Mathematics

Term 1
Topic: Sequence, algebraic notation,  equality and equivalence and ratio and scale. 
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  
Topic: Place value & ordering integers and decimals.  Fraction, decimal and percentage equivalence. 
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
Topic:  Solving problems with addition and subtraction. Solving problems with multiplication and division.  Fractions and percentages of amounts.
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 various situations?

Term 4
Topic:  Operations and equations with directed numbers. Addition and subtraction of fractions.
Enquiry Questions: 
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
Topic: Constructions, measuring and using geometric notation.  Developing geometric reasoning.
Enquiry Questions: 
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
Topic: Developing number sense. Transformations. Sets and probability.  Prime numbers and proof. 
Statistics.
Enquiry Questions: 
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?
 

 

Term 1
Topic: Ratio, proportion and conversion.  Area of 2D shapes. Operations with fractions.
Enquiry Questions: 
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
Topic: Solving equations. Plotting linear graphs. Scatter graphs, bar charts, and two-way tables.  Tables and probability
Enquiry Questions: 
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?

What does it mean for an event to be "fair” and how can probability help us design fair games or experiments?

Why do we use scatter graphs and what type of questions can they help us answer that other graphs cannot?

Term 3
Topic: Brackets, equations and inequalities.  Sequences.  Indices.
Enquiry Questions: 
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?

Term 4
Topic: Fractions and percentages.  Solving inequalities. Angles in parallel lines and polygons.
Enquiry Questions: 
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
Topic: Bearing, constructions and loci.   Transformations.  Area of trapezia and circles.Standard index form.
Enquiry Questions: 
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? 

How are the different types of transformations identified?

Term 6
Topic: Standard Index Form.  The data handling cycle.  Averages.  Box plots. 
Enquiry Questions: 
How does standard form help us to quickly understand the magnitude 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 and when is each one the most appropriate to use?

How does the "spread" 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?
 

 

Term 1
Topic: Ratio and proportion.  Percentages and including reverse.  Straight line graphs.  Factors, multiples and prime decomposition.  Pythagoras Theorem.
Enquiry Questions: 
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?

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 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?

Term 2
Topic: 3D shapes.  Sequences.  Loci and region.  Forming and solving equations.
Enquiry Questions: 
Why are certain 3D shapes used for specific purposes in real life?
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?
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
Topic: Probability.  Indices. Standard form. Simplifying and factorising expressions.
Enquiry Questions: 
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 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?

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

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

Why is it useful to be able to break down an expression into its 'building blocks' through factorisation?

Term 4
Topic:  Rearranging formula.  Solving simultaneous equations.  Transformation.  Compound measures
Enquiry Questions: 
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
Topic: Types of data.  Average and range, including grouped data.  Bearings and loci.
Enquiry Questions: 
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  and when is each one the most appropriate to use?

How does the "spread" 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
Topic: Trigonometry.  Direct and inverse proportion.   Angles in polygons and parallel lines
Enquiry Questions: 
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?
 

 

Term 1

Foundation tier
Topic: Algebraic expressions.  Constructions and loci.  Ratio and proportion.  Equations and inequalities.  Scatter graphs.
Enquiry Questions: 
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
Topic: Loci and bearing. Percentages (compound and reverse).  Probability tree diagrams.  Surds.  Algebraic expressions and  expanding 2 and 3 brackets.  Factorising including quadratics 
Enquiry Questions: 
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 tier
Topic: Percentages.  3D shapes, volume and surface area.  Rounding, estimation and bounds. Trigonometry  and Pythagoras. Four operations, including problem-solving. 
Enquiry Questions: 
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
Topic: 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 and solving quadratics.
Enquiry Questions: 
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 tier
Topic: Angles in parallel lines and polygons.  Drawing and interpreting straight lines and quadratic graphs.  Recipe problems, Best buys, direct and inverse proportion.  Simultaneous equations.  
Enquiry Questions: 
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
Topic: Angles in polygons and parallel lines.  Pythagoras and trigonometry in 3D.  Simultaneous equations - forming and  solving algebraically and graphically.  Drawing and interpreting quadratic graphs, including solving linear and quadratic equations graphically.  Averages - solving problems and from a table.
Enquiry Questions: 
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?

What is linear interpolation and how do we apply it to estimate the median?

Term 4

Foundation tier
Topic: 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. 
Enquiry Questions: 
If we complete a transformation with a shape, does it change size?

How do we interpret and compare pie charts and stem and  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
Topic: Completing the square & sketching curves.  Types of data, questionnaires, interviews and hypotheses.  Stem and leaf diagrams. Cumulative frequency and box plots. Histograms.
Enquiry Questions: 
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

Foundation tier
Topic: Population pyramid and choropleth maps.  Sampling methods, time series and  moving averages. Sets and Venn diagrams. Box plots and cumulative frequency curves.  Index number, RPI, CPI, GDP and rate of change.
Enquiry Questions: 
What are the different sampling methods and their advantages and disadvantages?

