# Maths Grade 10

## Overview

The Math Syllabus at GEMS Wesgreen International Secondary School aims to support students in building competency, confidence and fluency in their use of techniques and mathematical understanding. Throughout the year we recover and extend objectives as the focus is to develop in students their reasoning, problem-solving and analytical skills from a variety of abstract and real-life contexts.

## Learning Outcomes

The aims of all subjects state what a teacher may expect to teach and what a student may expect to experience and learn. These aims suggest how the student may be changed by the learning experience.

The aims of the Math Syllabus are to encourage and enable students to:

- become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

## Unit Overviews

### Term 1

**Number - Chapter 1**

**Approximate length: 3 weeks **

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*Th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Units of accuracy, ratio proportion, sequences, percentages, standard form, speed, distance and time.

Specific National Curriculum Objectives Covered:

- Use the four rules for calculations with whole numbers, decimals and fractions (including mixed numbers and improper fractions), including correct ordering of operations and use of brackets.
- Applies to positive and negative numbers.
- Use the language and notation of simple vulgar and decimal fractions and percentages in appropriate contexts.
- Recognise equivalence and convert between these forms.
- Includes the conversion of recurring decimals to fractions, e.g. change to a fraction. 0.7&
- Calculate with squares, square roots, cubes and cube roots and other powers and roots of numbers, e.g. work out 3
^{2 }x 4 square root of 16 - ·• Identify and use natural numbers, integers (positive, negative and zero), prime numbers, square numbers, common factors and common multiples, rational and irrational numbers (e.g. π, square root of 2), real numbers, reciprocals.
- ·• Includes expressing numbers as a product of prime factors.
- ·• Finding the Lowest Common Multiple (LCM) and Highest Common Factor (HCF) of two numbers.
- Continue a given number sequence.
- Recognise sequences of square, cube and triangular numbers.
- Recognise patterns in sequences including the term to term rule and relationships between different sequences; subscript notation might be used.
- Find and use the nth term of sequences in linear, simple quadratic and cubic sequences; for extended learners this is required for linear, quadratic, cubic and exponential sequences and simple combinations of these.
- Make estimates of numbers, quantities and lengths, give approximations to specified numbers of significant figures and decimal places and round off answers to reasonable accuracy in the context of a given problem.
- Give appropriate upper and lower bounds for data given to a specified accuracy, e.g. measured lengths.
- Obtain appropriate upper and lower bounds to solutions of simple problems given data to a specified accuracy, e.g. the calculation of the perimeter or the area of a rectangle.
- Understand the meaning of indices (fractional, negative and zero) and
- use the rule of indices 5
^{1/2}= square root of 5 - Find the value of 5
^{1/2}, 100^{1/2}, 8^{-2/3} - Work out 2
^{-3}x 2^{4 }, (2^{3})^{2}, (2^{-3}/ 2^{4}) - Use the standard form
*A*× 10^{n}where*n*is a positive or negative integer, and 1 ≤*A*< 10. - Convert numbers into and out of standard form.
- Calculate with values in standard form.
- Use a calculator efficiently.
- Apply appropriate checks of accuracy.
- Demonstrate an understanding of ratio and proportion.
- To include numerical problems involving direct and inverse proportion. Use ratio and scales in practical situations. Formulae for other rates will be given in the question e.g. pressure and density.
- Increase and decrease a quantity by a given ratio.
- Calculate using money and convert from one currency to another.
- Use given data to solve problems on personal and household finance involving earnings, simple interest and compound interest.
- Includes discount, profit and loss.
- Extract data from tables and charts.
- Includes discount, profit and loss.
- Knowledge of compound interest formula is required.
- Calculate a given percentage of a quantity.
- Express one quantity as a percentage of another.
- Calculate percentage increase or decrease.
- Carry out calculations involving reverse percentages, e.g. finding the cost price given the selling price and the percentage profit.
- Calculate times in terms of the 24-hour and 12-hour clock.
- Read clocks, dials and timetables.
- Calculate average speed.
- Use common measures of rate.

**Algebra 1 - Chapter 2**

**Approximate length: 2 weeks **

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*Th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Directed numbers, Formulae, Brackets and simplifying , Solving linear equations, simultaneous equations (linear and quadratic) , quadratic equations and factorizing.

