# C2 Worksheets – Core Advanced Mathematics

The C2 worksheets have questions on the following topic areas: Algebra & Functions, Sine & Cosine rule, Logarithms, Equation of a Circle, Binomial Expansion, Radians, Arcs & Sectors, Geometric Sequences & Series, Sketching Trigonometric Functions, Differentiation, Solving Trigonometric Equations and Definite Integration.

These worksheets are based on the UK A-Level C2 module but the worksheets can be used anywhere. See below to find out what the content of each question is based on.

## C2 Worksheet 1

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The C2 Worksheets have 11 questions on the following topic areas, note that a working knowledge of the C1 syllabus is assumed:

1. Algebra & Functions – simplify algebraic fractions by finding common factors on the top and bottom or by using polynomial division. Understand and apply factor and remainder theorem.
2. Sine & Cosine rule – understand and possibly prove the sine and cosine rule. Use them to find missing angles and lengths in a non-right-angled triangle.
3. Logarithms – understand and use logarithms of various bases. Use the logarithm laws to manipulate and solve equations involving logarithms.
4. Equation of a Circle – find the equation of a circle given two points that lie on it. Find the equation of a circle given the location of its centre and its radius.
5. Binomial Expansion – find the first few terms, or possibly all of, the expansion of $(a+b)^n$, where n is a positive integer. Use the expansion to estimate values of real numbers to a given power.
6. Radians, Arcs & Sectors – understand how to measure angles in radians. Find the length of an arc or the area of a sector in complex problems.
7. Geometric Sequences & Series – find the nth term and the sum of the first n terms of a geometric sequence. Know how to show that the formula for the sum of the first n terms is derived. Know when geometric series can be summed to infinity.
8. Sketching Trigonometric Functions – know how to sketch the graphs of familiar trigonometric functions particularly when angles are measured in radians. Evaluate the values of trigonometric functions at simple angle values. Use triangles to evaluate trigonometric functions at not-so-simple angle values.
9. Differentiation – use the derivative (from C1) to show when a function is increasing or decreasing. Know that the derivative is zero at a stationary point. Use the second derivative to classify it as a maximum or minimum.
10. Solving Trigonometric Equations – Know and apply the identities $\sin^2(x)+\cos^2(x)=1$ and $tan(x)=\frac{\sin(x)}{\cos(x)}$. Solve equations involving trigonometric functions.
11. Definite Integration – Evaluate integrals including those with limits. Use integration to find areas beneath curves and between curves.