# Mathematics

Subject Leader: Mr S Shah

Subject Leader Email Address: samir.shah@swale.at

Sometimes the questions are complicated and the answers are simple.

**DR. SEUSS**

### Subject overview

Mathematics is a creative and highly interconnected discipline that has developed over centuries, providing solutions to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education, therefore, provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject. The mathematics curriculum at The Sittingbourne School aims to develop a love of learning, development of character, a sense of community and achievement for all.

## Year 7

### Term 1:

In this term students strengthen their understanding of working with sequence. They explore different types of sequences such as linear, triangular, Fibonacci and begin to find the expressions for the nth term rule of linear sequences. Students will learn more about the function machines and how they relate to a rule. Equivalence, collecting like terms, substituting expressions and solving equations and drawing pie charts will be introduced in this term.

#### Enquiry Questions:

- How would you explain the difference between linear, geometric and Fibonacci sequences and find missing terms?
- How do you complete function machines and describe sequences given by algebraic rules?
- How do we form and solve equations when solving real-life problems and correctly use "equal to" and "equivalent to" signs?
- How do we interpret tables and pie charts?

### Term 2:

Students will be taught how to round to given decimal places and significant figures. Some high achieving students will also be able to round to the powers of 10 and learn how to read and write numbers in standard form. The relationship between fractions, decimals and percentages will be discussed and students will be taught how to change between them.

#### Enquiry Questions:

- Why is rounding important?
- What is the difference between decimal places and significant figures?
- How do we round to the given decimal places and significant figures?
- How do you convert between fractions, decimals and percentages for different contexts?

### Term 3:

Students will start this term by learning the strategies for mental addition and subtraction. Students will also learn how to work with frequency trees, mileage/distance charts and time-tables. The paper methods for multiplying and dividing numbers will be recapped along with order of operations, BIDMAS. Students will learn how to use multiplication and division to solve problems with the mean. How to find the fractions and percentages of amounts using different methods will be covered this term. High ability students will also learn how to solve complex multiplication and division problems and how to deal with percentages over 100%.

#### Enquiry Questions:

- How do you decide whether to use addition or subtraction to solve a problem?
- How do you use different forms for multiplication and division to solve problems?
- How do you find fractions and percentages using different models to represent different situations?

### Term 4:

Students will learn what are directed numbers and how to perform four operations with directed numbers. They will further explore the use of directed numbers in order of operations (BIDMAS), learn how to add and subtract with fractions and solve two step equations. High ability students will explore the use of powers with directed numbers and the connection between numerical and algebraic fractions.

#### Enquiry Questions:

- How do we use order of operations with directed numbers?
- How do we solve equations involving negative and fractional solutions?
- How do you use the knowledge of adding and subtracting fractions with algebraic fractions?

### Term 5:

This term, students will improve their understanding of working with angles and learn how to use mathematical equipment such as compass, protractor and ruler efficiently in constructing a variety of shapes. Finding the angles in triangles and quadrilaterals will be taught this term. High ability students will have the opportunity to learn how to find angles in parallel lines and polygons. They will also begin to understand how to prove results geometrically.

#### Enquiry Questions:

- How can different shapes be classified and how can you construct them?
- How can you find missing angles using the properties of shapes and angles?
- How do we reason geometrically?

### Term 6:

In this term students build on their understanding of rounding to estimate results of a calculation. They will further learn how estimation is useful in checking the accuracy of answers. The language relating probability (likely, unlikely, even chance, impossible) will be covered this term and students will learn how to calculate probability using numbers. Why probability is calculated using fractions, decimals and percentages will also become clearer. Students will become fluent in finding factors, multiples and prime factors. They will further improve their reasoning skills using counter-examples to disprove a conjecture and solve problems using prime factor decomposition.

#### Enquiry Questions:

- How can you use estimation to check the accuracy of answers?
- How can you apply the knowledge of probability into different contexts?
- How would you use prime factor decomposition to find the HCF and LCM of two or more numbers?

## Year 8

### Term 1:

In this term, students focus on the meaning of ratio and various models that can be used to represent ratios. They further learn how to share in a given ratio. Students will then move onto simplifying ratios and exploring links between ratios and fractions, including understanding and using Pi as the ratio of the circumference of a circle to its diameter. In order to further develop students' understanding they will continue to establish links in other areas of mathematics between ratio and scaling, including the idea of direct proportion, conversion of currencies, conversion graphs and maps and scales. During this term, students will be introduced to multiplying and dividing with fractions and their reciprocal.

