<p>Chapter 17: Managing money<br /> Chapter 18: Curved graphs<br /> Chapter 19: Symmetry<br /> Chapter 20: Histograms and frequency distribution<br /> diagrams</p>

<p>SL<br /> Algebra<br /> Functions and equations<br /> Circular functions and trigonometry<br /> Vectors<br /> Statistics and probability<br /> Calculus</p>

<p>Differentiation equation<br /> find an integrating factor for a first order linear<br /> differential equation, and use an integrating<br /> factor to find the general solution<br /> recall the meaning of the terms ‘complementary<br /> function’ and ‘particular integral’ in the context<br /> of linear differential equations, and recall<br /> that the general solution is the sum of the<br /> complementary function and a particular integral<br /> find the complementary function for a first or<br /> second order linear differential equation with<br /> constant coefficients</p>

<p>review notes</p> <p>understand the definitions of the hyperbolic<br /> functions sinh x, cosh x, tanhx, sech x, cosech x,<br /> coth x in terms of the exponential function<br /> sketch the graphs of hyperbolic functions<br /> prove and use identities involving hyperbolic<br /> functions<br /> understand and use the definitions of the inverse<br /> hyperbolic functions and derive and use the<br /> logarithmic forms.</p>

<p>review notes<br /> formulate a problem involving the solution of<br /> 3 linear simultaneous equations in 3 unknowns<br /> as a problem involving the solution of a matrix<br /> equation, or vice versa<br /> understand the cases that may arise concerning<br /> the consistency or inconsistency of 3 linear<br /> simultaneous equations, relate them to the<br /> singularity or otherwise of the corresponding<br /> matrix, solve consistent systems, and interpret<br /> geometrically in terms of lines and planes<br /> understand the terms ‘characteristic equation’,<br /> ‘eigenvalue’ and ‘eigenvector’, as applied to<br /> square matrices<br /> find eigenvalues and eigenvectors of 2 × 2 and<br /> 3 × 3 matrices</p>

<p>review notes</p> <p>integrate hyperbolic functions and recognise<br /> integrals of functions<br /> derive and use reduction formulae for the<br /> evaluation of definite integrals<br /> understand how the area under a curve may be<br /> approximated by areas of rectangles, and use<br /> rectangles to estimate or set bounds for the area<br /> under a curve or to derive inequalities or limits<br /> concerning sums<br /> use integration to find<br /> – arc lengths for curves with equations in<br /> Cartesian coordinates, including the use of a<br /> parameter, or in polar coordinates<br /> – surface areas of revolution about one of the<br /> axes for curves with equations in Cartesian<br /> coordinates, including the use of a parameter.</p>

<p>review notes<br /> differentiate hyperbolic functions and<br /> differentiate sin–1x, cos–1x, sinh–1x, cosh–1x and tanh–1x<br /> obtain an expression for in cases where the<br /> relation between x and y is defined implicitly or<br /> parametrically<br /> derive and use the first few terms of a<br /> Maclaurin’s series for a function.</p>

<p>Chapter 13: Understanding measurement<br /> Chapter 14: Further solving of equations and<br /> inequalities<br /> Chapter 15: Scale drawings, bearings and<br /> trigonometry<br /> Chapter 16: Scatter diagrams<br /> and correlation</p>

<p>review notes</p> <p>understand de Moivre’s theorem, for a positive<br /> or negative integer exponent, in terms of the<br /> geometrical effect of multiplication and division<br /> of complex numbers</p> <p>prove de Moivre’s theorem for a positive integer<br /> exponent</p> <p>use de Moivre’s theorem for a positive or<br /> negative rational exponent<br /> – to express trigonometrical ratios of multiple<br /> angles in terms of powers of trigonometrical<br /> ratios of the fundamental angle<br /> – to express powers of sin i and cos i in<br /> terms of multiple angles<br /> – in the summation of series<br /> – in finding and using the nth roots of unity.</p>

<p>Topical Past Papers are an essential tool for any student looking to succeed in their exams. These questions are regular past paper questions, but instead of covering all topics, they focus on a specific topic or theme. This allows students to test their knowledge in a more targeted way and identify any areas they may need to improve on. By practicing with Topical Past Papers, students have the opportunity to enhance their understanding of a subject and build their confidence ahead of the exam.</p>

<p>Candidates should be able to:<br /> • formulate a problem involving the solution of<br /> 3 linear simultaneous equations in 3 unknowns<br /> as a problem involving the solution of a matrix<br /> equation, or vice versa</p> <p>• understand the cases that may arise concerning<br /> the consistency or inconsistency of 3 linear<br /> simultaneous equations, relate them to the<br /> singularity or otherwise of the corresponding<br /> matrix, solve consistent systems, and interpret<br /> geometrically in terms of lines and planes</p> <p>• understand the terms ‘characteristic equation’,<br /> ‘eigenvalue’ and ‘eigenvector’, as applied to<br /> square matrices</p> <p>• find eigenvalues and eigenvectors of 2 × 2 and<br /> 3 × 3 matrices<br /> Restricted to cases where the eigenvalues are real<br /> and distinct.<br /> • express a square matrix in the form QDQ–1,<br /> where D is a diagonal matrix of eigenvalues and<br /> Q is a matrix whose columns are eigenvectors,<br /> and use this expression</p> <p>• use the fact that a square matrix satisfies its own<br /> characteristic equation.</p>

