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

Chapter-3. Coordinate Geometry

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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-3.1.5- 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.

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-5. Mensuration

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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 .

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.

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.

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.

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.

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.

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

Chapter-6. Trigonometry

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Lesson-6.1.1- Know and use Pythagoras’ theorem.

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.

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

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

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

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.

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.

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.

Chapter-7. Transformations and Vectors

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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°.

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)

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

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

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

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.

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.

Chapter-8. Probability

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

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

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.

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′) .

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.

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.

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

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

Mastering Cambridge O Level Mathematics (Syllabus D) (4024) Online

About Lesson

Venn diagrams are limited to two or three sets.
The following set of notation will be used:
• n(A) Number of elements in set A
• ∈ ‘… is an element of …’
• ∉ ‘… is not an element of …’
• A′ Complement of set A
• ∅ The empty set
• Universal set
• A ⊆ B A is a subset of B
• A ⊈ B A is not a subset of B
• A ∪ B Union of A and B
• A ∩ B Intersection of A and B.
Example definition of sets:
A = {x: x is a natural number}
B = {(x, y): y = mx + c}
C = {x: a ⩽ x ⩽ b}
D = {a, b, c, …}.

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