#### Enquiry Questions:

- How do you know when to multiply or divide using the bar model when solving ratio problems?
- How do you use direct proportion to solve a problem?
- How would you apply the use of scales to a real life scenario?
- How would you use fractions to solve multi-step problems?

### Term 2:

In term 2, students will build upon their prior knowledge of coordinates from Key Stage 2. They will start with lines parallel to the axes moving onto algebraic rules for straight lines. They will explore the notions of gradient and intercepts but the focus will be more upon using equations to produce lines rather than the interpretation of y = mx + c. Students will then begin to look at a portion of statistics involving bivariate data and linear correlation. Their knowledge of graphs and bar charts will be extended, where they will deal with both discrete and continuous data. Towards the end of the term students will revisit probability, particularly looking at sample space diagrams.

#### Enquiry Questions:

- How would you compare gradients and y-intercepts to identify a sketch of a graph?
- How would you use graphs to make estimations and predictions?
- How would you consider something to be fair or biassed?

### Term 3:

In this term students build on their understanding of equivalence and will explore expanding a single set of brackets and factorising. All students will revisit and extend their knowledge of solving equations, including those with brackets and unknowns on both sides. They will also learn to solve basic inequalities whilst learning the meaning of a solution set and exploring similarities and differences compared to solving equations. The emphasis will be on forming and solving equations. In year 7, students learnt about sequences. This topic will be revisited but extended to look at sequences with more complex algebraic rules. Students will learn about finding a rule for the nth term for linear sequences.Towards the end of the term students will begin to explore the ideas behind the addition and subtraction laws of indices. Here the foundation for students is to ensure they are comfortable with expressions involving powers.

#### Enquiry Questions:

- How would you select the appropriate technique to solve an inequality or equation?
- How would you solve multi-step problems involving sequences?
- How would you calculate using different indices rules in different contexts?

### Term 4:

In term 4, the focus will be on the relationships between fractions and percentages, including decimal equivalents, and using these to work out percentage increase and decrease. Students will study expressing one number as a fraction and percentage of another. Here students are required to develop both their calculator and non-calculator skills of working with aforementioned topics. In addition to this their financial maths will be developed through various contexts such as, profit, loss and interest. Building on from indices last term, students will extend their prior learning of standard form and make sense of the notation and its uses. During the last few weeks of this term students will revisit a lot of basic number sense skills. Students will have the opportunity to expand their knowledge of estimation and the use of mental strategies . They will also look at conversion of metric units and multiplying/dividing by 10, 100 and 1000 in context.

#### Enquiry Questions:

- How would you attempt to calculate repeated percentage changes?
- How would you explain why a number isn't in a standard form?
- How would you solve problems using time and calendar information?

### Term 5:

In this term, students build on their understanding of angle notation and relationships, extending to exploring angles in parallel lines and solving missing angle problems. Thus enabling students to identify and form links between the properties of polygons and quadrilaterals. Students will start to explore mathematical constructions with the use of rulers and pairs of compasses. Students will further be introduced to formulae for the area of trapeziums and circles. The key aspect is choosing and using the correct formula for the correct shape, reinforcing recognising the shapes, their properties, names and looking at compound shapes. During the latter weeks of the term, the teaching of transformation is split between that of rotation, reflection and translation. Students will also revisit and enhance their knowledge of special triangles and quadrilaterals and focus on key vocabulary such as object, image and congruent. Although this topic is quite small, time is taken to build confidence and deepen the understanding of different concepts.

#### Enquiry Questions:

- How would you solve a multi-step problem using angle rules and geometric shapes?
- How would you calculate area in different mathematical contexts?
- How would you use symmetry and reflection to find shapes in different contexts?

### Term 6:

In this final term, the focus shifts to statistics again with the focus shifting from the data handling cycle to that of using charts to compare different distributions and exploring when graphs may be misleading. During their studies students are introduced to key concepts of designing effective questionnaires, which link to the KS4 statistics curriculum. Earlier in KS3 students met and studied the median and the mean. This term sees the introduction of the mode and mean and when each average should be used. Students extend their knowledge by looking at the mean from grouped and ungrouped frequency tables. They will also learn about the outliers, the effect these have on the range and averages and whether they should be included or excluded from the calculations.