How are moving averages used to predict trends and seasonal variations?

How can we  calculate and interpret index numbers, including RPI and  CPI?

How can we  calculate rates of change over time, including crude birth and death rates?

Higher tier
Topic: Types of data, questionnaires, interviews and hypotheses.  Sampling methods.  Diagrams - stem and  leaf and pie charts.  Sets and Venn diagrams.  Histograms. Index no, RPI, CPI, GDP and rate of change
Enquiry Questions: 
How can we identify and interpret roots, intercepts  and turning points of quadratic functions graphically?

How can we deduce turning points by completing the square?

 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 tier
Topic: Solving equations with geometry.  Changing the subject of a formula. Solving quadratics
Percentages.  Consolidating and closing gaps in learning.
Enquiry Questions: 
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
Topic:  Moving averages, scatter graphs and Spearman's rank.  Solving fundamental inequalities.   Advanced trigonometry and Pythagoras.  Consolidating prior learning and closing gaps in knowledge.
Enquiry Questions: 
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?

 

Further Mathematics Level 2

Term 1
Topic: Advanced Algebra -  functions and  expansion. 
Enquiry Questions: 
What restricts a function from accepting certain inputs and how does an inverse function 'undo' its partner graphically and algebraically?

What patterns emerge when we multiply brackets repeatedly and how does Pascal's Triangle unlock these powers instantly?

Term 2
Topic: Algebraic fractions and proof . Equations and inequalities. 
Enquiry Questions: 
How do the rules of basic arithmetic adapt when numbers are replaced by complex algebraic variables?

What separates a mathematical coincidence from an absolute logical truth?

How does the Factor Theorem help us 'hunt' for the roots of a cubic equation?

What does it mean for a system to have three unknowns and how can we systematically reduce the complexity of multiple equations?

Term 3
Topic: Sequences. Coordinate geometry. 
Enquiry Questions: 
What happens to a mathematical expression when its variable grows infinitely large?

Can a sequence continue forever but still be bound by a strict numerical ceiling?

How does the algebra of completing the square physically rewrite the geometry of a circle on a graph?

What is the exact geometric relationship between a circle and a line that touches it at only one single point?

Term 4
Topic: Calculus.
Enquiry Questions: 
How do we measure the exact steepness of a curve at a single?

How can calculus help a business maximise its profits or an engineer minimise the materials needed for a project?

Term 5
Topic: Matrices and transformation.  Geometry and trigonometry. 
Enquiry Questions: 
How can an array of numbers act as a set of instructions to rotate, reflect or distort an entire 2D space?

Why does the order in which we multiply matrices completely alter the final physical transformation?

Term 6
Topic: consolidation of learning and closing of gaps.

Exam board specification link for GCSE maths:
OCR GCSE maths

Recommended websites to support your child’s learning:
Dr Frost Maths, Mathsgenie and  Corbettmaths.
 

Term 1

Foundation tier
Topic: 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 and  best buys. Basic probability and solving problems involving fractions and  ratios with probability. Tree diagrams, sets and Venn diagrams and  relative frequency.  Forming and solving equations from word problems and shapes 
Enquiry Questions:
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 tier
Topic: 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:
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

Foundation tier
Topic:  Loci and region.  Ratio problems of all types. Transformations.  Solving problems with simple interest, compound growth, decay and reverse percentage.
Enquiry Questions:
How do we use constructions and loci to solve real-life problems?
How do we share in a given ratio?

How are percentages used in real-life situations?
Higher tier
Topic:  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:
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 tier
Topic: Averages from  tables and in context. Straight  line graphs and  quadratic graphs (drawing and interpreting). Direct and inverse proportions. Similar and congruent shapes. 
Enquiry Questions:
What does gradient represent in linear graphs?

How would you use proportionality reasoning to solve problems?

Higher tier
Topic: Pythagoras and Trigonometry. Construction and loci. Similar length, area and volume. Proof algebraic and geometric.  Vectors.  Simultaneous equations (linear and quadratic).
Enquiry Questions:

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
Topic: Substituting into formulae (including SUVAT) and  rearranging formula (including SUVAT).  Compound measures including problem-solving.  Solve problems involving interior and exterior polygons, including parallel lines.  Estimating values, bounds of rounded numbers and  four operations with standard form.
Enquiry Questions:
How can changing a single variable alter the predicted motion or outcome of a real-world scenario?

Why is changing the subject of a formula mathematically identical to solving an equation?

How do we determine which formula to choose when given a set of motion values?
How do the angle properties of parallel lines allow us to calculate interior and exterior angles in complex shapes? 

