BSc/MEnvSci Environmental Science with an Integrated Foundation Year / Course details
Year of entry: 2023
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Course unit details:
|Unit level||Level 1|
|Teaching period(s)||Semester 1|
|Offered by||Department of Mathematics|
|Available as a free choice unit?||No|
The course unit aims to: provide a basic course in calculus and algebra to students in the Foundation Year with no post-GCSE mathematics.
On completion of this unit successful students will be able to:
1 - Define the exponential function and apply the rules of indices to simplify algebraic expressions.
2 - Use the definition of the logarithm, together with its rules, to solve logarithmic equations.
3 - Find the roots, degree, leading term and coefficients of a polynomial.
4 - Identify and solve quadratic equations using the quadratic formula.
5 - Determine the equation of a line given its gradient and a point through which it passes.
6 - Calculate the gradient of a line given: (a) two points it passes through; (b) the gradient of a line to which it is parallel/perpendicular.
7 - Find the coordinates of the intersection points of two curves.
8 - Write down the equation of a tangent to a curve at a point.
9 - Given two points in the plane, determine the equation of a circle centred at one point and passing through the other.
10 - Define the domain of a function and calculate its inverse.
11 - Determine and simplify the composition of two functions.
12 - Convert angles between degrees and radians.
13 - Using the unit circle, recall the definition of the trigonometric functions, and apply this to determine the values of these functions at commonly-encountered angles.
14 - Find the size of an angle using the inverse trigonometric functions together with geometric reasoning.
15 - Use trigonometric identities to determine all angles and side-lengths in a right-angled triangle, given a side-length and one other piece of information (side-length or angle).
16 - Use the chain/product/quotient rules to differentiate the composition/product/quotient of two functions.
17 - Apply the rules for differentiation to determine the coordinates of, and classify, the stationary points of a given function.
18 - Use integration to find the area between two curves.
Functions (3 lectures)
- Definition of a function
- Standard functions (polynomial, exponentials, logarithms etc.)
Solution of Equations (2-3 lectures)
- Accuracy and Rounding
- Linear, Quadratic and other polynomial equations
Trigonometry (4 lectures)
- Circular measure
- Trigonometric functions
- Inverse Trig Functions
- Trigonometric Identities
Coordinate Geometry (3-4 lectures)
- Straight lines,
- points of intersection,
- slopes and gradients
Differentiation (3 lectures)
- Derivatives of standard functions
- Product rule
- Quotient Rule
- Chain Rule
Stationary points (2 lectures)
- Maxima and Minima
- Curve Sketching
Integration (4 lectures)
- Derivatives and anti-derivatives
- Indefinite integration, specific integrals, use of tables
Definite integrals and areas under / between curves.
Coursework 1 (week 5); Weighting within unit 10%
Coursework 2 (week 10); Weighting within unit 10%
Computer assignments; Weighting within unit 10%
End of semester 1 examination; Weighting within unit 70%
CROFT, A & DAVISON, R. 2010. Foundation Maths (5th ed.) Pearson Education, Harlow. (ISBN9780273730767)
BOOTH, D. 1998. Foundation Mathematics (3rd ed.). Addison-Wesley, Harlow. (ISBN0201342944)
BOSTOCK, L., & CHANDLER, S. 1994. Core Maths for A-level (2nd ed.). Thornes, Cheltenham. (ISBN9780748717798)
|Scheduled activity hours|
|Independent study hours|
|Nikesh Solanki||Unit coordinator|
This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.
Please see Blackboard / course unit related emails for any further updates