#### Enquiry Questions:

- Why is interpreting data and graphs important for everyday life?
- How would you explain how an outlier impacts the averages and range in the data set?

## Year 9

### Term 1:

In this term, students will look to build on their knowledge from year 8. We now look to compare straight lines focussing more on gradients and intercepts. Students will then have the opportunity to learn how to form and solve equations in a variety of contexts. How to test conjectures and form conclusions based on given information will be taught in this term. Students will also learn how to design questionnaires and gather information through using them.

#### Enquiry Questions:

- How do we find the equation of a straight line?
- How would you solve a problem involving algebra?
- How do you prove conjectures?
- How to design an effective questionnaire.

### Term 2:

In this term, students will look at three dimensional shapes in more depth. Students will then move on to learning mathematical constructions, locus of points and identifying regions. Students will also explore congruency of shapes and build their skills of reasoning geometrically. In statistics, students will improve their understanding of various sampling methods used for statistical analysis and their advantages and disadvantages.

#### Enquiry Questions:

- How would you explain the difference between similarity and congruence?
- How would you demonstrate congruence?
- Which sampling method is most effective and why?

### Term 3:

Term 3 will see students look to apply their mathematical skills to real life situations. This covers estimation, fractions and standard form, which also have links with science. Students will learn how to calculate original price using reverse percentages, reductions in car price and solve repeated percentage problems. There will be a heavy focus on solving real life problems using percentages. Students will also be tackling money problems that involve bills, statements, interest and tax.

#### Enquiry Questions:

- How would estimation and fractions be used in real life situations?
- How would you apply complex percentages in real life situations?
- How would you use mathematical skills to calculate interest and taxes?

### Term 4:

This term students will recap basic angle rules and learn how to use the angle properties to form and solve equations with shapes. Students will then move on to learning transformations focussing on symmetry and rotation. Trigonometry and Pythagoras’ theorem will be introduced to students towards the end of the term. They will also have an opportunity to use trigonometry and Pythagoras’ theorem to solve problems with right angled triangles.

#### Enquiry Questions:

- How would you solve a problem using angles and algebra?
- How would you describe a transformation using two elements?
- How would you use Pythagoras’ theorem or trigonometry to solve problems involving triangles?

### Term 5:

Term 5 will see students continue their work on transformations with a specific focus on enlargement of shapes. Students then learn how to use direct and indirect proportion rules to solve real life problems. An important skill of reading graphs connecting variables used in everyday life and how to calculate the rates of change will be covered this term.

#### Enquiry Questions:

- How would you describe the enlargement of shapes?
- How would you apply direct/indirect proportion rules to real life situations?
- How do you calculate rates of change using graphs?

### Term 6:

Term 6 aims to complete the national curriculum for Key Stage 3 and get students ready for their next stage of learning in Key Stage 4. Students will learn the use of tree diagrams in probability and develop their understanding of drawing different graphs and their use in solving simultaneous equations. The application of the graphs and equations in real life will also be discussed this term.

#### Enquiry Questions:

- How is probability calculated when representing multiple events?
- How are quadratic graphs and simultaneous equations used in everyday life?

## Year 10

This is the first year of studying the GCSE mathematics curriculum. In addition, students will also study GCSE Statistics and sit this examination at the end of year 10. Pupils in this year group will have built a solid foundation of their mathematics skills from Key Stage 3 and will now extend their understanding of number, algebra and geometry and continue developing fluency. There will be a regular and strong emphasis on mathematical reasoning through problem solving. Pupils will begin developing links between topics and lay a strong foundation for the second and final year of Key Stage 4 curriculum. As a part of GCSE Statistics, students are introduced to the skills of statistical enquiry, and practise the underpinning statistical calculations and interpretation using real world data and authentic contexts.

### Why study this course?

GCSE Mathematics is an interconnected subject in which students are able to move fluently between representations of mathematical ideas throughout the year. The Key Stage 4 curriculum is organised into distinct domains, where pupils will build on work studied at Key Stage 3 and develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They will also have opportunities to apply their mathematical knowledge in science, geography, computing and other subjects.

The GCSE Statistics course perfectly complements the elements of GCSE mathematics. Both these courses provide transferable skills and allow students to recognise the importance of the subject in daily life. Besides preparing students for their examinations, both these qualifications aim to make students confident learners and prepare them to face the challenges of the modern world.

