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The Cambridge Home School’s International GCSE mathematics program will place a strong emphasis on the development of fundamental mathematical abilities that apply to all facets of daily life. The course will provide a solid foundation for future study. Key problem-solving abilities will be emphasized, and an awareness of numbers, patterns, and connections will be established. Students will be able to successfully articulate and reason using mathematical ideas by the conclusion of their studies.

Number

Overview

Reviewing numeric concepts in this first topic is important since they underpin almost everything that comes after. The ability to “feel” the connections between numbers will serve pupils well in Math classes at whichever level they choose to pursue. Students’ knowledge of precision units, ratio and proportion, sequences, percentages, standard form, speed, distance, and time will be expanded upon.

Learning Objectives

In this topic, students will learn how to:

  • identify and classify different types of numbers
  • find common factors and common multiples of numbers
  • write numbers as products of their prime factors
  • calculate squares, square roots, cubes, and cube roots of numbers
  • work with integers used in real-life situations
  • revise the basic rules for operating with numbers
  • perform basic calculations using mental methods and with a calculator.

Subtopics Covered

  • Number and language
  • Accuracy
  • Calculations and orders
  • Integers, fractions, decimals, and percentages
  • Further percentages
  • Ratio and proportion
  • Indices and standard form
  • Money and finance
  • Time
  • Set notation and Venn diagrams

Algebra and Graphs

Overview

This topic covers some of the fundamental ideas that students will encounter throughout the course. Students will be familiar with many of them, but it is crucial to make sure they have a firm grasp on these fundamentals before moving on to more challenging algebra and problem-solving exercises.

The fact that letters represent numbers and that the same rules apply to them as to numbers (i.e., that you must follow the order of operations rules (BODMAS) should be emphasized repeatedly since algebra often appears to intimidate some students.

Learning Objectives

In this topic, students will learn how to:

  • Use letters to represent numbers
  • Write expressions to represent mathematical information
  • Substitute letters with numbers to find the value of an expression
  • Add and subtract like terms to simplify expressions
  • Multiply and divide to simplify expressions
  • Expand expressions by removing grouping symbols
  • Use index notation in algebra
  • Learn and apply the laws of indices to simplify expressions
  • Work with fractional indices

Subtopics Covered

  • Algebraic representations and manipulation
  • Algebraic indices
  • Equations and inequalities
  • Linear programming
  • Sequences
  • Proportion
  • Graphs in practical situations
  • Graphs of functions
  • Differentiation and the gradient function
  • Functions

Geometry

Overview

Geometry is one of the oldest known areas of mathematics. Students should already be familiar with the basic angle facts and relationships. When discussing geometrical figures, mathematicians utilize specialized vocabulary and terminology. Students are required to understand the meanings of the words and be able to appropriately utilize them in their work. This topic will help the students build on their understanding of the fundamental rules of angles, Pythagoras theorem, and symmetry.

Learning Objectives

  • Use the relationships between areas of similar triangles, with corresponding results for similar figures and extension to volumes and surface areas of similar solids
  • Recognise symmetry properties of the prism (including cylinder) and the pyramid (including cone)
  • Use the following symmetry properties of circles:
    • equal chords are equidistant from the centre
    • the perpendicular bisector of a chord that passes through the centre tangents from an external point is equal in length
  • Calculate unknown angles using the following geometrical properties:
    • angle properties of irregular polygons
    • the angle at the centre of a circle is twice the angle at the circumference
    • angles in the same segment are equal
    • angles in opposite segments are supplementary; cyclic quadrilaterals

Subtopics Covered

  • Geometrical vocabulary and construction
  • Similarity and congruence
  • Symmetry
  • Angle properties

Mensuration

Overview

Even though you may not be familiar with the term “mensuration,” I’m sure you have used it in the past. What is the area of the Giza pyramids, how big a football can hold air, and what is the perimeter of the rice field in the picture? Our knowledge of mensuration allows us to respond to each of these queries. Students must be able to compute the perimeter, area, and volume of diverse shapes in a variety of contexts in order to pass the IGCSE math test. Moreso, they will deepen their knowledge of the area, arc length, sector area, chord of a circle, volume, and surface area in this lesson.

Learning Objectives

In this topic, students will learn how to:

  • calculate areas and perimeters of two-dimensional shapes
  • calculate areas and perimeters of shapes that can be separated into two or more simpler polygons
  • calculate areas and circumferences of circles
  • calculate perimeters and areas of circular sectors
  • understand nets for three-dimensional solids
  • calculate volumes and surface areas of solids
  • calculate volumes and surface area of pyramids, cones and spheres

Subtopics Covered

  • Measures
  • Perimeter, area, and volume

Coordinate Geometry

Overview

We will examine straight-line graphs in this topic. The use of graphs in many settings will be extremely familiar to the learner. However, this does not imply that students will find it simple to manipulate linear graphs. They will benefit much from seeing a variety of graphs, particularly those in context. The students will deepen their knowledge of sets, logical problems, vectors, column vectors, vector geometry, functions, and simple and combined transformations in this topic.

