Year 11 Maths

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UK GCSE Maths skills for Year 11 — completing the GCSE: functions, the sine & cosine rules, further circle theorems, iteration and conditional probability.

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Algebra, Proof & Sequences
Algebraic proof Iteration Expanding brackets with surds Multiplying & simplifying surds Rationalising (binomial denominator) Adding algebraic fractions Solving quadratic inequalities Quadratic sequences
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Functions
Composite functions Inverse functions Function transformations
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Geometry & Trigonometry
Sine rule — finding a side Sine rule — finding an angle Cosine rule — finding a side Cosine rule — finding an angle Area of a triangle (½ab sinC) Exact trigonometric values Arc length of a sector Area of a sector Circle theorem — tangent & radius Circle theorem — cyclic quadrilateral 3D Pythagoras Bearings
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Statistics & Probability
Box plots — interquartile range Venn diagrams Conditional probability Estimating the lower quartile
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Polynomials & Algebraic Manipulation
Adding & subtracting polynomials Multiplying a binomial by a trinomial Dividing a polynomial by a monomial Algebraic proof Function transformations — translation Function transformations — stretch Geometric sequences — nth term Domain of a function
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Trigonometry & Circle Theorems
Segment area Trig identity — sin² + cos² = 1 Solving simple trig equations Circle theorem — alternate segment Circle theorem — chord bisector Perimeter of a sector Bearings using the cosine rule Bearings using the sine rule
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Vectors & Geometric Proof
Position vectors Dividing a line in a ratio Proving points are collinear Proving a parallelogram Resultant of three vectors Similar triangles — indirect measurement Congruence — missing condition Similarity — unknown length
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Advanced Statistics & Probability
Histograms — unequal class widths Cumulative frequency graphs Comparing distributions — standard deviation Venn diagrams — P(A only) / P(neither) Conditional probability (Venn diagram) Mutually exclusive OR events Estimating the mean from a histogram Interpolation vs extrapolation
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Number, Proportion & Constructions
Compound percentage growth Compound percentage decay Direct proportion with cubes Inverse proportion with square roots Bounds in a multi-step calculation Standard form in real-world contexts Geometric constructions Loci