### What does this course lead on to?

Whilst some of our students progress onto studying A-level maths, for many students passing GCSE mathematics is a way of building up essential skills that are used on a daily basis. Passing GCSE mathematics also opens up doors to many colleges, sixth form places and apprenticeships. Also, as the use of technology increases, there will be more and more jobs which will require mathematical skills and knowledge.

### Term 1:

In this term, students will build on their skills from KS3 on ratio, mathematical constructions, and begin to learn how to perform a variety of calculations in standard form. In statistics, students will also learn about different types of correlations, finding the equations of trend lines and the meaning of the gradient in the given context.

#### Enquiry Questions:

**Foundation:**

- In how many ways can we share the amount in the given ratio?
- How can we use mathematical constructions in real life situations?
- How do we apply the four operations to numbers in standard form?
- How does SR relate to the correlation of scatter diagrams?
- How can we use equations as a problem solving tool?

**Higher:**

- How can we use mathematical constructions in real life?
- How can we find the rate of interest for compound and simple growth?
- How do we apply the four operations with standard form to solve problems?
- Why does a power of zero give a result of 1?
- How do we use probability to solve problems?

### Term 2:

In term 2, students will be taught how to work with percentages. The work covered will also focus on the use of percentages in real life. Students will also develop their understanding of rounding and truncation, solving problems with bounds and working with 3D shapes. In GCSE statistics, students will learn about how to calculate averages and decide which average is the most appropriate to use.

#### Enquiry Questions:

**Foundation:**

- How do we solve problems with growth and decay?
- How do we find the surface area and volume of different prisms?
- How do we find the error intervals of rounded and truncated numbers?
- How do we decide on the type of averages to use?

**Higher:**

- How do we use ratio to solve a variety of problems including double ratio?
- How do we find the equations of parallel and perpendicular lines?
- How is factorising used in changing the subject of formulae?
- How do we draw box plots and cf curves to compare distributions?

### Term 3:

Students will be taught how to work with direct and inverse proportions, angles in polygons and parallel lines. They will recap applying four mathematical operations with fractions and learn to solve problems with fractions. The work on changing between recurring decimals and fractions will also be covered in this term. In statistics, students will further learn to draw and interpret pie charts, stem and leaf diagrams. and how to make comparisons using these diagrams.

#### Enquiry Questions:

**Foundation:**

- How do we use direct and inverse proportion formulae to solve problems?
- How do we find interior and exterior angles of 2D shapes with 3 or more sides?
- How do we apply the four operations with fractions?
- How do we interpret and compare pie charts and stem & leaf diagrams?

**Higher:**

- How do we find interior and exterior angles of compound polygons?
- How do we solve inequalities graphically?
- How do we change recurring decimals into fractions?
- What do the solutions of quadratic equations mean (referring to the graph)?

### Term 4:

In term 4, students will build their understanding of working with probability. They will learn how to draw and use tree diagrams and use key rules relating to probability. The work on straight lines and simultaneous equations will be covered in this term. High ability students will also learn the importance of completing the square in the real life situation modelled using quadratic curves. In statistics, students will cover probability and how to estimate the median and the method of linear interpolation to locate the median.

#### Enquiry Questions:

**Foundation:**

- How do we use tree diagrams to solve problems with probability?
- How do we find the averages from frequency tables?
- How do we find the equations of straight lines?
- How do we form and solve simultaneous equations?

**Higher:**

- How do we find the surface area and volume of 3D shapes?
- How do we sketch a quadratic curve by completing the square?
- How does percentage change in one variable affect the other in direct and inverse relationships?
- What is linear interpolation and how do we apply it to estimate the median?

### Term 5:

This term aims to cover the remainder of the topics in statistics. Students will have the opportunity to learn types of data and different types of sampling methods. They will learn more about RPI and CPI, calculating rates of change, moving averages and seasonal variation. The use of box plots and cumulative frequency curves in comparing distributions will also be explored this term.

#### Enquiry Questions:

**Statistics**

- How to identify different types of data.
- What are the different sampling methods and their advantages and disadvantages?
- How are moving averages used to predict a trend and seasonal variation?
- How to use sets and Venn diagrams to calculate probability.
- How to use box plots and cf curves to compare distributions.
- How to calculate and interpret index numbers including RPI & CPI.
- How to calculate rates of change over time, including crude birth and death rates.

