# Core Mathematics C12

When studying pure mathematics at AS and A2 level you will be extending your knowledge of such topics as algebra and trigonometry as well as learning some brand new ideas such as calculus. While many of the ideas you will meet in pure mathematics are interesting in their own right, they also serve as an important foundation for other branches of mathematics, especially mechanics and statistics.

### Unit Content

1. Chapter 1 Algebra and Functions (C12) In this session, you will learn about Algebra and Functions, one of the 7 topics you need to be knowledgeable in to master the Unit C12 paper in Mathematics. ​After completing this session you will be able to simplify expressions and collect like terms, apply the rules of indices, multiply out brackets, factorise expressions including quadratics, manipulate surds, simplyfy algebraic fractions by dividing, divide a polynomial $$f(x)$$ by $$(x\pm p)$$, factorise a polynomial by using the factor theorem, as well as use the remainder theorem to find the remainder when a polynomial $$f(x)$$ is divided by $$(ax - b)$$.
21 Concepts, 15 Quizzes
2. Chapter 2 Coordinate Geometry in the (x, y) Plane (C12) In this session, you will learn about Coordinate Geometry in the (x, y) Plane, one of the 7 topics you need to be knowledgeable in to master the Unit C12 paper in Mathematics. ​After completing this session, you will be able to understand the link between the equation of a line, and its gradient and intercept, calculate the gradient of a line joining a pair of points, find the equation of a line in either the form $$y = mx + c$$ or alternatively $$ax + by = c$$, find the equation of a line passing through a pair of points, determine the point where a pair of straight lines intersect, as well as know and use the rule concerning perpendicular gradients. Also, you will be able to find the mid-point of a line, find the distance between a pair of points, know how to find the equation of a circle, as well as use the properties of a circle to solve geometric problems.
15 Concepts, 8 Quizzes
3. Chapter 3 Sequences and Series (C12) In this session, you will learn about Sequences and Series, one of the 7 topics you need to be knowledgeable in to master the Unit C12 paper in Mathematics. After completing this session, you will be able to generate a sequence from the $$n$$th term, or from a recurrence relationship, know how to find the $$n$$th term of an arithmetic sequence, $$U_n$$, know how to find the sum to $$n$$ terms of an arithmetic series, $$S_n$$, solve problems on arithmetic series using the formulae for $$U_n$$ and $$S_n$$, as well as know the meaning of the symbol $$\Sigma$$. Also, you will be able to recognise a geometric sequence and state its common ratio calculate the $$n$$th term of a geometric sequence, find the sum of a geometric series, solve problems involving growth and decay, as well as find the sum to infinity of a convergent geometric series. Furthermore, you will be able to use Pascal's Triangle to expand expressions of the form $$(a + b)^2$$, use combination and factorial notation to expand expressions of the form $$(a + b)^2$$, as well as use the expansion of $$(1+x)^2$$ to expand $$(a + b)^2$$.
16 Concepts, 10 Quizzes
4. Chapter 4 Exponentials and Logarithms (C12) In this session, you will learn about Exponentials and Logarithms, one of the 7 topics you need to be knowledgeable in to master the Unit C12 paper in Mathematics. After completing this session, you will be able to know the shape of the graph of $$y=\alpha^x$$, write an expression in logarithmic form, use the laws of logarithms, solve equations of the form $$\alpha^x = b$$, and change the base of a logarithm.
11 Concepts, 6 Quizzes
5. Chapter 5 Trigonometry (C12) In this session, you will learn about Trigonometry, one of the 7 topics you need to be knowledgeable in to master the Unit C12 paper in Mathematics. After completing this session, you will be able to use the relationships $$\tan (\theta) = \frac{\sin (\theta)}{\cos(\theta)}$$ and $$\sin^2 (\theta) + \cos^2 (\theta) = 1$$, solve simple trigonometrical equations of the form $$\sin(\theta) = k$$, and solve more complex trigonometrical equations of the form $$\sin(n(\theta) + \alpha) = k$$. Also, you will be able to calculate the sine, cosine and tangent of any angle, know the exact trigonometrical ratios for $$30^o, 45^o$$ and $$60^o$$, sketch the graphs of the sine, cosine, and tangent functions, as well as sketch simple transformations of these graphs. Furthermore, you will be able to convert between radians and degrees (and vice versa), know and use the formula in radians for the length of an arc, know and use the formula in radians for the area of a sector, as well as know and use the formula in radians for the segment of a circle.
19 Concepts, 14 Quizzes
6. Chapter 6 Differentiation (C12) In this session, you will learn about Differentiation, one of the 7 topics you need to be knowledgeable in to master the Unit C12 paper in Mathematics. After completing this session, you will be able to estimate the gradient of a curve, calculate the gradient function, $$\frac{dy}{dx}$$ for simple functions, calculate the gradient of a curve at any point, find the equation of the tangent and normal to a curve at a specified point, and calculate the second differential $$\frac{d^2y}{dx^2}$$. You will also know the difference between an increasing and decreasing function, how to find a stationary point, know how to distinguish between a maximum, a minimum, and a point of inflexion, as well as apply your knowledge of turning points to solve problems.
10 Concepts, 8 Quizzes
7. Chapter 7 Integration (C12) In this session, you will learn about Integration, one of the 7 topics you need to be knowledgeable in to master the Unit C12 paper in Mathematics. After completing this session, you will be able to integrate simple functions, understand the symbol $$\int dx$$, and find the constant of integration by substituting in a given point $$(x, y)$$. You will also be able to integrate simple functions within defined limits, use integration to find areas under curves and the area between a curve and a line, and approximate the area under a curve by using the trapezium rule.
14 Concepts, 7 Quizzes

### Prerequisites and Requirements

Students who have achieved a grade of 'C' or higher in their IGCSE, GCSE, or any other equivalent 'O' Level Mathematics.

### What's Next?

Core Mathematics
C12
Edexcel International A Level Mathematics