and a plane.

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Chapter-7. Transformations and Vectors

Lesson-7.1.1- Recognize, describe and draw the following transformations: 1 Reflection of a shape in a straight line. 2 Rotation of a shape about a Centre through multiples of 90°.

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Lesson-7.1.2- Recognize, describe and draw the following transformations: Enlargement of a shape from a centre by a scale factor. 4 Translation of a shape by a vector (x y)

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Lesson-7.1.3- Describe a translation using a vector represented by (x y), AB or a.

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Lesson-7.1.4- Add and subtract vectors. Multiply a vector by a scalar.

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Lesson-7.1.5- Calculate the magnitude of a vector (x y) as √x²+y²

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Lesson-7.1.6- Represent vectors by directed line segments. 2 Use position vectors. 3 Use the sum and difference of two or more vectors to express given vectors in terms of two coplanar vectors.

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Lesson-7.1.7- Use vectors to reason and to solve geometric problems. Examples include: • show that vectors are parallel • show that 3 points are collinear • solve vector problems involving ratio and similarity.

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Chapter-8. Probability

Lesson-8.1.1- Understand and use the probability scale from 0 to 1.

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Lesson-8.1.2- Understand and use probability notation. P(A) is the probability of A. P(A′) is the probability of not A.

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Lesson-8.1.3-Calculate the probability of a single event. Probabilities should be given as a fraction, decimal or percentage. Problems may require using information from tables, graphs or Venn diagrams.

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Lesson-8.1.4- Understand that the probability of an event not occurring = 1 – the probability of the event occurring. e.g. P(B) = 0.8, find P(B′) .

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Lesson-8.1.5- Understand relative frequency as an estimate of probability. e.g. use results of experiments with a spinner to estimate the probability of a given outcome.

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Lesson- 8.1.6- Calculate expected frequencies. e.g. use probability to estimate an expected value from a population. Includes understanding what is meant by fair and bias.

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Lesson- 8.1.7- Calculate the probability of combined events using, where appropriate: • sample space diagrams.

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Lesson-8.1.8- Calculate the probability of combined events using, where appropriate: Venn diagrams • tree diagrams. The notation P(A ∩ B) and P(A ∪ B) may be used in the context of Venn diagrams. On tree diagrams outcomes will be written at the end of the branches and probabilities by the side of the branches

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Chapter-9. Statistics

Lesson-9.1.1- Classify and tabulate statistical data. e.g. tally tables, two-way tables.

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Lesson-9.1.2- Read, interpret and draw inferences from tables and statistical diagrams.

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Lesson-9.1.3- Compare sets of data using tables, graphs and statistical measures. e.g. compare averages and measures of spread between two data sets.

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Lesson-9.1.4- Appreciate restrictions on drawing conclusions from given data.

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Lesson-9.1.5- Calculate the mean, median, mode and range for individual data and distinguish between the purposes for which these are used.

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Lesson-9.1.6- 2 Calculate an estimate of the mean for grouped discrete or grouped continuous data.

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Lesson-9.1.7- Identify the modal class from a grouped frequency distribution.

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Lesson-9.1.8- Draw and interpret: (a) bar charts (b) pie charts (c) pictograms (d) simple frequency distributions.

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Lesson-9.1.9- Draw and interpret scatter diagrams. Plotted points should be clearly marked, for example as small crosses (×).

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Lesson-9.1.10-Understand what is meant by positive, negative and zero correlation.

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Lesson-9.1.11- Draw by eye, interpret and use a straight line of best fit. A line of best fit: • should be a single ruled line drawn by inspection • should extend across the full data set • does not need to coincide exactly with any of the points but there should be a roughly even distribution of points either side of the line over its entire length.

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Lesson-9.1.12- Draw and interpret cumulative frequency tables and diagrams. Plotted points on a cumulative frequency diagram should be clearly marked, for example as small crosses (×), and be joined with a smooth curve.

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Lesson-9.1.13- Estimate and interpret the median, percentiles, quartiles and interquartile range from cumulative frequency diagrams.

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Lesson-9.1.14- Draw and interpret histograms. On histograms, the vertical axis is labelled ‘Frequency density’.

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Lesson-9.1.15- Calculate with frequency density. Frequency density is defined as frequency density = frequency ÷ class width .

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About Course

Cambridge OLevel Mathematics Syllabus D Crash Course

What Will You Learn?