How do upper and lower bounds affect the certainty and precision of real-life calculations? 

Higher tier
Topic: Advance trigonometry.  Rates of change under the curve.  Quadratic, cubic and reciprocal graphs.
Enquiry Questions:
How do small changes or errors in input values impact final outcomes across algebraic, geometric and numerical calculations?

Why are structural connections such as rearranging formulae, angle proofs and standard form essential for solving complex, non-routine problems?

How do we determine and justify the most efficient mathematical method when tackling multi-step higher-tier problems?

Term 5

Foundation tier
Topic: consolidation, closing gaps and revision in preparation for GCSE maths examinations.

Higher tier
Topic: Combined transformation. Iteration, quadratic inequalities and quadratic formula.  Closing gaps and revision for GCSE maths examinations.
Enquiry Questions:
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.

How is the course assessed?
100% exam.
3 exam papers.

Exam board specification link for GCSE maths:
OCR GCSE maths

Recommended websites to support your child’s learning:
Dr Frost Maths, Mathsgenie and  Corbettmaths.
 

 

GCSE Maths Resit/functional skills.

This course is designed for students who need to retake their GCSE Mathematics examination to achieve a Grade 4 in the November exam series. Students with grade 3 are enrolled on the GCSE Resit programme, while students with grade 2 or lower have the opportunity to take Functional skills (stepping stone qualification to GCSE). The programme focuses on consolidating fundamental mathematical skills, building confidence and developing effective exam techniques. We aim to provide a structured and supportive learning environment that addresses individual learning needs and prepares students for success.

 

A-level Mathematics 

Year 12

Term 1
Topics pure module: surds, quadratics, inequalities and indices.   Quadratics through modelling scenarios,  transformations and combinations of transformations that can be applied to a variety of curves. Inequalities this term.
Topics statistics module:  Extensive data set and how to collect data from it. Identify types of data and calculate simple statistics.  Calculate the measure of central tendency, location, spread, variance and standard deviation. Understand and use coding.  Identify outliers, draw  and  interpret box plots, cf curves and histograms. Compare two data sets.
Enquiry Questions:
How do we collect the data from the extensive data set?
Can you justify, represent and interpret a range of statistical techniques, sampling methods and diagrams? 

How can we use coding?

How do we use quadratics to model real-life scenarios?

How do we apply various transformations to graphs?

Term 2
Topics pure module: The use of Pascal’s triangle in expanding brackets. Factorial notation and how to use this when  expanding brackets using binomial expansion.  Solve a variety of geometrical problems. Calculus differentiation.

Topics statistics module:  Representation of data.

Topics mechanics module:  How the concept of a mathematical model applies to mechanics. Derive constant acceleration formulas  and  use them to solve problems involving vertical motion and under gravity.   Interpret displacement-time and velocity-time graphs.
Enquiry Questions:
How can acceleration, forces and motion be used to explain and model contextual problems? 

How do we solve a range of mathematical problems involving straight lines and circles? 

How does an understanding of binomial expansion help estimate the answers? 

Term 3
Topics  pure module:  Angles in all four quadrants, the sign properties of sin, cos and tan in all four quadrants. Prove sin^x + cos^x = 1 and use it to simplify expressions, prove identities and solve trigonometric equations. Differentiation and how to differentiate various functions. Understand differentiation as a rate of change or gradient. The equations of tangents and normals. Modelling problems using differentiation. 
Work on integration, the second chapter of calculus will also begin this term.

Topics statistics module:  Calculate probabilities of single events, draw tree diagrams and draw and interpret Venn diagrams. Mutually exclusive and independent events and determine whether two events are independent.   Use of simple discrete probability distributions, binomial distributions and learn to calculate probabilities and cumulative probabilities for the binomial distribution.
Enquiry Questions:
How can regression, probability and statistical distributions be used to explain contextual problems?

How do we calculate cumulative probabilities for the binomial distribution?

How does  understanding of trigonometric ratios, equations and identities enable you to solve contextualised problems?
How is calculus used in modelling real-life scenarios and how to work with increasing and decreasing functions?

Term 4
Topics  pure module: Integration as the reverse of differentiation. Integrate expressions to find general solutions and particular solutions. Use of  integration to find the area under  curves or between curves and lines. Logs and application of  the laws of logs to simplify expressions and solve equations. How to work with mathematical models using logs. 

Topics mechanics module:  understand and use Newton’s first, second and third laws of motion. Calculate resultant forces by adding vectors and solve problems involving connected particles. Use calculus to solve kinematics problems and to derive constant acceleration formulae. 

Enquiry Questions:
How do we find a particular solution of an equation using integration?
How is integration used to find the area under the curve or between a curve and a line?
How can we use logs to represent non-linear data as linear and solve modelling problems?
How can acceleration, forces and motion be used to explain and model contextual problems?

