Lesson-1.1.1- The ordinary processes of number manipulation. - Arif Sir's Science Hub

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Course Content

Chapter-1. Numbers

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Lesson-1.1.1- The ordinary processes of number manipulation.

Lesson-1.1.2- Prime numbers, factors, multiples.

Lesson-1.1.3- Indices, powers and roots (Use index notation and index laws for multiplication and division involving integer, fractional and negative powers)

Lesson-1.1.4- Simple manipulation of surds.

Lesson-1.1.5- Rationalizing the denominator.

Lesson-1.1.6- Natural numbers, integers and rational and irrational numbers.

Lesson-1.1.7- Weights, measures and money.

Lesson-1.1.8- Fractions, decimals, ratio, proportion and percentage.

Lesson-1.1.9- Expressing numbers to a given degree of accuracy.

Lesson-1.1.10- Solve problems using upper and lower bounds where values are given to a degree of accuracy.

Lesson-1.1.11- Numbers in standard form.

Chapter-2. Sets

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Lesson-2.1.1- The idea of a set.

Lesson-2.2.2- Set language and notation.

Lesson-2.2.3- Union and intersection of sets.

Lesson-2.2.4- Number of elements in a set.

Lesson-2.2.5- Complementary sets.

Lesson-2.2.6- Subsets.

Lesson-2.2.7- Universal set, null set.

Lesson-2.2.8- Venn diagrams and their use in simple logical problems.

Lesson-2.2.9- Use of symbols to represent sets.

Chapter-3. Algebra

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Lesson-2.3.1- The basic processes of algebra.

Lesson-3.3.2-The construction, interpretation and use of formulae and their manipulation.

Lesson-3.3.3- The factorization of simple algebraic expressions.

Lesson-3.3.4- Use of the factor theorem.

Lesson-3.3.5- Algebraic division of a cubic by a linear factor.

Lesson-3.3.6- The manipulation of simple algebraic fractions, the denominators being numerical, linear or quadratic.

Lesson-3.3.7- Solution of equations of 1st, 2nd and 3rd degree containing one unknown quantity.

Lesson-3.3.8- Solution of linear simultaneous equations in two unknowns.

Lesson-3.3.9- Solve simultaneous equations in two unknowns, one equation being linear and the other being quadratic.

Lesson-3.3.10- Solution of linear inequalities, and the representations of solutions on the number line and two-dimensional space.

Lesson-3.3.11- Solve quadratic inequalities in one unknown and represent the solution set on a number line.

Lesson-3.3.12- The idea of a sequence.

Chapter-4. Functions.

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Lesson-4.1.1- The idea of a function of a variable

Lesson-4.1.2- Function as a mapping or as a correspondence between the elements of two sets.

Lesson-4.1.3- Use functional notations of the form f(x) =… and f: x  …

Lesson-4.1.4- Composite functions.

Lesson-4.1.5- Inverse functions

Lesson-4.1.6- Variation, direct and indirect proportion.

Lesson-4.1.7- Rectangular Cartesian co-ordinates.

Lesson-4.1.8- Recognise that equations of the form y = mx + c are straight–line graphs with gradient m and intercept on the y-axis at the point (0, c).

Lesson-4.1.9- Graphs and graphical treatment of the equation: 3 2 2 E F y Ax Bx Cx D x x = + + +++ in which the constants are numerical and at least three of them are zero.

Lesson-4.1.10- The gradients of graphs above by drawing.

Lesson-4.1.11- Differentiation of integer powers of x.

Lesson-4.1.12- Determination of gradients, rates of change, maxima and minima, stationary points and turning points.

Lesson-4.1.13- Applications to linear kinematics and to other simple practical problems.

Chapter-5. Matrices

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Lesson-5.1.1- Representation of data by a matrix.

Lesson-5.1.2- Addition and multiplication of matrices.

Lesson-5.1.3- Multiplication of a matrix by a scalar.

