# KS4 Mathematics

Pupils in years 9 -11 will be taught the following topics in increasing depth:

Number:

- Estimate the powers and roots to any given positive number- to include work on surds
- Calculate with numbers in standard form and know how to adjust answers accurately
- change recurring decimals into their corresponding fractions and vice versa
- Choose appropriate degrees of accuracy when rounding numbers and understand how these have limits in accuracy
- Use inequality notation to specify simple error intervals
- calculate exactly with fractions, surds and multiples of π: simplify surd expressions involving squares and rationalise denominators

Algebra:

- Understand and us the concepts of inequalities and identities
- Solve linear inequalities
- Multiplying out and double brackets and factorising expressions in the form ax
^{2}+ bx + c - Finding the difference of two squares
- Solve simultaneous and quadratic equations algebraically and using a graph
- Recognise, sketch and interpret graphs of simple quadratic functions
- interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’.
- identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square
- recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function y = 1/ x with x ≠ 0, exponential functions y= k
^{x}for positive values of k, and the trigonometric functions (with arguments in degrees) y = sinx, y = cosx and y = tanx for angles of any size - sketch translations and reflections of a given function

Geometry and measures:

- Geometry of triangle; Pythagoras theorem and trigonometry
- Shape constructions, including plans and elevations of 3D shapes
- Calculating arc lengths, angles and areas of sectors of circles
- describe the changes and invariance achieved by combinations of rotations, reflections and translations
- identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment
- apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results
- describe translations as 2D vectors
- apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors; use vectors to construct geometric arguments and proofs

Probability:

- Listing outcomes using tree diagrams
- Understand how experimental probability tends towards theoretical probability with an increased sample size
- Calculate the probability of independent and dependent events
- Straight line graphs- finding the equations of lines through coordinates and finding the gradient

Ratio, proportion and rates of change:

- use ratio notation, including reduction to simplest form
- divide a given quantity into two parts in a given part: part or part: whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)
- express a multiplicative relationship between two quantities as a ratio or a fraction
- understand and use proportion as equality of ratios 8. relate ratios to fractions and to linear functions
- interpret the gradient of a straight line graph as a rate of change; recognise and interpret graphs that illustrate direct and inverse proportion
- interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts
- set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes.

Statistics:

- Interpret and construct tables, charts and diagrams
- Scatter graphs, correlation and using lines of best fit to make predictions
- construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals and cumulative frequency graphs, and know their appropriate use

Pupils who meet age related expectations will be able to demonstrate the following (in relation to each topic):

- develop fluent knowledge, skills and understanding of mathematical methods and concepts
- acquire, select and apply mathematical techniques to solve problems
- reason mathematically, make deductions and inferences and draw conclusions
- comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context.