Mathematics For Scientists

This unit is expiring
The expiry date of this unit is 31/07/2025.

Overview

Framework:
Access to HE
Level:
Level 3
Unit No:
QU006182
Credits:
6
Guided learning hours:
Not available

Qualification Grading Type

Graded

Grade Descriptors

  • GD3-Application of skills
  • GD7-Quality

Unit Learning Outcomes

1.

Be able to perform calculations with real numbers expressed in a variety of forms.

Assessment Criteria

  • 1.1
    Round numbers expressed as scientific measures to a given number of significant figures.
  • 1.2
    Select appropriate representation of numbers in carrying out simple calculations.
  • 1.3
    Distinguish between rational and irrational numbers. Explain, giving examples of each type.
  • 1.4
    Check answers to calculations by using estimation.
  • 1.5
    Calculate absolute and relative errors in relation to scientific problems, expressing answers as percentages.
  • 1.6
    Without using a calculator use standard form to manipulate large and small numbers as they arise in scientific work.
2.

Be able to manipulate algebraic expressions.

Assessment Criteria

  • 2.1
    Perform algebraic simplifications, which require the use of laws of indices for positive, negative and fractional indices.
  • 2.2
    Multiply out brackets in order to simplify algebraic expressions which are no more complex than quadratic expressions.
  • 2.3
    Use factorisation to simplify algebraic fractions.
  • 2.4
    Solve any linear equation in one unknown after suitable algebraic manipulation.
  • 2.5
    Solve quadratic equations of the type 3x2 - 11x + 6 = 0 using factorisation or the quadratic formula' where appropriate.
  • 2.6
    Transpose formulae of the type used frequently in scientific work including cases involving roots and others requiring factorisation.
3.

Be able to draw graphs of linear and quadratic functions and use graphical methods to solve problems.

Assessment Criteria

  • 3.1
    Use algebra to solve problems related to direct and inverse proportion.
  • 3.2
    Find the gradient and intercept using y = mx + c.
  • 3.3
    Use the relationship y - y1 = m (x - x1) to determine the equation of a line joining two points.
  • 3.4
    Draw a graph of a quadratic function by calculating suitable values.
  • 3.5
    Solve a pair of simultaneous equations using graphs, in which one is linear and one quadratic.
4.

Be able to calculate lengths areas and volumes for standard figures.

Assessment Criteria

  • 4.1
    State the required formula and calculate areas and perimeters of rectangles, triangles, trapezia and circles giving answers to an appropriate level of accuracy.
  • 4.2
    Convert all metric units by changing the prefix of the unit, including area and volume.
  • 4.3
    Calculate volumes and surface areas of cuboids, spheres, cylinders and other shapes with uniform area of cross-section.
  • 4.4
    Apply Pythagoras' theorem and trigonometry to solve practical problems involving right angled triangles.
  • 4.5
    Sketch graphs of sine, cosine and tangent functions using radian measure.
  • 4.6
    Solve problems related to periodic functions; time period, wavelength, frequency.
5.

Be able to demonstrate an understanding of the laws of exponential growth and decay.

Assessment Criteria

  • 5.1
    Calculate the ratio to show that exponential growth has a constant ratio greater than one.
  • 5.2
    Calculate the ratio to show that exponential decay has a constant ration of less than one.
  • 5.3
    Calculate the half-life for a quantity from its exponential decay graph and calculate the amount remaining of a quantity after a number of half-lives.