Mathematics

Term 1: 

• Sequences
•  Understand & use algebraic notation
•  Equality and equivalence
•  Ratio and scale

Enquiry Questions:  By the end of the term, your child should be able to answer the following 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?

What is a ratio, and how do we use ratios mathematically in real life?

Term 2:  

•  Place value & ordering integers and decimals.
•  Internal assessment
•  Fraction, decimal and percentage equivalence. 

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

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: 

•  Solving problems with addition and subtraction.
•  Solving problems with multiplication and division.
•  Fractions and percentages of amounts.

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

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 various situations?

Term 4: 

•  Operations & equations with directed numbers. 
•  Addition & subtraction of fractions.

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How would you form and solve equations to address real-life problems?

How would you use fractions and algebra to solve a real-life problem?

Term 5: 

• Constructions, measuring & using geometric notation.
•  Developing geometric reasoning.
•  Trust assessment revision and exam

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How can different shapes be classified, and how can they be constructed?

How can you identify missing angles using the properties of shapes and angles?

Term 6: 

• Developing number sense.
• Transformations
• Sets and probability.
• Prime numbers and proof. 
•  Statistics

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How can you use estimation to check the accuracy of answers?

How would you describe a combination of transformations?

How can you apply the knowledge of probability in different contexts? 

How can proofs be used to answer true/false questions?

Recommended websites to support your child’s learning:

Drfrostmaths, mathsgenie, corbettmaths
 

Term 1: 

•  Ratio, proportion and conversion. 
• Area of 2D shapes
•  Operations with fractions

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Why do we use ratios and proportions in the real world?

What is the fundamental difference between a ratio and a fraction? When might you choose to use one over the other?

If you know the area of a rectangle, how can you use that to derive the formula for the area of a right-angled triangle? What about any triangle? 

Why does the formula for a parallelogram (base x perpendicular height) use perpendicular height and not the slant height? 

Term 2: 

• Solving equations.
•  Plotting linear graphs.
• Scatter graphs, bar charts, and two-way tables
• Tables and probability

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How can we use algebra to represent unknown quantities and relationships in the world around us?
What does it mean to "solve" an equation, and why is this process like balancing a scale

What do the "steepness" and "starting point" of a line tell us about the relationship between two quantities?
How can straight line graphs help us predict, compare, and understand patterns in the real world?

How can mathematics help us predict the likelihood of future events, even when we can't be certain?
What does it mean for an event to be "fair," and how can probability help us design fair games or experiments?
How does understanding probability help us make better decisions in everyday life, from playing games to making health choices?

Why do we use scatter graphs? What kind of questions can they help us answer that other graphs can't?
When might a scatter graph not be the best way to represent data? 

Term 3: 

•  Brackets, equations and inequalities.
•  Sequences
•  Indices

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How do indices provide a powerful shorthand for repeated multiplication, and why is this shorthand useful?

Where do we see the power of indices used in the real world to describe very large or tiny numbers, or rapid growth/decay?
What is a pattern, and how can we use mathematical rules to describe and predict patterns in numbers or shapes?
How can we find the 'rule' for a sequence, and why is this rule so powerful?

If we change one side of an equation, what must we do to the other side to maintain balance? Why?
Can an equation have more than one solution? Can it have no solutions?

Term 4: 

• Fractions and percentages
• Solving inequalities 
• Angles in Parallel lines and polygons.

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How does understanding percentages help us compare quantities and make informed decisions in everyday life?
How can we use percentages to describe change and growth over time?
How do parallel lines create predictable angle relationships, and why are these relationships always true?

What does the number of sides in a polygon tell us about the sum of its interior and exterior angles?

Term 5: 

• Bearing, constructions and Loci
• Transformations 2
• Area of trapezia and circles
• Standard index form

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How do we precisely describe position and direction, and why is accuracy crucial in navigation and design?
How can geometric rules help us map out all possible locations that fit a specific condition?
How do Bearings and Loci help us understand and describe movement or boundaries in the real world?

How can we precisely describe how a shape has moved or changed its position, orientation, or size? What specific information do we need?
Are there any properties of a shape that never change, no matter what transformation we apply? .
How are the different types of transformations (translation, reflection, rotation, enlargement)
identified?