Specific National Curriculum Objectives Covered:

- Use directed numbers in practical situations, e.g. temperature changes, flood levels.
- Manipulate directed numbers.
- Use letters to express generalized numbers and express basic arithmetic processes algebraically.
- Substitute numbers for words and letters in complicated formulae.
- Use brackets and extract common factors, e.g. expand 3x(2x – 4y)
- Expand products of algebraic expressions (two brackets only), e.g. expand (x + 4)(x – 7); for extended include products of more than two brackets, e.g. (x + 4)(x – 7)(2x + 1)
- Derive and solve simple linear equations in one unknown.
- Derive and solve simultaneous linear equations in two unknowns.
- Factorise 9x
^{2}+ 15xy - Factorise where possible expressions of the form:
*ax*+*bx*+*kay*+*kby ; a*–^{2}x^{2}*b*;^{2}y^{2}*a*+ 2^{2}*ab*+*b*;^{2}*ax*+^{2}*bx*+*c* - ·• Derive and solve quadratic equations by factorisation, completing the square and by use of the formula.
- ·• Derive and solve simultaneous equations, involving one linear and one quadratic.

**Mensuration – Chapter 3**

**Approximate length: 2 weeks **

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*Th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Area, Arc length, sector area, chord of a circle, Volume and Surface area.

Specific National Curriculum Objectives Covered:

- identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment
- calculate arc lengths, angles and areas of sectors of circles
- calculate surface areas and volumes of spheres, pyramids, cones and composite solids

**Geometry – Chapter 4**

**Approximate length: 3 week **

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*Th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Fundamental rules of angles, Pythagoras theorem and symmetry .

Specific National Curriculum Objectives Covered:

- apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in two {and three} dimensional figures

**Algebra 2 -Chapter 5 Approximate length: 4 week**

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*Th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Algebraic fractions, changing subject of a formula, variation and indices.

Specific National Curriculum Objectives Covered:

- understand that X is inversely proportional to Y is equivalent to X is proportional to 1 Y construct and interpret equations that describe direct and inverse proportion

### Term 2

**Geometry and measures - Chapter 6**

**Approximate length: 2 weeks **

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*Th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Right -angled Triangles, Scale Drawing, Three dimensional problems, Sine, cosine and tangent of any angle, the sine rule and the cosine rule.

Specific National Curriculum Objectives Covered:

- Read and make scale drawings.
- Interpret and use three-figure bearings.
*Notes/Examples Measured clockwise from the North, i.e. 000°–360°.* - Apply Pythagoras’ theorem and the sine, cosine and tangent ratios for the acute angles to the calculation of a side or of an angle of a right- angled triangle.
- Apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles {and, where possible, general triangles} in two {and three} dimensional figures.
- Solve trigonometrical problems in two dimensions involving angles of elevation and depression
- Recognise, sketch and interpret graphs of simple trigonometric functions.
- Graph and know the properties of trigonometric functions
- Solve simple trigonometrical equations for values between 0° and 360°
- Solve problems using the sine and cosine rules for any triangle and the formula area of triangle =1/2 ab sinC
- Solve simple trigonometrical problems in three dimensions including angle between a line and a plane.

**Graphs – Chapter 7**

**Approximate length: 2 weeks **

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*Th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Drawing accurate graphs, Gradients, The form y = mx +c, Plotting curves, Interpreting graphs, Graphical solution of equations, Distance – time graphs, speed – time graphs and Differentiation.

Specific National Curriculum Objectives Covered:

- Interpret and use graphs in practical situations including travel graphs and conversion graphs.
- Draw graphs from given data.
- Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration.
- Calculate distance travelled as area under a speed–time graph.
- Calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts.
- Construct tables of values and draw graphs for functions of the form axn (and simple sums of these) and functions of the form ab
^{x}+ c. - Solve associated equations approximately, including finding and interpreting roots by graphical methods.
- Draw and interpret graphs representing exponential growth and decay problems. Recognise, sketch and interpret graphs of functions.
- Plot and interpret graphs (including reciprocal graphs {and exponential graphs}) and graphs of non-standard functions in real contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration.
- Recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function π¦= 1/x with π₯≠0. {the exponential function y = k
^{x}for positive values of k, and the trigonometric functions (with arguments in degrees) with y = sin x, y = cos x and y = tan x for angles of any size} . - Find approximate solutions using a graph.
- Sketch translations and reflections of the graph of a given function.
- Estimate gradients of curves by drawing tangents.
- Understand the idea of a derived function. Use the derivatives of functions of the form ax
^{n}, and simple sums of not more than three of these. - Apply differentiation to gradients and turning points (stationary points). Identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically {and turning points by completing the square}.
- Discriminate between maxima and minima by any method. Demonstrate familiarity with Cartesian coordinates in two dimensions.
- Find the gradient of a straight line. Calculate the gradient of a straight line from the coordinates of two points on it.
- Use the form y=mx+ c to identify parallel {and perpendicular} lines; find the equation of the line through two given points, or through one point with a given gradient.
- Calculate the length and the coordinates of the midpoint of a straight line from the coordinates of its end points.
- Interpret and obtain the equation of a straight- line graph.
- Determine the equation of a straight line parallel to a given line.
- Find the gradient of parallel and perpendicular lines.
- Know that the perpendicular distance from a point to a line is the shortest distance to the line.

