## Module overview

This module is designed to provide students with the mathematics knowledge and skills required for a successful transition to degree-level study in disciplines related to the chemical and biological sciences. The material covered is at a level corresponding to pre-university qualifications such as ASlevel in the UK.

## Aims and Objectives

### Learning Outcomes

#### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

- recall, select and use knowledge of mathematical techniques appropriate to the study of the sciences;
- demonstrate knowledge and understanding of mathematical processes.

#### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

- apply mathematical processes, skills and knowledge to some real scientific situations and to solve simple problems;
- interpret data and a variety of graphs and communicate information mathematically.

#### Transferable and Generic Skills

Having successfully completed this module you will be able to:

- manage your own learning;
- apply mathematical methods to solve simple problems.

## Syllabus

Topic 1 :Revision

Revision of numerical & algebraic skills

Note: Numerical fractions, algebraic fractions, cancelling & crossmultiplication, transposition of formulae, indices and surds.

Topic 2: Equations and Polynomials

- set up and solve simple equations as well as linear simultaneous equations in two unknowns using substitution and elimination
- set up and solve quadratic equations using factorisation and formula . Note: do not need to be able to use completing the square

Topic 3: Indices and Logarithms

- understand rational indices (positive, negative & zero) including indices expressed as fractions and use them to simplify algebraic expressions
- be able to express a number in the form x´10n
- understand the relationship between indices and logs with special reference to log10 and loge (ln)
- use the laws of logarithms to simplify expressions
- be able to change the base of logs
- be familiar with graphs of e x and e-x use logs to solve equations of the form ax = b and a 2x + ax + b = 0

Topic 4: Graphs

- use coordinates to plot graphs of algebraic equations
- find gradients and equations of straight lines
- understand the relationship between gradients of parallel and perpendicular lines
- plot graphs of pairs of equations

Topic 5: Linear laws

- use the equation of the straight line y = mx+ c in determining a linear law
- determine non-linear laws reducible to linear form, such as y = ax 2 + b, y =

Topic 6: Trigonometry

- be aware of the 6 trigonometric functions, and use sin, cos and tan to solve problems in 2D and 3D
- know forms of graphs for sin, cos and tan and understand the derivation of the positive and negative values
- know the values of sin, cos and tan for common angles in the range 0o £x £ 360 o e.g. 0o, 30o, 45o,etc in surd form
- be able to use the sine and cosine rules
- know that area of triangle = ½ bh = ½ absinC
- understand definition of a radian and be able to convert degrees«radians
- use formulae s = rq and A = ½r 2q

Topic 7: Statistics

- promote understanding of statistical terms, the ways of gathering and displaying data as well as an awareness of bias
- use analytical techniques to explain, justify and predict from data

Topic 8: Matrices

- add subtract and multiply matrices
- identify null and identity matrices
- evaluate determinant of 2x2 matrices
- understand and use AA-1 = A -1A = I
- formulate and solve linear simultaneous equations for 2 unknowns as matrix equations and solve using the inverse matrix method

Topic 9: Differentiation

- understand the gradient of a curve at a point as the limit of the gradients of a sequence of chords
- Notes: should understand how to find derivatives of simple functions from first principles
- use the derivative of x n, lnx, ex, sinx, cosx, tanx and constant multiples, sums/differences of these
- find gradient of a curve at a point
- find equation of tangent/normal to a curve at a point
- use the product and quotient rules
- use the chain rule to differentiate functions of the form f(g(x))
- understand that a derivative gives a rate of change
- find the second derivative of a function
- locate stationary points and distinguish between maxima and minima (by any method)

Note: should know that not all stationary points are maxima or minima but don't need to know conditions for points of inflexion

Topic 10: Integration

- understand integration as the reverse of differentiation; integrate xn (including n = -1) ex sinx cosx sin2x together with sums/differences and constant multiples of these
- use integration to find a region bounded by a curve and two ordinates or by two curves
- use the trapezium rule and Simpson's rule to obtain approximate values for definite integrals
- apply integration to find volumes of revolution about the x-axis

## Learning and Teaching

### Teaching and learning methods

Teaching methods include:

- lectures, to include worked examples and question/answer sessions;
- ativities guided through work packs;
- discussion and workshops.

Learning activities include:

- Lectures and group taught sessions;
- individual work on examples, supported by tutor input, scussion and workshop sessions;
- work pack activities and additional worksheets;
- open book sessments to support learning in this module; .
- private study and use of recommended text books;
- resources hosted on the Virtual Learning Environment.

Study Time allocation:

- Contact Hours: 120
- Private Study hours: 180
- Total study time: 180 hours

Type | Hours |
---|---|

Supervised time in studio/workshop | 48 |

Preparation for scheduled sessions | 36 |

Lecture | 72 |

Follow-up work | 90 |

Revision | 18 |

Wider reading or practice | 36 |

Total study time | 300 |

### Resources & Reading list

#### Textbooks

Anthony Croft and Robert Davison (5th). *Foundation Maths*.

## Assessment

### Summative

**Summative** assessment description

Method | Percentage contribution |
---|---|

Assignment | 40% |

Assignment | 60% |

### Referral

**Referral** assessment description

Method | Percentage contribution |
---|---|

Assignment | 60% |

Assignment | 40% |

### Repeat Information

Repeat type: Internal & External