Term 5
Topics pure module:  Vectors in 2D. Explore position vectors and how to model using vectors. Solve a variety of problems involving vectors, making links with mechanics. 

Topic statistics module:
Students will learn the methods of testing hypotheses.
Topic mechanics module:  Variable acceleration.

Enquiry Questions:
How can you apply your knowledge of the magnitude and direction of vectors to solve geometrical problems?

How do we find the range and domain of a variety of functions, including modulus functions?

How can we carry out a one-tailed test and a two-tailed test for the proportion of the binomial distribution and interpret the results?

Term 6
Topics  pure module:  Proving  results by counter-example and contradiction. How to split a single fraction with a variety of denominators into partial fractions and use the binomial formula for negative or fractional powers. Binomial expansion as a series.  The range of values for which any expansion is valid. The work on arithmetic and geometric series, sigma notation and recurrence relationship. 

Topics statistics module:  understand exponential models in bivariate data, use a change of variable to estimate coefficients in an exponential model, understand and calculate the product-moment correlation coefficient.  Carry out a hypothesis test for zero correlation. 

Topics mechanics module:  exploring the concept of moments. How to calculate the turning effect of a force applied to a rigid body, calculate resultant moment and solve problems involving uniform and non-uniform rods.
Enquiry Questions:
How do we prove results by contradiction?
How do we split fractions into partial fractions and use the binomial series formula for fractional or negative powers?
How do we identify various types of series, use sigma notation and solve modelling problems?

How do we carry out a hypothesis test for zero correlation and calculate the product-moment correlation coefficient?
How do we solve problems involving uniform and non-uniform rods using the concept of moments?

 

Year 13 content

Term 1
Topics pure module:  Understanding of working with angles in radians. Trigonometric identities. Proving trigonometric identities, solving  equations and modelling. 

Topics mechanics module:  how to resolve forces into components.   Use of  the triangle law to find a resultant force.  Solve problems involving smooth or rough inclined planes.   Understand friction, coefficient of friction and use F <=𝜇R. Projectiles and solve problems involving particles projected at an angle.
Enquiry Questions:
How do we find arc length and area of sectors when the angles are given in radians?

How do we solve more complex modelling problems involving trigonometric?

How do we solve complex equations and prove identities with trigonometry?

How can moments, forces, friction, kinematics and projectiles be used to explain and model contextual problems?

How can moments, forces, friction, kinematics and projectiles be used to explain and model contextual problems?

Term 2
Topics  pure module:  Change parametric equations into Cartesian form and vice versa. Find the range and domain of curves described parametrically, differentiate parametric functions and explore a variety of functions. Solve problems connected to rates of change and learn the product and quotient rules. Integrate various functions.  

Topics  mechanics module:  How to find an unknown force when a system is in equilibrium and solve static problems involving weight, tension and pulleys. Understand and solve problems involving limiting equilibrium, motion on rough or smooth inclined planes and connected particles that require the resolution of forces. 

Topics  statistics module:  Understand set notation in probability, conditional probabilities and solve conditional probability problems.
Enquiry Questions:
How to change between parametric and Cartesian equations?

How do we use calculus with parametric equations?

How do we use connected rates of change to form differential equations?

How can moments, forces, friction, kinematics and projectiles be used to explain and model contextual problems?

How can we use probability formulae and tree diagrams to solve problems?

Term 3
Topics pure module:  The methods of substitution and integration by parts. Standard patterns to integrate functions.  How to find  the area under the curve and solve differential equations. Locate the roots using numerical methods and apply the Newton-Raphson method to find approximations. 

Topics statistics module:  Probability.  Normal distribution.  How to convert binomial distribution into normally distributed models and test hypotheses with normal distribution. 
Enquiry Questions:
How do we solve first-order differential equations?

How do we use numerical methods to locate the roots and solve problems in context?

How do we solve modelling problems using calculus?

How can we use probability formulae and tree diagrams to solve problems?

How do we carry out a hypothesis test for the mean of a normal distribution?

How do we approximate a binomial distribution using a normal distribution and solve real-life problems by selecting appropriate distributions?

Term 4
Topics pure module:  Numerical methods. . Vectors in 3D.  Consolidation of learning, closing gaps and examination practice.   

Topic statistics module:  Normal distribution.

Topics mechanics module:  Use calculus with harder functions of time involving variable acceleration and learn to differentiate and integrate vectors with respect to time.

Enquiry Questions:
How do we find approximations to the solutions of equations?

Terms 5 and  6
Topics:  consolidation and exam preparation. 

Method of assessment:
100% exam. 
3 exam papers.

Exam board link: 
Pearson A level maths specification

Recommended revision website:
ExamSolutions
Physics & Maths Tutor
Bicen Maths - YouTube
Maths Genie