University level test about topics of relevance, as follows: Expanding brackets and factorising, solving linear equations, solving quadratic equations (finding the roots), solving... University level test about topics of relevance, as follows: Expanding brackets and factorising, solving linear equations, solving quadratic equations (finding the roots), solving simultaneous equations, inverse of a function, differentiation of various types of function, chain, product and quotient rules, integration of various types of function, including integration by substitution and by parts, partial fraction decomposition, solving equations using logs, trigonometric identities, parametric equations, solving ordinary differential equations using separation of variables, recognition of fundamental graphs, laws of logs, exponentials and powers, symmetry and periodicity of trigonometric functions, sine and cosine rules, fundamental functions, logs as inverses of powers, function transformations, classifying functions as odd/even/neither, stationary points, domain and range, dot product of vectors, tangent and normal to a curve, position and displacement vectors, magnitude of a vector, problems involving vectors, using dot product to find the angle between two vectors, work done by a force, laws of indices, simple curvesketching, composite functions, equation of a circle, binomial expansion/Pascal's triangle, evaluating definite integrals, vectors in 2D and 3D, finding a unit vector, rates of change log_a(x) as inverse of a^x, calculating the 2nd derivative of various functions, basic sequences and series, straightline modelling questions, basic probability questions.
Understand the Problem
The question lists various topics related to advanced mathematics that could be included in a universitylevel test. It outlines areas such as algebra, calculus, trigonometry, and vector analysis. The purpose is to aggregate essential concepts for assessment in these mathematical domains.
Answer
Algebra, Calculus, Trigonometry, Vector Analysis
Answer for screen readers
The essential concepts for a universitylevel test in advanced mathematics include:
 Algebra: solving equations, functions, and polynomials
 Calculus: limits, derivatives, and integrals
 Trigonometry: identities, functions, and relationships between angles
 Vector Analysis: vector operations, dot and cross products
Steps to Solve

Identify the topics listed
First, make a list of the topics related to advanced mathematics provided in the question. This includes areas such as algebra, calculus, trigonometry, and vector analysis. 
Organize the topics
Next, organize the identified topics into categories or groups, if necessary. For example, you could group them based on their complexity or relationships between them. 
Select essential concepts
Determine the essential concepts that need to be assessed within each identified topic. For instance, in calculus, you might include limits, derivatives, and integrals. 
Create a cohesive summary
Summarize the important concepts you decided upon for each topic in a single coherent statement that encapsulates what is essential for universitylevel assessment.
The essential concepts for a universitylevel test in advanced mathematics include:
 Algebra: solving equations, functions, and polynomials
 Calculus: limits, derivatives, and integrals
 Trigonometry: identities, functions, and relationships between angles
 Vector Analysis: vector operations, dot and cross products
More Information
Understanding these crucial concepts prepares students for tackling more advanced topics and applications in mathematics, engineering, and the sciences. Mastery of these areas can lead to better problemsolving skills and analytical thinking.
Tips
 Failing to understand the relationship between topics can lead to incomplete study. Ensure you know how topics like algebra and calculus interconnect.
 Not prioritizing essential concepts might result in overlooking critical areas during preparation. Focus on what is most frequently tested.