**Geometry and measures - Chapter 8**

**Approximate length: 2 weeks**

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Sets, Logical Problems, Vectors, Column Vectors, Vector Geometry, Functions and Simple and Combined Transformations.

Specific National Curriculum Objectives Covered:

- Understand notation of Venn diagrams. Definition of sets e.g. A = {x: x is a natural number} B = {a, b, c, …}
- Interpret simple expressions as functions with inputs and outputs; {interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’}
- Use function notation, e.g. f(
*x***) =**3*x***–**5, f:*x*βΌ 3*x***–**5, to describe simple functions. Find inverse - functions f
^{-1}(*x*). Form composite functions as defined by gf(*x*)**=**g(f(*x*)). - Describe translations as 2D vectors
- Apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; {use vectors to construct geometric arguments and proofs}.
- Describe a translation by using a vector represented by e.g. τxyτ ABτ¬τ¬τ¬τ¬τ¬β or a. Add and subtract vectors. Multiply a vector by a scalar.
- Calculate the magnitude of a vector (X Y) as square root of (x
^{2}+ y^{2}). Represent vectors by directed line segments. Use the sum and difference of two vectors to express given vectors in terms of two coplanar vectors. Use position vectors. - Reflect simple plane figures in horizontal or vertical lines.
- Rotate simple plane figures about the origin, vertices or midpoints of edges of the figures, through multiples of 90°.
- Construct given translations and enlargements of simple plane figures.
- Recognise and describe reflections, rotations, translations and enlargements.
- Interpret and use fractional {and negative} scale factors for enlargements
- Describe the changes and invariance achieved by combinations of rotations, reflections and translations.

**Chapter 9 – Statistics**

**Approximate length: 2 week **

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Data display, mean, median and mode, Cumulative frequency, Comparing data sets, Box-plot and Scatter graphs.

Specific National Curriculum Objectives Covered:

- interpret and construct tables and line graphs for time series data
- {construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use}
- interpret, analyse and compare the distributions of data sets from univariate empirical distributions through
- appropriate graphical representation involving discrete, continuous and grouped data, {including box plots}
- appropriate measures of central tendency (including modal class) and spread {including quartiles and inter-quartile range}
- use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends whilst knowing the dangers of so doing

**Chapter 10 – Probability**

**Approximate length: 2 week **

**Syllabus - Cambridge IGCSE® Mathematics 0580 and Complete Mathematics for Cambridge IGCSE 5**

*Th*

*Edition-EXTENDED- David Rayner*In this unit the children will build on their understanding of Simple probability, Relative frequency, Exclusive and independent events, Tree diagrams, Probability in Venn- diagrams, Conditional probability.

Specific National Curriculum Objectives Covered:

- apply the property that the probabilities of an exhaustive set of mutually exclusive events sum to one
- use a probability model to predict the outcomes of future experiments; understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
- calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
- {calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams}.
- Extensive practice of the entire
**Cambridge IGCSE® Mathematics 0580**syllabus covered till date through past papers of CIE / IGCSE 0580.

## Blended Learning

Throughout this year there will be blended learning and we are using multiple teaching methods in order to help our students learn more effectively. All students whether face to face or learning from home will have the opportunity access all the lessons and resources. Students will use Phoenix, Teams, myimaths and GCSE Pod. Each lesson begins with a set of clearly stated objectives and an explanation of its place in the overall IGCSE syllabus. Effective learning is encouraged through frequent activities and self-assessment questions.

Links for solving past papers and links related to concepts covered to reinforce classroom learning followed will be available to students. Students will have access to worksheets with progression of difficulty, online assessments, tasks/open ended questions and fun activities through online platforms.

## Assessment

**Formative: **

Throughout the units, the children will complete graded work, quizzes and problem- solving activities which allows the teacher to assess the students’ attainment and inform their planning.

For each unit the students complete written quizzes, online quizzes as well as Chapter- wise tests (Topic Tests). Quizzes are taken based on 1-chapter assessment, where Tests are combined as per the requirement i.e. 2 to 3 chapters/topics – sections. This allows us to see progress across the units and align our planning.

**Summative: **

At the end of each term we complete internal and standardized tests. This allows us to measure the students’ progress throughout the term and year. The tests will have IGCSE format combined questions from both papers and two separate exams for P-2 and P-4 for Mock Exam. This is practice / preparation for their final IGCSE examinations. At the end of the year students appear for their final IGCSE examination for Syllabus - Cambridge IGCSE® Mathematics 0580.