### Term 6:

In the final term, students will learn more about factorising quadratic equations, using percentages in real life and applying Pythagoras’ theorem and trigonometry in a variety of contexts. How to find the missing sides or angles of right angled triangles using exact trigonometric values will also be taught to students. High ability students will extend their understanding of finding nth term rule to quadratic and geometric sequences and also learn to find regions that satisfy given rule/s.

#### Enquiry Questions:

**Foundation:**

- How to find missing sides and angles of right angled triangles.
- How to use factorising to solve quadratic equations.
- How to use percentages to solve real life problems.

**Higher:**

- How to find the sides and angles of non-right angled triangles.
- How to find the nth term rule of quadratic and geometric sequences.
- How do we use mathematical constructions in real life?

## Year 11

This is the final year of the two year Key Stage 4 mathematics curriculum. By the end of this year pupils will have developed fluency in key skills and will now be focussing much more on the application to problem solving and using mathematical knowledge from a range of topics to solve more complex problems. Year 11 will focus on finishing the content of the GCSE and revision of the course. The skills learned during the two years allow pupils to use and apply the standard techniques of mathematics, to reason, interpret and communicate mathematically and to solve problems within mathematics and other contexts. Students will also learn the skills of statistical enquiry, and practise the underpinning statistical calculations and interpretation using real world data and authentic contexts as a part of the GCSE Statistics curriculum.

### Term 1:

By the end of term 1, foundation tier students in Year 11 will be able to calculate the area and perimeter of 2D shapes and solve problems with area and perimeter in different contexts. They will also solve problems involving ratio, exchange rates and recipes. We will then top this up with the data analysis skills where students will use their skills of finding probability to complete tree diagrams and make predictions. We intend to make our students problem solvers by teaching them how to form and solve equations in a variety of scenarios.

Higher tier students will be competent in all the skills required at foundation tier and also be able to find the area and volume of 3D shapes and apply these skills in real life contexts. They will be able to use their knowledge of trigonometry and Pythagoras to solve geometrical problems, calculate with direct and inverse proportion.

#### Enquiry Questions:

**Foundation Tier**

- How would you work out how much carpet or paint needed for a room?
- How do we share in a given ratio?
- How do you calculate probabilities?
- How can I solve equations with the unknown on both sides?

**Higher Tier**

- How would you calculate surface area and volume of 3D shapes?
- How would you calculate how long it takes to complete a job with respect to the number of people?
- How would you use Pythagoras’ theorem and trigonometry to solve problems involving 3D shapes?
- How to find maximum and minimum values using bounds.

### Term 2:

This term, students will be able to solve problems that include the locus of a point from a fixed point, from a fixed line, from two fixed points and also from two fixed lines including real life contexts. They will build on their skills of writing linear equations and solving simultaneous equations in solving problems in a variety of contexts.

Higher tier students will further consolidate their understanding of and ability to apply the standard circle theorems. They would be able to apply the standard circle theorems concerning angles, radii, tangents and chords to prove related results. The students will have an opportunity to extend their understanding of finding the nth term rule of linear sequences to quadratic sequences.

#### Enquiry Questions:

**Foundation**

- How do we use loci and construction in real life?
- How would you solve a simultaneous equation?
- How to decide what average to use and when.
- How do we calculate interest rate on investment or credit cards?

**Higher Tier**

- How would you find the area of sectors and segments?
- Describe as many circle theorems as you can recollect.
- How do you find the equation of circles?
- How would you find the nth term for quadratic sequences?
- How do we use loci and construction to solve geometrical problems?

### Term 3:

In term 3, students will learn about compound measures, gradient of linear graphs and solve problems involving averages. We will focus on the relationship between speed, distance and time and how they are interconnected. Students will work with both imperial (mph) and metric measures (kph and m/s), but are not expected to convert between them.

Higher Tier students will strengthen their understanding of basic probability and learn how to find the probability of mutually exclusive, independent and conditional events. Pupils will also learn to draw and interpret histograms of unequal class width and estimate the mean from histograms. The students will also learn how to find the area under the velocity-time graph and find rates of change from the distance-time and velocity-time graphs.

#### Enquiry Questions:

**Foundation Tier**

- What does gradient represent in linear graphs?
- How would you calculate the density of 3D shapes?
- How would you calculate how fast an object is travelling?
- How do we find the estimated mean?

**Higher Tier**

- How would you use probability to predict the likelihood of an event?
- How would you determine the area under the curve?
- What is the difference between a histogram and a bar chart?
- How do you estimate the mean from the given histogram?
- How do you calculate rates of change?