Term 6: 

• Standard Index Form
• The data handling cycle
• Averages
• Box plots 

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Why do mathematicians and scientists need a special way to write extremely large and extremely small numbers?

How does standard form help us to quickly understand the magnitude (size) of a number, even before we know its exact value?

How does standard form simplify calculations with extremely large or small numbers?

How can we decide whether a piece of information is best represented by words, categories, numbers we can count, or numbers we can measure?

What are the strengths and weaknesses of different data types for answering real-world questions?

Why do we have different types of averages (mean, median, mode), and when is each one the most appropriate to use?

How does the "spread" (range) of data affect our understanding of a set of numbers?

How can understanding averages and range help us make sense of information in the real world and avoid being misled by statistics?

Recommended websites to support your child’s learning:
Drfrostmaths, mathsgenie, corbettmaths
 

Term 1: 

• Ratio and proportion
• Percentages
• Percentages including reverse
• Straight line graphs
• Factors, multiples and prime decomposition
• Pythagoras theorem

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Why do we use ratios and proportions in the real world?
What is the fundamental difference between a ratio and a fraction? When might you choose to use one over the other?

How does understanding percentages help us compare quantities and make informed decisions in everyday life?
How can we use percentages to describe change and growth over time?
What do the "steepness" and "starting point" of a line tell us about the relationship between two quantities?
How can straight line graphs help us predict, compare, and understand patterns in the real world?

What makes some numbers special (like prime numbers or square numbers) when we think about their factors and multiples?
How can knowing about factors and multiples help us solve problems involving sharing, grouping, or repeating patterns?

How does Pythagoras' Theorem describe a fundamental relationship within right-angled triangles, and why is this relationship always true?

How does Pythagoras' Theorem allow us to measure distances indirectly in the real world?

Term 2: 

• 3D shapes
•  Sequences
•  Loci and region
•  forming and solving equations

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Why are certain 3D shapes used for specific purposes in real life (e.g., cans, balls, boxes)?
How would you design a container that holds the most volume with the least surface area?
What is a pattern, and how can we use mathematical rules to describe and predict patterns in numbers or shapes?
How can we find the 'rule' for a sequence, and why is this rule so powerful?
How do lines, points, and shapes help us to define precise locations or areas based on certain rules?
Where do we encounter the concept of "locus" in the real world, even if we don't call it that?
How can we use algebra to represent unknown quantities and relationships in the world around us?

What does it mean to "solve" an equation, and why is this process like balancing scales?

Term 3

• Probability
• Indices
• Standard form
• Simplifying and factorising expressions

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How can mathematics help us predict the likelihood of future events, even when we can't be certain?
What does it mean for an event to be "fair," and how can probability help us design fair games or experiments?
How does understanding probability help us make better decisions in everyday life, from playing games to making health choices?

How do indices provide a powerful shorthand for repeated multiplication, and why is this shorthand useful?

Where do we see the power of indices used in the real world to describe very large or very small numbers, or rapid growth/decay?

Why do mathematicians and scientists need a special way to write very large and very small numbers?
How does standard form help us to quickly understand the magnitude (size) of a number, even before we know its exact value?
How does standard form simplify calculations with extremely large or small numbers?

What's the difference between an 'expression' and an 'equation'? 
Why is it important to know the difference when you're working with them?
Why is it useful to be able to break down an expression into its 'building blocks' through factorisation?
 
Term 4: 

•  Rearranging formula
• solving simultaneous equations
• Recap transformation
•  Compound measures

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How is rearranging a formula similar to solving an equation, and what makes it different?
Why do we rearrange formulae, and what new information does it allow us to find?
What does it mean for a variable to be the 'subject' of a formula?

What does it mean for two equations to be "simultaneous," and what does their "solution" represent?

How can we use simultaneous equations to model and solve problems where multiple conditions or unknowns are interacting?

 How can transformations help us describe and predict the movement of shapes in space?
What properties of a shape stay the same, and what properties change, after a transformation?

How can rearranging a formula help us find different unknown quantities in a compound measure problem?
Why do units matter so much when working with compound measures?

