# C1 Worksheets – Core Advanced Mathematics

The worksheets are based on the UK Core Maths module, C1, studied at AS-Level. Click here for Past C1 Papers.

The C1 Worksheets each have 8 questions on the following topic areas: Algebra & Functions, Quadratics, Equations & Inequalities, Curve Sketching, Coordinate Geometry, Sequences & Series, Differentiation and Integration:

1. Algebra & Functions – Question 1 in the C1 Worksheets will test you on some prior knowledge of GCSE Maths as well as the new topics taught in C1. This will include the various kinds of factorising, composite powers, simplifying surds and rationalising denominators.
2. Quadratics – To tackle the questions on quadratics you must be able to sketch graphs of quadratics, complete the square, find discriminants and apply knowledge of discriminants in finding the number of roots the quadratic has.
3. Equations & Inequalities – the third question on each of the sheets will require you to either solve simultaneous equations, solve inequalities or manipulate equations.
4. Curve Sketching – as well as being able to sketch quadratics, these questions will test your ability to sketch cubic equations by identifying roots and understanding what general shape a cubic will take. You may also be asked apply transformations to a given graph and also know hat the graph of $\frac{1}{x}$ looks like.
5. Coordinate Geometry – in these questions you may be asked to find the equation of a straight line given two points, find the midpoint of a line segment or find the length of a line segment. You must have a good understanding of where lines cross axes and how to find a gradient.
6. Sequences & Series – you might be asked what the nth term or what the sum of the first n term is for an arithmetic sequence. You may also be asked similar questions for non-arithmetic sequences where the nth term is defined recursively. You must also be familiar with sigma, $\sum$, notation.
7. Differentiation – know how to differentiate, possibly more than once. Understand that the derivative allows you to find gradients and be prepared to use it in questions where the equation of a tangent is required.
8. Integration – know how to integrate and use it to find the equation of a curve given the derivative and find the integration constant when a point on the curve is known.

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