Year 12 Curriculum - Maths
Pure Mathematics
Unit |
Title |
Estimated lessons |
|
|
Algebra and functions |
|
|
a |
Algebraic expressions – basic algebraic manipulation, indices and surds |
3 |
|
b |
Quadratic functions – factorising, solving, graphs and the discriminants |
4 |
|
c |
Equations – quadratic/linear simultaneous |
4 |
|
d |
Inequalities – linear and quadratic (including graphical solutions) |
5 |
|
e |
Graphs – cubic, quartic and reciprocal |
5 |
|
f |
Transformations – transforming graphs – f(x) notation |
5 |
|
2 |
|
Coordinate geometry in the (x, y) plane |
|
a |
Straight-line graphs, parallel/perpendicular, length and area problems |
6 |
|
b |
Circles – equation of a circle, geometric problems on a grid |
7 |
|
3
|
|
Further algebra |
|
a |
Algebraic division, factor theorem and proof |
8 |
|
b |
The binomial expansion |
7 |
|
4
|
|
Trigonometry |
|
a |
Trigonometric ratios and graphs |
6 |
|
b |
Trigonometric identities and equations |
10 |
|
5
|
|
Vectors (2D) |
|
a |
Definitions, magnitude/direction, addition and scalar multiplication |
7 |
|
b |
Position vectors, distance between two points, geometric problems |
7 |
|
6
|
|
Differentiation |
|
a |
Definition, differentiating polynomials, second derivatives |
6 |
|
b |
Gradients, tangents, normals, maxima and minima |
6 |
|
7
|
|
Integration |
|
a |
Definition as opposite of differentiation, indefinite integrals of xn |
6 |
|
b |
Definite integrals and areas under curves |
5 |
|
8 |
|
Exponentials and logarithms: Exponential functions and natural logarithms |
12 |
|
|
120 hours |
Applied Mathematics - Mechanics and Statistics
Unit |
Title |
Estimated hours |
|
1 |
|
Statistical sampling |
|
a |
Introduction to sampling terminology; Advantages and disadvantages of sampling |
1 |
|
b |
Understand and use sampling techniques; Compare sampling techniques in context |
2 |
|
2 |
|
Data presentation and interpretation |
|
a |
Calculation and interpretation of measures of location; Calculation and interpretation of measures of variation; Understand and use coding |
4 |
|
b |
Interpret diagrams for single-variable data; Interpret scatter diagrams and regression lines; Recognise and interpret outliers; Draw simple conclusions from statistical problems |
8 |
|
3 |
|
Probability: Mutually exclusive events; Independent events |
3 |
4 |
|
Statistical distributions: Use discrete distributions to model real-world situations; Identify the discrete uniform distribution; Calculate probabilities using the binomial distribution (calculator use expected) |
5 |
5 |
|
Statistical hypothesis testing |
|
a |
Language of hypothesis testing; Significance levels |
2 |
|
b |
Carry out hypothesis tests involving the binomial distribution |
5 |
|
|
30 hours |
||
6
|
|
Quantities and units in mechanics |
|
a |
Introduction to mathematical modelling and standard S.I. units of length, time and mass |
1 |
|
b |
Definitions of force, velocity, speed, acceleration and weight and displacement; Vector and scalar quantities |
2 |
|
7
|
|
Kinematics 1 (constant acceleration) |
|
a |
Graphical representation of velocity, acceleration and displacement |
4 |
|
b |
Motion in a straight line under constant acceleration; suvat formulae for constant acceleration; Vertical motion under gravity |
6 |
|
8
|
|
Forces & Newton’s laws |
|
a |
Newton’s first law, force diagrams, equilibrium, introduction to i, j system |
4 |
|
b |
Newton’s second law, ‘F = ma’, connected particles (no resolving forces or use of F = μR); Newton’s third law: equilibrium, problems involving smooth pulleys |
6 |
|
9 |
|
Kinematics 2 (variable acceleration) |
|
a |
Variable force; Calculus to determine rates of change for kinematics |
4 |
|
b |
Use of integration for kinematics problems i.e. |
3 |
|
|
30 hours |