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St Paul's School
for Girls

Year 12 Curriculum - Maths

Pure Mathematics

Unit

Title

Estimated lessons

1

 

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

Section A – Statistics

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

Section B – Mechanics

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 ij system

4

b

Newton’s second law, ‘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