Maths Library

Year 12 maths, age 16 to 17, KS5

In Year 12, students begin post-16 study such as AS or A level Mathematics or Core Maths. They deepen their algebraic fluency with polynomial manipulation, coordinate geometry, and indices while introducing calculus and advanced trigonometry. Mechanics and statistics units introduce mathematical modelling of physical systems and probability distributions.

Start a Year 12 sheet

Equivalent levels

Topics

Number

TopicFocusCodes
Powers and Index Lawssecure

Algebra

TopicFocusCodes
Simplifying Algebraic Expressionssecure
Factorisingsecure
Expanding bracketssecure
Solving Quadratic Equationssecure
Linear inequalitiessecure
Simultaneous equationssecure
Straight-line graphs and gradientsecure
Substitution into Formulaeintroduce

Geometry

TopicFocusCodes
Pythagoras' Theoremsecure

Measurement

TopicFocusCodes
Speed, Distance and Timeintroduce

Curriculum items

Indicative, from National Curriculum for England. See the official document for the authoritative text.

  • Manipulate algebraic expressions with negative and rational exponents using the laws of indices.
  • Factorise and expand polynomials to simplify complex algebraic fractions and expressions.
  • Solve quadratic equations and inequalities using factorisation, completing the square, and discriminant analysis.
  • Solve simultaneous equations involving one linear and one non-linear quadratic equation.
  • Use coordinate geometry of straight lines to determine equations, gradients, and intersections.
  • Apply Pythagoras' theorem in coordinate geometry and vector problems to find lengths and distances.
  • Model kinematics problems using constant acceleration formulae linking displacement, velocity, and time.

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