Term 5 

• Types of data
• Average and range, including grouped data
• Bearings and Loci

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.
How can we decide whether a piece of information is best represented by words, categories, numbers we can count, or numbers we can measure?
What are the strengths and weaknesses of different data types for answering real-world questions?

Why do we have different types of averages (mean, median, mode), and when is each one the most appropriate to use?
How does the "spread" (range) of data affect our understanding of a set of numbers?
How can understanding averages and range help us make sense of information in the real world and avoid being misled by statistics?

How do we precisely describe position and direction, and why is accuracy crucial in navigation and design?
How can geometric rules help us map out all possible locations that fit a specific condition?
How do Bearings and Loci help us understand and describe movement or boundaries in the real world?

Term 6

• Trigonometry
• Direct and inverse proportion
• Angles in polygons and parallel lines

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

How can understanding the relationships between the sides and angles in a right-angled triangle help us find missing measurements indirectly?
Why do specific angle measurements always lead to the same ratios of side lengths in any right-angled triangle, regardless of its size?

How can mathematics describe how one quantity changes in response to another?
What are the key differences between a "directly proportional" relationship and an "inversely proportional" relationship?
How do parallel lines create predictable angle relationships, and why are these relationships always true?
What does the number of sides in a polygon tell us about the sum of its interior and exterior angles?

Recommended websites to support your child’s learning:
Drfrostmaths, mathsgenie, corbettmaths

 

Course overview: 
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. It will now extend their understanding of number, algebra and geometry and continue developing fluency. There will be a 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 the 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 can 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, including equipping you with the following skills:

• Problem-solving: Mathematics equips you with the skills to approach problems systematically and find solutions.
• Logical thinking: It helps develop your ability to think critically, analyse information, and make sound judgments.
• Career opportunities: Mathematics is a valuable subject for a wide range of careers, including engineering, computer science, finance, and teaching.
• Everyday life: Mathematics is essential for everyday tasks like budgeting, cooking, and understanding measurements.

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 daily. 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. 

• Problem-solving: Mathematics equips you with the skills to approach problems systematically and find solutions.
• Logical thinking: It helps develop your ability to think critically, analyse information, and make sound judgments.
• Career opportunities: Mathematics is a valuable subject for a wide range of careers, including engineering, computer science, finance, and teaching.
• Everyday life: Mathematics is essential for everyday tasks like budgeting, cooking, and understanding measurements.

By studying mathematics, you will develop a strong foundation for further learning and succeed in various aspects of life.

Term 1: 

Foundation

• Algebraic expressions
• Constructions and loci
• Ratio and proportion
• Equations and inequalities
• Scatter graphs

Higher 

• Loci and bearing 
• Percentages (compound and reverse)
• Probability tree diagrams
• Surds
• Algebraic expressions, expanding 2 and 3 brackets 
• Factorising including quadratics 

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Foundation 
How can we use variables to represent unknowns?

How can we use mathematical constructions in real-life situations?

In how many ways can we share the amount in the given ratio? 

How does SR relate to the correlation of scatter diagrams? 

How can we use equations as a problem-solving tool?

Higher Tier

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 use probability to solve problems?

Why does a power of zero give a result of 1?

How can we expand binomials? 

Term 2: 
Foundation

• Percentages
• 3D shapes: volume and surface area
• Rounding, estimation and bounds 
• Recap of trig and Pythagoras
• Four operations, including problem-solving 

Higher 

• Recurring decimals. 
• Sharing into a ratio including double ratios
• Trigonometry with right-angle triangles, including exact values
• Straight lines - graphs, equations, perpendicular and parallel lines.
• Direct and inverse proportion, including problem solving 
• Changing the subject & solving quadratics

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

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 can we calculate the length of the diagonal in our books?
How do we use fractions in problem-solving?

Higher tier

How do we change recurring decimals into fractions?
How do we use ratios to solve a variety of problems, including double ratios?
How do we know which trigonometric ratio to use in a right-angled triangle 
How do we find the equations of parallel and perpendicular lines?
How does the percentage change in one variable affect the other in direct and inverse relationships?
How is factorising used in changing the subject of formulae?