Learning Objectives

In this topic, students will learn how to:

  • construct a table of values and plot points to draw graphs
  • find the gradient of a straight-line graph
  • recognise and determine the equation of a line
  • determine the equation of a line parallel to a given line
  • calculate the gradient of a line using coordinates of points on the line
  • find the gradient of parallel and perpendicular lines
  • find the length of a line segment and the coordinates of its midpoint
  • expand products of algebraic expressions
  • factorise quadratic expressions
  • solve quadratic equations by factorisation

Subtopics Covered

  • Straight line graphs

Trigonometry

Overview

The ratios of the sides of right-angled triangles are used in trigonometry. You may calculate bearings considerably more precisely by using the methods provided in the sections that follow. You must make sure that your calculator is set to degree mode for the rest of this topic. The following bearings and scale drawing works should be recognizable to students. This part teaches students how to compute missing angles and sides precisely using trigonometric ratios.

Learning Objectives

In this topic, students will learn how to:

  • make scale drawings
  • interpret scale drawings
  • calculate bearings
  • calculate sine, cosine and tangent ratios for right-angled triangles
  • use sine, cosine and tangent ratios to calculate the lengths of sides and angles of right-angled triangles
  • solve trigonometric equations finding all the solutions between 0° and 360°
  • apply the sine and cosine rules to calculate unknown sides and angles in triangles that are not right-angled
  • calculate the area of a triangle that is not right-angled using the sine ratio
  • use the sine, cosine and tangent ratios, together with Pythagoras’ theorem in three-dimensions.

Subtopics Covered

  • Bearings
  • Trigonometry
  • Further trigonometry

Matrices and Transformations

Overview

Change is what transformation is. A transformation in mathematics is a modification to an object’s location or size (or point). The geometry of transformation deals with the systematic movement or transformation of forms. Four different forms of transformations will be covered in this section: reflection, rotation, translation, and enlargement. Students will update their knowledge of transformations, use vectors, and deal with more accurate mathematical formulations of transformations. These concepts ought to be familiar to students from their work with transformations and column vectors.

Learning Objectives

In this topic, students will learn how to:

  • Negative scale factors for enlargements
  • Represent vectors by directed line segments
  • Use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors
  • Display information in the form of a matrix of any order
  • Calculate the sum and product (where appropriate) of two matrices and scalar quantity
  • Use the following transformations of the plane: reflection (M), rotation (R), translation (T), enlargement (E), and their combinations
  • Identify and give precise descriptions of transformations connecting given figures
  • Describe transformations using coordinates and matrices (singular matrices are excluded)

Subtopics Covered

  • Vectors
  • Transformations

Probability

Overview

The study of chance, or the possibility that something will happen, is called probability. What the theory predicts, however, does not always occur in reality since the likelihood is dependent on chance. Students will discover how to express the results of simple coupled events using tree diagrams in this topic. Additionally, they will deepen their understanding of how to utilize tree diagrams to estimate the likelihood of various outcomes.

Learning Objectives

In this topic, students will learn how to:

  • express probabilities mathematically
  • calculate probabilities associated with simple experiments
  • use possibility diagrams to help you calculate the probability of combined events
  • identify when events are independent
  • identify when events are mutually exclusive

Subtopics Covered

  • Probability
  • Further probability

Statistics

Overview

The study of statistics is a branch of mathematics that deals with data collection. At this stage, their focus will be on asking questions, obtaining information, and arranging or presenting it so that they may reply to questions. The many types of data, methods for acquiring data, and strategies for organizing and displaying data should all be familiar to students at this stage. They will be required to summarize the facts so that they may be understood. It is not always required to draw a figure; instead, the average and spread may be determined mathematically. Numerical summaries may be used to compare different sets of data, but as with any statistical analysis, you must be careful how you interpret the results. Throughout this topic, students will increase their understanding of data presentation, mean, median, and mode, cumulative frequency, by comparing data sets, box plots, and scatter graphs.

Learning Objectives

In this topic, students will learn how to:

  • calculate the mean, median, and mode of sets of data
  • calculate and interpret the range as a measure of spread
  • interpret the meaning of each result and compare data using these measures
  • construct and use frequency distribution tables for grouped data
  • identify the class that contains the median of grouped data
  • calculate and work with quartiles
  • divide data into quartiles and calculate the interquartile range
  • identify the modal class from a grouped frequency distribution.
  • Construct and interpret box-and-whisker plots.

Subtopics Covered

  • Mean, median, mode, and range
  • Collecting, displaying, and interpreting data
  • Cumulative frequency

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