# Maths (Y10-13)

Mathematics is the ubiquitous language that holds solutions to a wide range of problems. The skills learnt at here will be used to further education, inspire research and to pay your gas bill. Mathematics can describe how the planets orbit the sun, the optimum size for a drinks bottle and to budget for your personal finances.

Not all areas of maths are useful or accessible to all, what we will do is allow the students to discover the importance of the subject for their individual needs whilst guiding them to an important qualification. The school will offer a scheme of work to a learner led audience.

A typical maths lesson will not be didactic or conventional; it will provide an opportunity to explore functional problems as well as discuss abstract concepts. We will offer the opportunity to innovate and research as well as offer the support and guidance to those whom the subject does not come naturally.

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## GCSE

Term 1 | Term 2 | Term 3 | |

Year 10 |
Number Skills - Indices, standard form, surds, fractions decimals and percentages 1) Indices, standard form, surds.(1.5weeks) • Fractional and negative indices, calculations in standard form, manipulating surds. 2) Fractions, decimals and percentages. (1 weeks) • Operations with fractions, decimals and percentages including appreciation and depreciation. . Algebra - formulae, equations and sequences. 3) Formulae. (1 week) • Substitution and rearrangement. 4) Equations and sequences. (2 weeks) • Solving equations involving fractions, linear and quadratic sequences. Representing Data- graphs, tables and charts. 5) Graphs, tables and charts. (1 week) • Back to back stem&leaf, averages from grouped data. Angles and Trigonometry. 6) Angles & trigonometry (2 weeks) • Angles in parallel lines, exterior and interior angles, triangles. • Using Pythagoras, sin, cos and tan ratios. |
Area and volume 1) Area and volume. (2 weeks) Prisms, sectors, cylinders, spheres, pyramids and cones. 2) Graphs (2 weeks) • Linear graphs, rates of change, distance-time graphs and reallife graphs, quadratic graphs, cubic graphs. Equations and Inequalities. 3) Equations and inequalities. 2 weeks) • Completing the square, quadratic formulae, linear and quadratic simultaneous equations, linear and quadratic inequalities. Probability. 4) Probability (1 weeks) • Conditional probability, Venn diagrams and set notation. Multiplicative Reasoning. 5) Multiplicative reasoning. (1 week) • Growth and decay, compound measures, direct and inverse proportion. |
Similarity and Congruence 1) Similarity and congruence (1 week) Geometric proof and similarity, similarity and 3D solids. Trigonometry 2) Graphs, sine, cosine rule, area of triangle (2weeks). • Trig graphs, sine and cosine rule, area of triangle, transformations of trig graphs Further Statistics 3) Sampling and representing data (2 weeks) • Sampling, cumulative frequency, box plots, histograms. Algebra - equations and graphs. 4) Quadratics and cubic graphs (2 weeks) • Solving quadratics graphically, solving simultaneous equations graphically, representing inequalities graphically, graphs of cubic functions. |

Year 11 |
Circle theorems 1) Circle theorems and application.(1.5weeks) • Angles in circles, tangents and chords, application of circle theorems. Algebra - formulae and equations. 2) Formulae and equations. (2 week) • Rearrangement, algebraic fractions, surds, functions. Vectors and Geometric Proof. 3) Vectors and proof. (2 weeks) • Vector notation, vector arithmetic, solving geometric problems. Proportion and Graphs. 4) Proportion and graphs (2 weeks) • Direct and inverse proportion, exponential functions, non-linear graphs, graphical translations and transformations. Excess weeks allowed for assessment and regular revision weeks. |
This term is devoted to formal mocks and a review of the syllabus. General revision of entire syllabus before mocks approx. 2 weeks. 1) Review: Area and volume. (1 weeks) 2) Review: Graphs (1 weeks) Review: Equations and Inequalities. (1 week) 3) Equations and inequalities. Review: Probability. 4) Probability (1 weeks) . Review: Trigonometry (2 weeks) Review: Algebra - equations and graphs (2 weeks). Review: Multiplicative Reasoning. (1 week) |
This term is devoted to exam preparation which includes a formal mock, exam paper analysis, exam technique analysis, and a review of topics linked to PLC’s. |

