# A-Level Maths C2 Module The C2 Module consists of the following topic areas: algebra & functions, the sine and cosine rule, logarithms, circle equations, binomial expansion, circle sectors, geometric series, trigonometric functions, more differentiation, trigonometric identities and more integration. We have designed our C2 worksheets so that each question corresponds to each of the topic areas and the questions increase in difficulty from worksheet to worksheet. See below for a more details of each of the topic areas or…

1. Algebra & Functions – learn how to 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. You will also learn how to find the area of non-right-angles triangles.
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 span the diameter or given the location of its centre and its radius directly.
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 or to simplify more complicated expressions.
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 and use it. Know when and how to sum a geometric series 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 $\tan(x)=\sin(x)\div\cos(x)$. Solve equations involving trigonometric functions.
11. Definite Integration – Evaluate integrals including those with limits. Use integration to find areas beneath curves and between curves.