Course Content

Chapter-1. Number

Lesson-1.1.1- natural numbers, integers (positive, zero and negative), prime numbers

Lesson-1.1.2- Square numbers • Cube numbers • Common factors • Common multiples

Lesson-1.1.3- Rational and irrational numbers • reciprocals.

Lesson-1.1.4- Understand and use set language, notation and Venn diagrams to describe sets and represent relationships between sets.

Lesson-1.1.5- Calculate with the following: • squares • square roots • cubes • cube roots • other powers and roots of numbers.

Lesson-1.1.6- Use the language and notation of the following in appropriate contexts: • proper fractions • improper fractions • mixed numbers • decimals • percentages.

Lesson-1.1.7- Recognize equivalence and convert between these forms. Includes converting between recurring decimals and fractions and vice versa, e.g. write 0 1. 7 o as a fraction.

Lesson-1.1.8- Order quantities by magnitude and demonstrate familiarity with the symbols =, ≠, >, < , ⩾ and ⩽.

Lesson-1.1.9- Use the four operations for calculations with integers, fractions and decimals, including correct ordering of operations and use of brackets. Includes: • negative numbers • improper fractions • mixed numbers • practical situations, e.g. temperature changes.

Lesson-1.1.10- Understand and use indices (positive, zero, negative and fractional).

Lesson-1.1.11- Understand and use the rules of indices.

Lesson-1.1.12- Use the standard form A × 10n where n is a positive or negative integer and 1 ⩽ A < 10.

Lesson-1.1.13- Convert numbers into and out of standard form. Calculate with values in standard form.

Lesson-1.1.14- Round values to a specified degree of accuracy. Includes decimal places and significant figures. e.g. Write 5764 correct to the nearest thousand.

Lesson-1.1.15- Make estimates for calculations involving numbers, quantities and measurements.

Lesson-1.1.16- Round answers to a reasonable degree of accuracy in the context of a given problem.

Lesson-1.1.17- Give upper and lower bounds for data rounded to a specified accuracy. e.g. write down the upper bound of a length measured correct to the nearest metre.

Lesson-1.1.18- Find upper and lower bounds of the results of calculations which have used data rounded to a specified accuracy.

Lesson-1.1.19- Understand and use ratio and proportion to: • give ratios in their simplest form • divide a quantity in a given ratio • use proportional reasoning and ratios in context.

Lesson-1.1.20- Use common measures of rate. e.g. calculate with: • hourly rates of pay • exchange rates between currencies • flow rates • fuel consumption.

Lesson-1.1.21- Apply other measures of rate. e.g. calculate with: • pressure • density • population density. Required formulas will be given in the question.

Lesson-1.1.23- Calculate a given percentage of a quantity. Express one quantity as a percentage of another. Calculate percentage increase or decrease.

Lesson-1.1.24- Calculate with simple and compound interest. Problems may include repeated percentage change. Formulas are not given.

Lesson-1.1.25- Calculate using reverse percentages. e.g. find the cost price given the selling price and the percentage profit. Percentage calculations may include: • deposit • discount • profit and loss (as an amount or a percentage) • earnings • percentages over 100%.

Lesson-1.1.26- Use a calculator efficiently. e.g. know not to round values within a calculation and to only round the final answer.

Lesson-1.1.27- Enter values appropriately on a calculator. e.g. enter 2 hours 30 minutes as 2.5 hours or 2° 30’ 0’’.

Lesson-1.1.28- 3 Interpret the calculator display appropriately. e.g. in money 4.8 means $4.80; in time 3.25 means 3 hours 15 minutes.

Lesson-1.1.29- Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units. Calculate times in terms of the 24-hour and 12-hour clock. 3 Read clocks and timetables.

Lesson-1.1.30- Calculate with money. Convert from one currency to another.

Lesson-1.1.31- Use exponential growth and decay. e.g. depreciation, population change. Knowledge of e is not required.

Lesson-1.1.32- Understand and use surds, including simplifying expressions.

Lesson-1.1.33- Rationalize the denominator.

Chapter-2. Algebra and graphs

Lesson-2.1.1- Know that letters can be used to represent generalized numbers.

Lesson-2.1.2- Substitute numbers into expressions and formulas.

Lesson-2.1.3- Simplify expressions by collecting like terms. Simplify means give the answer in its simplest form, e.g. 2a^2 + 3ab – 1 + 5a^2 – 9ab + 4 = 7a^2 – 6ab + 3.

Lesson-2.1.4- Expand products of algebraic expressions. e.g. expand 3x(2x – 4y), (3x + y)(x – 4y). Includes products of more than two brackets, e.g. expand (x – 2)(x + 3)(2x + 1).

