Algebra and functions Algebraic expressions – basic algebraic manipulation, indices and surds Quadratic functions – factorising, solving, graphs and the discriminants Equations – quadratic/linear simultaneous Inequalities – linear and quadratic (including graphical solutions) Graphs – cubic, quartic and reciprocal Transformations – transforming graphs – f(x) notation
Assessment: Internal test of 50 minutes duration on all topics covered during Unit 1. Pure Maths is 62.5% of the Year 12 course. It is assessed through a 2 hour exam (internal) at the end of Year 12. A suitable calculator is required (Casio Class Wizz).
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Further algebra; The binomial expansion Algebraic division, factor theorem and proof Coordinate geometry in the (x, y) plane; Straight-line graphs, parallel/perpendicular, length and area problems Circles – equation of a circle, geometric problems on a grid Trigonometry; Trigonometric ratios and graphs Trigonometric identities and equations
Internal assessment of 50 minutes duration on the topics coveredd in this unit. Pure Maths is 62.5% of the Year 12 course. It is assessed through a 2 hour exam (internal) at the end of Year 12. A suitable calculator is required (Casio Class Wizz).
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Create a supportive community:
Differentiation Definition, differentiating polynomials, second derivatives. Gradients, tangents, normals, maxima and minima. Integration Definition as opposite of differentiation, indefinite integrals of xn Definite integrals and areas under curves Vectors (2D) Definitions, magnitude/direction, addition and scalar multiplication Position vectors, distance between two points, geometric problems Exponentials and logarithms: Exponential functions and natural logarithms
Internal assessment of 50 minutes duration on the topics coveredd in this unit. Pure Maths is 62.5% of the Year 12 course. It is assessed through a 2 hour exam (internal) at the end of Year 12. A suitable calculator is required (Casio Class Wizz).
Develop the individual:
Create a supportive community:
Data presentation and interpretation (part 1): Calculation and interpretation of measures of location; Calculation and interpretation of measures of variation; Understand and use coding Statistical distributions: Use discrete distributions to model real-world situations; Identify the discrete uniform distribution; Calculate probabilities using the binomial distribution (calculator use expected) Probability: Mutually exclusive events; Independent events Statistical sampling Introduction to sampling terminology; Advantages and disadvantages of sampling Understand and use sampling techniques; Compare sampling techniques in context. Statistical hypothesis testing Language of hypothesis testing; Significance levels Carry out hypothesis tests involving the binomial distribution Data presentation and interpretation (part 2): Interpret diagrams for single-variable data; Interpret scatter diagrams and regression lines; Recognise and interpret outliers; Draw simple conclusions.
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Algebraic Methods and Proof
Students begin with proof by contradiction, developing rigorous mathematical reasoning. This is followed by a comprehensive study of algebraic fractions, including simplification, partial fractions (with and without repeated factors), and algebraic division.
Binomial Expansion and Series
Students extend algebraic manipulation skills through binomial expansion, including (1+x)b(1+x)^b(1+x)b and (a+bx)n(a+bx)^n(a+bx)n, alongside applications involving partial fractions in a series context.
Trigonometry
The trigonometry section focuses on solving trigonometric equations, building fluency and problem-solving skills. Students also study small angle approximations, linking algebraic reasoning to applied contexts.
Mechanics: Forces, Moments, and Equilibrium
Mechanics content includes resolving forces, inclined planes, and friction, leading to a Unit Test: Forces and Friction.
Students also study resultant forces, equilibrium, centres of mass, and tilting.
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Further development of Pure Maths skills: Proof Algebraic and partial fractions Functions and modelling
During term 6 students are assessed on the whole curriculum covered during Year 12 through formal end of year exams.
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