Year 10 Maths

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UK GCSE Maths skills for Year 10 — surds, quadratics, trigonometry, circle theorems and more, with instant feedback and worked explanations.

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Number & Surds
Simplifying surds Adding & subtracting like surds Rationalising the denominator Standard form — multiplying Standard form — dividing
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Algebra
Expanding brackets with a negative Factorising quadratics Solving quadratics by factorising The quadratic formula Completing the square Simplifying algebraic fractions Solving equations with fractions Rearranging formulae (squared terms) Direct proportion with powers Inverse proportion with powers Function notation
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Geometry & Trigonometry
Trigonometry — finding an angle Trigonometry — using cosine Trigonometry — using tangent Circle theorem — angle in a semicircle Circle theorem — angle at the centre Circle theorem — same segment Similar shapes — missing length Congruent triangles Vectors — adding column vectors Volume of a sphere Volume of a cone
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Statistics & Probability
Tree diagrams — combined probability Tree diagrams — exactly once Estimating the median (grouped data) Histograms — frequency density
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Equations, Functions & Sequences
Composite functions Inverse functions Simultaneous equations (linear & quadratic) Solving quadratic inequalities Iteration nth term of a quadratic sequence Adding algebraic fractions Sketching quadratics — turning point
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Surds, Indices & Accuracy
Expanding brackets with surds Rationalising a binomial denominator Fractional & negative indices combined Upper and lower bounds in a calculation Standard form — adding & subtracting Harder recurring decimals to fractions Simplifying mixed surd expressions Error intervals
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Sine/Cosine Rules & 3D
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 sin C 3D Pythagoras 3D trigonometry Circle theorem — tangent & radius
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Vectors & Transformations
Vectors — subtracting column vectors Vectors — magnitude Vector geometry — midpoint Vector geometry — showing parallel vectors Enlargement — negative scale factor Combined transformations Similar shapes — volume scale factor Similar shapes — area & volume combined
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Advanced Statistics & Probability
Conditional probability Venn diagrams — probability Histograms — frequency from density Box plots — interpreting Comparing two distributions Cumulative frequency — IQR Probability tree — at least one Standard deviation