<p>IGCSE 0580 is a mathematics course designed for students who seek a solid foundation in the subject but may not be aiming for a career in science, technology, engineering, or mathematics (STEM) fields. This course covers the core mathematical concepts, including algebra, geometry, probability, and statistics, in a way that is accessible and engaging for all students.<br /> In this course, we will employ a variety of teaching methods to engage students and promote active learning. These methods include lectures, group discussions, problem-solving sessions, and hands-on activities. We will also utilize digital tools and resources to enhance the learning process and make it more interactive and engaging.</p>

<p>The United Kingdom Mathematics Trust (UKMT) was founded in 1996 and stands as a registered charity, whose charitable aim is to advance the education of young people in mathematics by offering a wide range of national-level competitions and activities for students from 11 to 18 years old in the UK.UKMT is also responsible for selecting UK National Mathematical Olympiad team to participate in the IMO. UKMT has a comprehensive mathematics assessment system, which not only encourages wide participation, develops interest, and experiences JMC/IMC/SMC and also includes BMO for selecting a national team.<br /> BMO has two rounds: BMO Round 1 and BMO Round 2. Only the top 10% in BMO Round 1 can participate in Round 2. UKMT will select the top UK students from Round 2 to take part in the UK National Mathematical Olympiad camp and select the national team. Different from the multiple choice questions of the SMC, BMO is mainly a proof question, which requires students to specify the steps and process of solving the problem, and to investigate students’ comprehensive mathematical academic strength in depth. In the UK, only students with excellent SMC results are eligible to participate in BMO Round 1.</p>

<p>IGCSE 0580 is a mathematics course designed for students who seek a solid foundation in the subject but may not be aiming for a career in science, technology, engineering, or mathematics (STEM) fields. This course covers the core mathematical concepts, including algebra, geometry, probability, and statistics, in a way that is accessible and engaging for all students.<br /> In this course, we will employ a variety of teaching methods to engage students and promote active learning. These methods include lectures, group discussions, problem-solving sessions, and hands-on activities. We will also utilize digital tools and resources to enhance the learning process and make it more interactive and engaging.</p>

<p>IGCSE 0580 is a mathematics course designed for students who seek a solid foundation in the subject but may not be aiming for a career in science, technology, engineering, or mathematics (STEM) fields. This course covers the core mathematical concepts, including algebra, geometry, probability, and statistics, in a way that is accessible and engaging for all students.<br /> In this course, we will employ a variety of teaching methods to engage students and promote active learning. These methods include lectures, group discussions, problem-solving sessions, and hands-on activities. We will also utilize digital tools and resources to enhance the learning process and make it more interactive and engaging.</p>

<p>IGCSE 0580 is a mathematics course designed for students who seek a solid foundation in the subject but may not be aiming for a career in science, technology, engineering, or mathematics (STEM) fields. This course covers the core mathematical concepts, including algebra, geometry, probability, and statistics, in a way that is accessible and engaging for all students.<br /> In this course, we will employ a variety of teaching methods to engage students and promote active learning. These methods include lectures, group discussions, problem-solving sessions, and hands-on activities. We will also utilize digital tools and resources to enhance the learning process and make it more interactive and engaging.</p>

<p>IGCSE 0580 is a mathematics course designed for students who seek a solid foundation in the subject but may not be aiming for a career in science, technology, engineering, or mathematics (STEM) fields. This course covers the core mathematical concepts, including algebra, geometry, probability, and statistics, in a way that is accessible and engaging for all students.<br /> In this course, we will employ a variety of teaching methods to engage students and promote active learning. These methods include lectures, group discussions, problem-solving sessions, and hands-on activities. We will also utilize digital tools and resources to enhance the learning process and make it more interactive and engaging.</p>

<p>Topical Past Papers are an essential tool for any student looking to succeed in their exams. These questions are similar to regular past paper questions, but instead of covering all topics, they focus on a specific topic or theme. This allows students to test their knowledge in a more targeted way and identify any areas they may need to improve on. By practicing with Topical Past Papers, students have the opportunity to enhance their understanding of a subject and build their confidence ahead of the exam.</p>

<p>Topical Past Papers are an essential tool for any student looking to succeed in their exams. These questions are similar to regular past paper questions, but instead of covering all topics, they focus on a specific topic or theme. This allows students to test their knowledge in a more targeted way and identify any areas they may need to improve on. By practicing with Topical Past Papers, students have the opportunity to enhance their understanding of a subject and build their confidence ahead of the exam.</p>

<p>Topical Past Papers are an essential tool for any student looking to succeed in their exams. These questions are similar to regular past paper questions, but instead of covering all topics, they focus on a specific topic or theme. This allows students to test their knowledge in a more targeted way and identify any areas they may need to improve on. By practicing with Topical Past Papers, students have the opportunity to enhance their understanding of a subject and build their confidence ahead of the exam.</p>

<p>Topical Past Papers are an essential tool for any student looking to succeed in their exams. These questions are similar to regular past paper questions, but instead of covering all topics, they focus on a specific topic or theme. This allows students to test their knowledge in a more targeted way and identify any areas they may need to improve on. By practicing with Topical Past Papers, students have the opportunity to enhance their understanding of a subject and build their confidence ahead of the exam.</p>