Term 3: 
Foundation

• Angles in parallel lines and polygons
•  Drawing and interpreting straight lines and quadratic graphs 
•  Recipe problems, Best buys, direct and inverse proportion 
• Simultaneous equations 
•  Simultaneous equations - Graphically and problem solving 

Higher 

• Angles in polygons and parallel lines 
• Pythag & trig in 3
• Simultaneous equations - forming & solving algebraically and graphically
• Drawing and interpreting quadratic graphs, including solving linear and quadratic equations graphically
• Averages - solving problems & from a table

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Foundation

How do we find the interior and exterior angles of 2D shapes with 3 or more sides?

How do we find the equation of a straight line?

How do we use direct and inverse proportion formulae to solve problems?

How do we form and solve simultaneous equations?

Higher tier 

How do we find the interior and exterior angles of compound polygons?
How do we know which trigonometric ratio to use in a right-angled triangle?
How do we form and solve simultaneous equations?
What do the solutions of quadratic equations mean (referring to the graph)?
What is linear interpolation, and how do we apply it to estimate the median?

Term 4
Foundation

•  Recap transformations
•  Drawing pie charts and stem and leaf diagrams 
• Probability tree, including conditional probability
• Averages problem solving, including from tables to include Stem and Leaf diagrams.
•  Compound measures 

Higher 

• Completing the square & sketching curves
• Types of data, questionnaires, interviews and hypotheses
• Stem and leaf diagrams 
• Cumulative frequency and box plots
• Histograms

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Foundation
If we complete a transformation with a shape, does it change size?
How do we interpret and compare pie charts and stem & leaf diagrams?
How do we use tree diagrams to solve problems with probability? 
How do we decide on the type of averages to use?
How do we use SDT in everyday scenarios?

Higher tier 
How do we sketch a quadratic curve by completing the square?
How do we draw box plots and cf curves to compare distributions?
How do we interpret and compare pie charts and stem & leaf diagrams?

Term 5: 
Population Pyramid and Choropleth maps
Sampling methods, time series, moving averages
Sets and Venn diagrams
Box plots and cumulative frequency curves
 Index number, RPI, CPI, GDP and rate of change.

Higher Tier
Types of data, questionnaires, interviews, and hypotheses
Sampling methods
Diagrams - stem & leaf and pie charts
Sets and Venn diagrams
Histograms
Index no, RPI, CPI, GDP and rate of change

Ebac
 Higher - Scatter graphs
  Higher-  Sets, Venn diagrams and   histograms 
 Transformations 

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

(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 trends and seasonal variations?
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.

Higher - 
 How does SR relate to the correlation of scatter diagrams? 
 How can we use sets and Venn diagrams to represent information
 How do we describe transformations?

Term 6: 
Foundation
Gap based on Mock/Practice
Solving equations with geometry
Changing the subject of a formula
Solving quadratics
 Percentage recap

Higher Tier
 Moving averages + Scatter graphs and Spearman's rank
Gaps based on mock + exam practice
Solving fundamental inequalities, showing on no line & solving graphically
Trig advanced and Pythagoras        
Quadratic recap    
Completing the square recap
Ebac

 Vectors
Solving quadratic inequalities, showing on no line & solving graphically
Trig graphs involving problem solving
 Trig advanced and Pythagoras
Quadratic recap
Completing the square recap

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Foundation
How can we connect algebra and geometry? 

 What is meant by changing the subject

How do we use factorising to solve quadratic equations?

How do we use percentages to solve real-life problems?

Higher tier 

How do we solve inequalities graphically?
Knowing when best to solve quadratics using the quadratic formulas?
What is the difference between a cosine and a sine graph?
How do we know when to use the cosine rule or the sine rule?

How does the percentage change in one variable affect the other in direct and inverse relationships?

How do we sketch a quadratic curve by completing the squares?

 

 

 

 

Course information

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. They will now focus more on applying these skills 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 part of the GCSE Statistics curriculum.  