Lesson-2.1.5- Factorize by extracting common factors. Factorise means factorise fully, e.g. 9x^2 + 15xy = 3x(3x + 5y).

Lesson-2.1.6- Factorise expressions of the form: • ax + bx + kay + kby • a^2 x^2 − b^2 y^2 • a^2 + 2ab + b2 • ax^2 + bx + c • ax^3 + bx2 + cx .

Lesson-2.1.7- Manipulate algebraic fractions.

Lesson-2.1.8- Factorize and simplify rational expressions.

Lesson-2.1.9- Understand and use indices (positive, zero, negative and fractional). e.g. solve: • 32^x = 2 , 5^(x + 1) = 25^x .

Lesson-2.1.10- Understand and use the rules of indices.

Lesson-2.1.11- Construct expressions, equations and formulas. e.g. write an expression for the product of two consecutive even numbers. Includes constructing simultaneous equations.

Lesson-2.1.12- Solve linear equations in one unknown. Examples include: • 3x + 4 = 10 , 5 – 2x = 3(x + 7).

Lesson-2.1.13- Solve simultaneous linear equations in two unknowns.

Lesson-2.1.14- Solve quadratic equations by factorization, completing the square and by use of the quadratic formula. Includes writing a quadratic expression in completed square form. Candidates may be expected to give solutions in surd form. The quadratic formula is given in the List of formulas.

Lesson-2.1.15- Change the subject of formulas. e.g. change the subject of a formula where: • the subject appears twice • there is a power or root of the subject.

Lesson-2.1.17- Construct, solve and interpret linear inequalities. Examples include: • 3x < 2x + 4 • –3 ⩽ 3x – 2 < 7 .

Lesson-2.1.19- List inequalities that define a given region. Linear programming problems are not included.

Lesson-2.1.19- Continue a given number sequence or pattern. Subscript notation may be used, e.g. Tn is the nth term of sequence T

Lesson-2.1.20 -Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences. Includes linear, quadratic, cubic and exponential sequences and simple combinations of these.

Lesson-2.1.21- Find and use the nth term of sequences.

Lesson-2.1.22- Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities. Includes linear, square, square root, cube and cube root proportion. Knowledge of proportional symbol (∞) is required.

Lesson-2.1.23- Use and interpret graphs in practical situations including travel graphs and conversion graphs. Includes estimation and interpretation of the gradient of a tangent at a point.

Lesson-2.1.24- Draw graphs from given data.

Lesson-2.1.25- Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration.

Lesson-2.1.26- Calculate distance travelled as area under a speed–time graph. Areas will involve linear sections only.

Lesson-2.1.27- Construct tables of values, and draw, recognize and interpret graphs for functions

Lesson-2.1.28- Solve associated equations graphically, including finding and interpreting roots by graphical methods. e.g. finding the intersection of a line and a curve.

Lesson-2.1.29- Draw and interpret graphs representing exponential growth and decay problems.

Lesson-2.1.30 -Estimate gradients of curves by drawing tangents.

Lesson-2.1.31- Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic

Lesson-2.1.32- Recognize, sketch and interpret graphs of the following functions: (c) cubic (d) reciprocal (e) exponential.

Lesson-2.1.33- Understand functions, domain and range, and use function notation.

Lesson-2.1.34- Understand and find inverse functions f^–1(x).

Lesson-2.1.35- Form composite functions as defined by gf(x) = g(f(x)).

Chapter-3. Coordinate Geometry

Lesson-3.1.1- Use and interpret Cartesian coordinates in two dimensions.

Lesson-3.1.2- Draw straight-line graphs for linear equations. Examples include: • y = –2x + 5 • y = 7 – 4x • 3x + 2y = 5 .

Lesson-3.1.3- Find the gradient of a straight line. Calculate the gradient of a straight line from the coordinates of two points on it.

Lesson-3.1.4- Calculate the length of a line segment. Find the coordinates of the midpoint of a line segment.

Lesson-3.1.6- Find the gradient and equation of a straight line parallel to a given line. e.g. Find the equation of the line parallel to y = 4x – 1 that passes through (1, –3).

Lesson-3.1.7- Find the gradient and equation of a straight line perpendicular to a given line. Examples include: • Find the gradient of a line perpendicular to 2y = 3x + 1 . • Find the equation of the perpendicular bisector of the line joining the points (–3, 8) and (9, –2).

Chapter-4. Geometry