### Term 4:

Students will combine their skills in using Pythagoras' theorem and trigonometry in order to solve problems in 2-D. They will practice identifying when to use Pythagoras' theorem and which trigonometric ratio(s) to use in order to solve problems. Students will further be taught how to apply four operations to vectors and also how to draw given vectors.

At the higher level, students will recap the work covered on rotation, reflection, enlargement, and translation of shapes. They will further learn to locate the roots of an equation between a given set of values and also estimate the roots using iteration. Drawing sine and cosine curves and the differences and similarities between them will also be taught this term.

#### Enquiry Questions:

**Foundation Tier**

- How is trigonometry used in engineering?
- How would you use proportionality reasoning to solve problems?
- What are vectors and how would you add or subtract them?

**Higher Tier**

- How to prove the results algebraically.
- Is every transformation unique? Explain why/why not.
- How to locate the roots of equations. How to use iteration to estimate solutions.
- How to draw sine and cosine graphs. What is the same and what is different?
- How to solve geometric problems involving vectors.

### Term 5:

Students studying foundation tier would have finished their GCSE mathematics curriculum by now and will focus on revision and examination practice in light of the examinations towards the end of this term. Higher tier students will learn how to solve quadratic inequalities before commencing revision and examination practice.

#### Enquiry Questions:

- How do you solve quadratic inequalities?
- How do you decide what region of the graph correctly answers the question?

### Term 6:

All students finish their GCSE mathematics and GCSE statistics examination this term.

## Sixth Form - GCSE Resit

The course covers three main areas of mathematics: pure mathematics, statistics and mechanics. Students will develop an enhanced understanding of a range of topics that they will already be familiar with from the higher tier GCSE in mathematics. These include algebra, trigonometry, geometry, statistics and sequences. They will apply their knowledge of these topics to solve a range of problems. Students will also cover a variety of new topics including differentiation, integration, exponentials, logarithms, mechanics, probability and hypothesis testing. Students will need to draw on a range of skills from across all topics to solve problems and interpret questions focused on different contexts.

### Why study this course?

A-level mathematics is one of the most exciting qualifications that one can study in the sixth form. The course enables students to understand mathematics and mathematical processes in a way that promotes confidence, fosters enjoyment and provides a strong foundation for those who opt to progress further in the disciplines related to the subject. A-level mathematics helps students extend their range of mathematical skills and techniques and understand how different areas of mathematics are connected. The course enables learners to use their mathematical knowledge to make logical and reasoned decisions in solving challenging problems. It also builds the understanding of how mathematical models are used to track and predict events such as earthquakes, volcanic eruptions or tsunamis.

### What does this course lead on to?

Whilst some of the students opt to continue their mathematical studies at university, many also take this course to prepare for higher education in related areas such as engineering, economics, physics, teacher training or more general courses. Many employers offer apprenticeships to candidates with an A-level mathematics qualification. In addition, this qualification will help you to pursue a career in accountancy, insurance and the financial sector. Transferable skills such as problem solving and analytical, logical approaches are also welcomed by a range of employers.

### Term 1:

In the pure module, students will strengthen their understanding of working with surds, indices and quadratics from GCSE. They will learn the use of the discriminant in identifying numbers of roots and solve problems. The knowledge of completing the square will be applied to mathematical models to predict what will happen next. Students will further learn how to find a common solution that satisfies more than one inequality and how to transform a variety of graphs.

In the statistics/mechanics module, students will learn different types of data and sampling methods. Measure of location and spread including variance and standard deviation will be covered this term. Students will improve their understanding of how to draw and interpret box plots, cumulative frequency curves and histograms and learn when to use a regression line to make predictions.

#### Enquiry Questions:

**Statistics/Mechanics:**

- How to decide on the sampling methods for the given data set.
- How to find/estimate the mean and standard deviation for the coded data.
- How to use interpolation to estimate the percentiles, IQR and interpercentile range.
- When to use a regression line to make predictions and how to calculate and interpret the equation of a regression line.

**Pure:**

- What do the number of roots of quadratic equations tell us about the discriminant?
- How to use and apply models that involve quadratic functions.
- How to find a common solution to multiple inequalities.
- How to transform different graphs.
- How to use straight line graphs to construct mathematical models.