Term 1: 

Foundation

• Solving problems with area & volume, including circle, semi-circles, arc length and sectors 
• Bearing, scale ratio, and basic constructions
•  Solving problems with proportions: recipe problems, exchange rates, best buys
•  Basic probability and solving problems involving fractions & ratios with probability
• Tree diagrams, Sets andVennn diagrams, relative frequency
• Forming and solving equations from word problems and shapes 

Higher

•  Surface Area and Volume of 3D Shapes
•  Histogram
• Solve bounds and truncation problems
•  Laws of indices, surds and recurring decimals to fractions
• Quadratic and geometric sequence

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Foundation

How can you work inversely to solve area and volume problems?
How do we use bearings, scale and constructions in everyday life?
How do we use ratios and proportions in real life?
How do we calculate probabilities?
How can I solve equations with the unknown on both sides?

 Higher 
How would you calculate the surface area and volume of 3D shapes?

How do we use bounds in calculations?

How would you change a recurring decimal into a fraction?

How would you find the nth term for quadratic sequences?

Term 2: 
loci and region
Ratio problems of all types(total given, difference given, one amount given and double ratio)
Transformations: rotation, reflections (from given lines), translations(vector arithmetic), enlargement (with & without centre), Combination of transformations
Solving problems with simple interest, compound growth & decay and reverse %

Higher Tier
 Ratio problems
Averages from a table and a Histogram 
Arc length and area of sectors
 Equation of circles and tangents
Simplifying algebraic fractions

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Foundation

How do we use constructions and loci to solve real-life problems (finding regions)?
How do we share in a given ratio?

How are percentages used in real-life situations?
Higher 

How do you solve problems with ratios when more than two parts are involved?

How do you solve problems with a histogram that has unequal class widths?

How would you find the area of sectors and segments?

How do you find the equation of a circle?

How would you simplify and solve algebraic fractions?

Term 3: 
Foundation
Recap- averages from the tables & in context (rest of the time to be used for revision)
St line graphs & quadratic graphs (drawing and interpreting)
Direct & inverse proportions 
 Similar and congruent shapes (focus more on proofs)

Higher 

Pythagoras and Trig, including 3D Trigonometry
Construction and Loci
 Similar length, area and volume
 Proof algebraic and geometric
Vectors
 Simultaneous equations (linear and quadratic)

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Foundation

What does gradient represent in linear graphs?

How would you use proportionality reasoning to solve problems?

Higher 

Pythagoras and trigonometry in 3-D, plus advanced trigonometry(sine and cosine rules)

How would you use Pythagoras’ theorem and trigonometry to solve problems involving 3D shapes?

How do we use loci and construction to solve geometrical problems?
How do we prove shapes are similar using area and volume? 
How do you prove an outcome algebraically?

How do you solve geometric problems involving vectors?

How do we use substitution to solve quadratic simultaneous equations?

Term 4: 
Foundation Tier
Substituting into formulae (including SUVAT), rearranging formula (including SUVAT), 
Compound measures, including problem-solving
 Feedback covers weaker areas
 Solve problems involving interior and exterior polygons, including parallel lines (recap)
Estimating values, bounds of rounded numbers, Four operations with standard form (recap)

 Surface Area and Volume of 3D Shapes
 Histogram
Solve bounds and truncation problems
 Laws of indices, surds and recurring decimals to fractions
Quadratic and geometric sequence
Advance trigonometry
Rates of change under the curve
 Quadratic, cubic and reciprocal graphs

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Foundation

What is a formula, and how can we use it?

How would you calculate the density of 3D shapes?

Higher 

How would you use Pythagoras’ theorem and trigonometry to solve problems involving 3D shapes?

 How would we calculate the area under the curve of the distance-speed time graph?

How to draw sine and cosine graphs. What is the same and what is different?

Term 5: Students studying the foundation tier will have finished their GCSE mathematics curriculum by now and will focus on revision and examination practice in preparation for the examinations towards the end of this term. Higher-tier students will learn how to solve quadratic inequalities before commencing revision and examination practice.

Higher Tier
 Combined transformation
 Iteration, quadratic inequalities and quadratic formula

Enquiry Questions:  By the end of the term, your child should be able to answer the following enquiry questions below.

Higher Tier

Is every transformation unique? Explain why/why not.

Can you explain the iterative process and use it to derive a solution?

Term 6: All students finish their GCSE mathematics and GCSE statistics examinations this term.

 

 

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.