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St Paul's School
for Girls

Year 11 Curriculum - Maths




Mastery Objectives

Essential Knowledge

Autumn Term (1st Half term)


Perimeter, area and circles

· Calculate perimeters and areas of composite shapes made from circles and parts of circles (including semicircles, quarter-circles, combinations of these and also incorporating other polygons);

· Calculate arc lengths, angles and areas of sectors of circles;

· Give answers in terms of π;

· Form equations involving more complex shapes and solve these equations.

· Recall and use the formulae for the area of a triangle, rectangle, trapezium and parallelogram using a variety of metric measures


3D forms and volume, cylinders, cones and spheres

· Calculate surface area and volume of spheres, pyramids, cones and composite functions

· Know the formulae for the volume of a sphere, cone and pyramid

· Know the formulae for the surface area of a sphere, a cone and a pyramid


Accuracy and bounds

· Apply and interpret limits of accuracy, including upper and lower bounds



Collecting data

· Infer properties of populations or distributions from a sample

· Know the limitations of sampling

Autumn Term (2ndHalf term)


Cumulative frequency, box plots and histograms

· Construct and interpret cumulative frequency graphs

· Interpret, analyse and compare box plots

· Interpret, analyse and compare the distributions of data through measures of spread and quartiles and inter-quartile range

· Construct and interpret histograms with equal and unequal class intervals

· Know the appropriate use of cumulative frequency graphs

· Know appropriate use of box plots

· Know appropriate use of histograms

· Know interquartile range = upper quartile – lower quartile

· Know how to construct a box plot


Graphs of trigonometric functions

· Sketch or plot and interpret graphs of y = sin x, y = cos x, y = tan x

· Know the graphs of the trigonometric functions y = sin x, y = cos x, y = tan x for angles of any size


Further trigonometry

· Apply the trigonometric ratios in three dimensional figures

· Apply the sine rule and cosine rule to find unknown lengths and angles

· Apply the sine rule for area to calculate the area, sides or angles of any triangle

· Know the sine rule  and

the cosine rule a2 = b2 + c2 -2bc cos A

· Know area = ½ absinC


Quadratics, expanding more than two brackets, sketching graphs, graphs of circles, cubes and quadratics

· Expanding brackets of more than two binomials

· Deduce turning points of quadratic functions by completing the square

· Sketch translations and reflections of a given function

· Know the meaning of roots, intercepts and turning points

Spring Term (1st Half term)


Circle theorems

· Apply the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results

· Know the circle theorems


Circle geometry

· Apply concepts of rate of change (gradient of chords and tangents) in numerical, algebraic and graphical contexts

· Recognise and use the equation of circle with centre origin

· Find the equation of a tangent to a circle at a given point


Changing the subject of formulae (more complex), rationalising surds, proof

· Calculate exactly with surds and rationalise denominators

· Re-arrange the subject of a formulae with multiple step or where the subject appears twice

· Interpret the reverse process as an inverse function

· Interpret the reverse process as the ‘inverse function’


Spring Term (2nd Half Term)


Vectors and geometric proof

· 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


Reciprocal and exponential graphs; Gradient and area under graphs

· Plot and interpret graphs of non-standard functions in real life contexts, to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

· Sketch or plot and interpret exponential and reciprocal graphs

· Calculate or estimate gradients of graphs are areas under graphs and interpret results in such cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts

· Know that graphs of exponential functions y = kx for positive values of k

· Know the characteristic shape of the graph of an exponential function

· Know the definition of acceleration


Direct and inverse proportion

· Interpret and construct equations that describe direct and inverse proportion

· Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y

· Know how to set up an equation involving direct or inverse proportion

· Recognise graphs that illustrate direct and inverse proportion