Lesson-5.1.4- Unit (identity) matrix and zero (null) matrix.

Lesson-5.1.5- Determinants and inverses of non-singular 2 × 2 matrices.

Lesson-5.1.6- Transformations of the plane associated with 2 × 2 matrices.

Lesson-5.1.7- Combination of transformations.

Chapter-6. Geometry

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Lesson-6.1.1- Geometrical properties of Euclidean space, as listed below.

Lesson-6.1.2- Geometrical reasoning.

Lesson- 6.1.3- Angle properties of parallel lines, triangles and polygons, including regular polygons.

Lesson-6.1.4- Properties of the parallelogram, rectangle, square, rhombus, trapezium and kite.

Lesson-6.1.5- Symmetry about a point, line or plane.

Lesson-6.1.6- Use of Pythagoras’ theorem in 2D and 3D.

Lesson-6.1.7- Similarity: areas and volumes of similar figures.

Lesson-6.1.8- Prove the similarity of two triangles.

Lesson-6.1.9- Congruent shapes.

Lesson-6.1.10- Understand and use SSS, SAS, ASA and RHS conditions to prove the congruence of triangles.

Lesson-6.1.11- Chord, angle and tangent properties of circles.

Lesson-6.1.12- Properties of a cyclic quadrilateral.

Lesson-6.1.13- Loci in two dimensions.

Lesson-6.1.14- Constructions of bisector of an angle and of perpendicular bisector (mediator) of a straight line.

Chapter-7. Mensuration.

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Lesson-7.1.1- Length, area, and volume.

Lesson-7.1.2- Mensuration of two-dimensional shapes, rectangle, parallelogram, trapezium, triangle, circle.

Lesson-7.1.3- Mensuration of three-dimensional shapes, right circular cylinder, right circular cone and sphere, cuboid, pyramid, prism.

Lesson-7.1.4- Length of an arc, area of a sector of a circle.

Chapter-8. Vectors and Transformation Geometry.

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Lesson-8.1.1- Scalar and vector quantities.

Lesson-8.1.2- Understand and use vector notation.

Lesson-8.1.3- Representation of a vector by a directed line segment.

Lesson-8.1.4- Parallel vectors, unit vectors and position vectors.

Lesson-8.1.5- Sum and difference of two vectors.

Lesson-8.1.6- Modulus (magnitude) of a vector.

Lesson-8.1.7- Multiplication of a vector by a scalar.

Lesson-8.1.8- Find the resultant of two or more vectors.

Lesson-8.1.9- Apply vector methods to simple geometrical problems.

Lesson-8.1.10- Transformations of the plane.

Lesson-8.1.11- Combination of transformations.

Lesson-8.1.12- Multiplication of a vector by a matrix.

Chapter-9. Trigonometry.

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Lesson-9.1.1- Use of sine, cosine and tangent of angles up to 180°

Lesson-9.1.2- Solution of problems in two and three dimensions by calculation and by drawing.

Lesson-9.1.3- Angles of elevation and depression.

Lesson-9.1.4- Bearings

Chapter-10. Statistics and probability.

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Lesson-10.1.1- Graphical representation of numerical data.

Lesson-10.1.2- Determination of the mean, median and mode for a discrete data set.

Lesson-10.1.3- Calculation of an estimate of the mean of a larger number of quantities given in grouped frequencies.

Lesson-10.1.4- Determination of a modal class and the class containing the median for grouped data.

Lesson-10.1.5- Understand the language and basic concepts of probability.

Lesson-10.1.6- Use of addition rule for two or more mutually exclusive events.

Lesson-10.1.7- Use of product rule for two or more independent events.

Lesson-10.1.8- Determination of the probability of two or more independent events.

Lesson-10.1.9- Using simple conditional probability for combined events.

Lesson-10.1.10- Finding very simple conditional probability.

Lesson-10.1.11- Understand and use the term ‘expected frequency’

Edexcel Olevel Math B revision notes