## Maths Studies

Term 1a | Term 1b | Term 2a | Term 2b | Term 3a | Term 3b | |

Year 12 |
Numbers and Algebra The Story of 1 DVD, international mindedness Basic use of four operations; order of operations Prime numbers, factors, and multiples Ratio, percentage, and proportions Evaluating expressions; manipulating algebraic expressions and rearranging formulae Solving linear equations in one variable Solving linear inequalities Natural numbers, N; integers, Z; rational numbers, Q; and real numbers, R Approximation: decimal places, significant figures. Percentage errors Estimation Scientific notation Operations with Scientific notation SI (Systeme International) and other basic units of measurement Currency conversions - using commonly accepted world currencies |
Mathematical Models Concept of a function, domain, range, and graph Function notation, e.g. f(x), v(t), C(n) Equation of a line in two dimensions: the forms y = mx + c and ax + by + d = 0 Gradients; intercepts Point of intersection of lines Lines with gradients, Linear models Linear functions and their graphs Coordinates in two dimensions. Midpoints, distance between points. The distance between two points; eg between two vertices or vertices with midpoints or midpoints with midpoints Drawing accurate graphs Creating a sketch from information given Reading, interpreting and making predictions using graphs Included all the functions above and additions and subtractions |
Logic Sets and Probability - Probability of an event Probability of a complementary event Expected value Probability of combined events, mutually exclusive events, independent events Use of tree diagrams, Venn diagrams, sample space diagrams and table of outcomes. Probability using ‘with replacement’ and ‘without replacement’ Conditional probability |
Descriptive Statistics The collection of data and its representation in bar charts, pie charts and pictograms Classification of data as discrete or continuous Simple discrete data: frequency tables Grouped discrete or continuous data: frequency tables; Frequency histograms cumulative frequency curves, median, and quartiles Box-and-whisker diagram Measures of central tendency: for simple discrete data Measures of dispersion: range, interquartile range, and standard deviation |
We will use this time to introduce the project to students. Math Studies SL will be informed that they must carry out a project which demonstrates their knowledge of the course objectives. We will discuss the purpose of the project, the guidelines of student’s responsibilities, and students will have time to brainstorm and begin the development of their project. | |

Year 13 |
Statistical Application Normal distribution The concept of a random variable; of the parameters μ and s; of the bell shape; the symmetry about x = μ Diagrammatic representation [using GDC] Normal probability calculations Expected value Inverse normal calculations Bivariate data: the concept of correlation Scatter diagrams; line of best fit, by eye, passing through the mean point Pearson’s product-moment correlation coefficient, r. Interpretation of positive, zero and negative, strong, or weak correlations The regression line for y on x Use of the regression line for prediction purposes The x2 test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; degrees of freedom; p-values |
Project An individual piece of work involving the collection of information or the generation of measurements, and subsequent the analysis and evaluation. | Geometry and trigonometry | Introduction to different calculus | EXAMS |

## Maths Standard

Term 1a | Term 1b | Term 2a | Term 2b | Term 3a | Term 3b | |

Year 12 |
Algebra Laws of indices and Laws of Logs Binomial expansions and their applications Graphing Exponentials and logs Solving equations involving exponentials and logs |
Circle geometry Trigonometry Transforming graphs |
Calculus 1 (Introduction) Calculus 2 (applications) Calculus 3 (Intro to integration) Calculus 3 ( applications of integration) Calculus 4( more functions) |
Statistics Descriptive stats and diagrams including types of data Statistical measures including quantiles mean and variance etc Bivariate data Probability theory Binomial distribution Normal distribution |
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Year 13 |
Exploration Introduction to the process and an opportunity to talk about some ideas and look through examples Exploration (practice) Opportunity to do a practice exploration with the support of peers to really understand what is required and the time constraints involved |
Calculus Extension of Differentiation Chain rule, product and quotient rule Applications of differentiation using more advanced techniques Calculus Extension of Integration of trig functions. Sight integrals and a more formal approach by using integration by substitution Volumes of revolution Calculus Kinematics |
Mathematical exploration Introduction Proposal Vectors 1definition of a vector and the manipulation of vectors Calculation of the magnitude of a vector Mathematical exploration First draft Vectors 2 |
Mathematical exploration Final submission Feedback on draft given and time then allowed for final version to be completed and handed in. |
Remainder of year to be used to review and prepare for exams. |

## Maths Higher

Term 1a | Term 1b | Term 2a | Term 2b | Term 3a | Term 3b | |

Year 12 |
Quadratic Equations and Functions Graphing and Transforming Functions |
Review of Sequence and Series Review of Log and Exponential Counting and Binomial Expansion Mathematical Induction Advanced trigonometry |
Graphs of circular Functions Solutions of Trig Equations Solutions of Triangles Statistics |
Complex Numbers Polynomials |
Mathematical Exploration Calculus |
Probability |

Year 13 |
Vectors Calculus |
Statistical Distributions Vectors: Lines and Planes in Space |
Calculus: Integration | Option | Consolidation and Review | EXAMS |