United Kingdom · National Curriculum Attainment Targets
Year 11 Mathematics
A comprehensive mastery course for Year 11 students focusing on the synthesis of algebraic, geometric, and statistical concepts. It prepares learners for higher level assessment through rigorous proof and real world problem solving applications.
01The Power of Algebra
Deepening understanding of non linear equations, functions, and the manipulation of complex algebraic fractions.
Students will factorise quadratic expressions to find their roots, understanding the relationship between factors and solutions.
Students will learn to complete the square to solve quadratic equations and transform expressions into vertex form.
Students will apply the quadratic formula to solve equations, including those with irrational or no real solutions.
Students will solve systems involving one linear and one quadratic equation using substitution and graphical methods.
Students will sketch and interpret graphs of quadratic functions, identifying roots, turning points, and intercepts.
Students will explore how adding/subtracting constants or multiplying by -1 translates and reflects function graphs.
Students will investigate how multiplying a function or its variable by a constant stretches or compresses its graph.
Students will combine two or more functions to form a new function, understanding the order of operations.
Students will find the inverse of a function algebraically and graphically, understanding its relationship to the original function.
Students will simplify complex algebraic fractions by factorising numerators and denominators.
Students will combine algebraic fractions by finding common denominators and simplifying the resulting expressions.
Students will perform multiplication and division operations on algebraic fractions, simplifying where possible.
02Geometry of Space and Shape
Investigating circle theorems, vector geometry, and the properties of three dimensional shapes.
Students will discover and prove theorems related to angles subtended at the centre and circumference of a circle.
Students will explore theorems involving tangents, chords, and radii, including the alternate segment theorem.
Students will perform vector addition and subtraction, understanding resultant vectors and displacement.
Students will calculate the magnitude of a vector and express vectors in component form and column vectors.
Students will apply vector methods to prove geometric properties such as collinearity and parallelism.
Students will calculate the surface area of prisms, pyramids, cones, and spheres.
Students will calculate the volume of prisms, pyramids, cones, and spheres, including composite shapes.
Students will apply Pythagoras' theorem and trigonometric ratios to solve problems in three dimensions.
Students will apply the sine rule and cosine rule to find unknown sides and angles in non-right-angled triangles.
Students will calculate the area of any triangle using the formula involving two sides and the included angle.
Students will construct loci of points equidistant from points/lines and at a fixed distance from a point.
Students will perform and describe enlargements using negative scale factors, understanding the effect on orientation.
03Numerical Fluency and Proportion
Mastering surds, indices, and complex proportional reasoning in varying contexts.
Students will simplify surds by extracting square factors and expressing them in their simplest form.
Students will perform addition, subtraction, multiplication, and division with surds.
Students will rationalise denominators involving single surds and binomial surds.
Students will model and solve problems involving direct proportion, including graphical representation.
Students will model and solve problems involving inverse proportion, including graphical representation.
Students will calculate compound interest and depreciation using multipliers over multiple periods.
Students will calculate original values after a percentage increase or decrease has been applied.
Students will apply the laws of indices for multiplication, division, and powers of integer exponents.
Students will extend their understanding of index laws to include fractional and negative exponents.
Students will write and calculate with numbers in standard form, understanding its use for very large or small numbers.
Students will model and solve problems involving exponential growth and decay using percentage multipliers.
Students will calculate and interpret average rates of change from graphs and tables, and introduce instantaneous rates.
Students will solve problems involving compound measures such as speed, density, and pressure.
Students will solve complex problems involving ratios, including sharing in a given ratio and inverse ratio.
04Probability and Risk
Evaluating the likelihood of independent and dependent events using set theory and tree diagrams.
Students will differentiate between independent and dependent events and calculate their probabilities.
Students will use tree diagrams to model and calculate probabilities of sequences of dependent events.
Students will use Venn diagrams to represent events and calculate probabilities involving unions, intersections, and complements.
05Data Interpretation and Statistics
Analyzing distribution, spread, and correlation through advanced graphical representations.
Students will construct and interpret cumulative frequency graphs to estimate medians and quartiles.
Students will construct and interpret box plots to compare distributions and identify outliers using the interquartile range.
Students will construct and interpret histograms for continuous data with equal class intervals.
Students will construct and interpret histograms where frequency density is used to represent data with unequal class intervals.
Students will plot and interpret scatter graphs, identifying types of correlation and drawing lines of best fit.
06Calculus and Rates of Change
An introduction to the gradient of curves and the concept of instantaneous rates of change.
Students will review calculating the gradient of a straight line from two points or an equation.
Students will estimate the gradient at a specific point on a non-linear graph by drawing tangents.
Students will learn the basic rules of differentiation for polynomials to find exact gradients.
Students will find the equations of tangents and normals to curves at specific points using differentiation.
Students will use differentiation to find the coordinates of stationary points (maxima and minima) on a curve.
Students will use the trapezium rule to estimate the area under a curve, understanding its limitations.
Students will explore real-world applications of finding the area under a curve, such as distance from velocity-time graphs.
Students will solve equations by finding intersection points of graphs, including estimating solutions.
Students will explore the graphs and properties of exponential functions, modeling real-world growth and decay.
Students will review equations of straight lines (y=mx+c, ax+by=c), parallel and perpendicular lines.
Students will interpret and draw distance-time and velocity-time graphs, calculating speed, acceleration, and distance.
Students will apply their understanding of gradients to solve practical problems involving rates of change in various contexts.