### Term 2:

In the pure module, students will improve their understanding of finding equations of straight lines and circles and learn how to model with straight lines. The properties of tangents and chords in solving problems with circles and straight lines will be taught this term. Students will begin to apply factor and remainder theorems to identify factors and factorise cubic expressions. The use of binomial theorem will be introduced in this term.

In the statistics/mechanics module, students continue to learn more about scatter diagrams, correlation and regression lines. They will learn how the concept of mathematical model applies to mechanics and the differences between the scalar and vector quantities. A detailed study of displacement-time graphs, velocity-time graphs and constant acceleration formulae will take place this term.

#### Enquiry Questions:

**Statistics/Mechanics:**

- How to calculate the magnitude of a vector quantity.
- How to derive the constant acceleration formulae and use them to solve problems.
- How to model horizontal motion and vertical motion under gravity, and solve problems.

**Pure:**

- How do we use the properties of circles to solve geometrical problems?
- How to find a factor of a polynomial and factorise cubic expressions.
- How to find constants using given terms with binomial theorem.

### Term 3:

In the pure module, students will recap sine rule, cosine rule and area of non right angled triangles. They will learn how to solve trigonometric equations to find solutions in all four quadrants and also learn to prove trigonometric identities. Students will start to explore a very important branch of mathematics called calculus this term and learn how to differentiate expressions and find the coordinates of turning points.

In the statistics/mechanics module, students explore the uses of probability through Venn and tree diagrams and learn to decide if two events are independent. They will further study probability and binomial distribution and how to calculate cumulative probabilities for the binomial distribution.

#### Enquiry Questions:

**Statistics/Mechanics:**

- How to find probabilities of mutually exclusive and independent events.
- How to decide if two events are independent.
- What is the difference between probability and binomial distribution and how to solve problems with them?

**Pure:**

- How to prove trig identities and solve trig equations in degrees & radians.
- How to find the coordinates of stationary points, maxima and minima.

### Term 4:

In the pure module, students will continue to learn more about calculus with a specific focus on integration. They will learn how to work with definite integrals and find areas under curves or curves and lines. Laws of logarithms and how to work with natural logarithms will be taught this term.

In the statistics/mechanics module, the language concept of hypothesis testing will be taught. Students will learn how to find critical values of a binomial distribution using tables and how to carry out one-tailed or two-tailed tests for the proportion of the binomial distribution and interpret the results. Newton’s three laws along with solving problems with connected particles will be covered in this term.

#### Enquiry Questions:

**Statistics/Mechanics:**

- What is a critical region and how does that affect hypothesis testing?
- How to calculate critical values of a binomial distribution.
- What are one-tailed and two-tailed tests? How do we carry them out and interpret results?
- What are Newton's laws of motion and how do we use them to solve problems involving connected particles?

**Pure:**

- How to find the area under the curves.
- How to solve equations and prove results with natural log.

### Term 5:

This term, students will finish off their first year curriculum by learning vectors and variable acceleration. The rest of the time in the term will be used for the revision purpose prior to sitting the AS examinations towards the end of the term and starting the second year curriculum.

#### Enquiry Questions:

**Statistics/Mechanics:**

- How is calculus used to solve problems involving maxima and minima?
- How to use calculus to derive constant acceleration formulae.

**Pure:**

- How to calculate the vector magnitude and use vectors in speed and distance calculations.
- How to use vectors to solve problems in context.

### Term 6:

This term, students will start learning the curriculum for the second year. In the pure module, students will learn how to prove or disprove results by contradiction and how to write single algebraic fractions as partial fractions. They will also study modulus functions and their graphs, combining transformations and how to apply binomial theorem to partial fractions.

In the mechanics module, students improve their understanding of working with moments. They will also solve problems with moments involving uniform rods and non-uniform rods. Students will further their understanding of working with forces this term. They will learn to resolve forces into components for smooth and rough inclined planes. They will also learn to deal with exponential models and calculate product moment correlation coefficient in the statistics module.

#### Enquiry Questions:

**Statistics/Mechanics:**

- When and how to use one-tailed and two-tailed tests?
- How to solve problems with uniform and non-uniform rods using moments?
- How to resolve forces on an inclined plane for smooth and rough surfaces?
- How to solve problems involving frictional force?

**Pure:**

- How to prove results by contradiction.
- How to convert an improper fraction into partial fraction form.
- How to transform the functions of the form y = |f(x)| and y = f(|x|).
- How to use binomial theorem with partial fractions.