United Kingdom · National Curriculum Attainment Targets
Year 12 Mathematics
This curriculum bridges the gap between GCSE and advanced calculus, focusing on rigorous proof and mathematical modeling. Students develop the ability to construct logical arguments and apply complex algebraic and statistical tools to real world scenarios.
Algebraic Proof and Functional Analysis
Exploration of the logical structures underpinning algebra including proof by deduction and exhaustion. Students analyze the behavior of quadratic, cubic, and quartic functions alongside coordinate geometry.
Mastering the formal methods of proving mathematical statements through deduction, exhaustion, and counter-example.
Analyzing the properties of higher degree polynomials and the relationship between algebraic factors and graphical intercepts.
Extending linear geometry to circular paths and exploring the properties of tangents and normals.
The Calculus of Change
An introduction to differential and integral calculus focusing on rates of change and the accumulation of area.
Developing the concept of the derivative as a limit and its application in finding gradients of curves.
Understanding integration as the inverse of differentiation and its use in calculating areas under curves.
Trigonometry and Periodic Phenomena
Expanding trigonometric ratios to functions and exploring identities to solve complex circular equations.
Generalizing trigonometry beyond right-angled triangles using the unit circle and sine/cosine rules.
Deriving and applying identities to simplify expressions and solve trigonometric equations.
Exponential Growth and Logarithmic Scales
Studying the unique properties of exponential functions and using logarithms to linearize non-linear data.
Investigating the function e^x and its inverse, the natural logarithm.
Using log-log and semi-log graphs to identify relationships in experimental data.
Statistical Sampling and Probability
Analyzing data collection methods and using the binomial distribution to model discrete random variables.
Evaluating different sampling techniques and their impact on the validity of statistical conclusions.
Modeling scenarios with two possible outcomes and calculating probabilities of success over multiple trials.
Using probability distributions to make decisions about the validity of a null hypothesis.
Kinematics and Forces
Applying mathematical models to the physical world, focusing on constant acceleration and Newton's laws of motion.
Deriving and applying the equations of motion for particles moving in a straight line.
Investigating the relationship between force, mass, and acceleration using vector diagrams.