# Core Mathematics C34

### About This Unit

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 (C34) In this session, you will learn about Algebra and Functions, one of the 9 topics you need to be knowledgeable in to master the Unit C34 paper in Mathematics. After completing this session, you will be able to ‘cancel down’ algebraic fractions, multiply together two or more algebraic fractions, divide algebraic fractions, add or subtract algebraic fractions, convert an improper faction into a mixed number fraction, represent a mapping by a diagram y an equation and by a graph, understand the terms ‘function’, ‘domain’ and ‘range’, combine two or more functions to make a composite function, know the difference between a ‘one to one’ and ‘one to many’ function, know how to find the inverse of a function, know the relationship between the graph of a function and its inverse, sketch the graph of the modulus function $$y = |f(x)|$$, sketch the graph of the function $$y = f(|x|)$$, solve equations involving the modulus function, apply a combination of two (or more) transformations to the same curve, as well as sketch transformations of a graph $$y = f(x)$$.
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2. Chapter 2 Sequences and Series (C34) In this session, you will learn about Sequences and Series, one of the 9 topics you need to be knowledgeable in to master the Unit C34 paper in Mathematics. After completing this session, you will be able to expand $$(1 + x)^n$$ for any constant n, expand $$(a + bx)^n$$ for any constants $$a, b$$ and $$n$$, determine the range of values of x for which the expansion is valid, use partial fractions to expand more complex fractional expressions.
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3. Chapter 3 Trigonometry (C34) In this session, you will learn about Trigonometry, one of the 9 topics you need to be knowledgeable in to master the Unit C34 paper in Mathematics. After completing this session, you will know the functions $$secant(\theta), cosecant(\theta)$$ and $$cotangent(\theta)$$, the graphs of $$sec(\theta), cosec(\theta)$$ and $$cot(\theta)$$, how to solve equations and prove identities involving $$sec(\theta), cosec(\theta)$$ and $$cot(\theta)$$, how to prove and use the identities $$‘1 + tan^2(\theta) = sec^2(\theta)’$$ and $$‘1 + cot^2(\theta) = cosec^2(\theta)$$, how to sketch and use the inverse trigonometric functions $$arcsinx, arccosx$$ and $$arctanx$$, use the addition formulae, use the double angle formulae, write expressions of the form $$acos(\theta) \pm bsin(\theta)$$ in the form $$Rcos(\theta \pm \alpha)$$ and/or $$Rsin(\theta \pm \alpha)$$, use the factor formulae, as well as use all of the above to solve equations and prove identities.
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4. Chapter 4 Exponentials and Logarithms (C34) In this session, you will learn about Expoenetials and Logarithms, one of the 9 topics you need to be knowledgeable in to master the Unit C34 paper in Mathematics. After completing this session, you will be able to sketch simple transformations of the graph $$y = e^x$$, sketch simple transformations of the graph $$y = ln x$$, solve equations involving $$e^x$$ and $$ln x$$, know what is meant by the terms ‘exponential growth’ and ‘decay’, as well as solve real life examples of exponential growth and decay.
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5. Chapter 5 Coordinate Geometry in the (x, y) Plane (C34) In this session, you will learn about Coordinate Geometry in the (x, y) in the Plane, one of the 9 topics you need to be knowledgeable in to master the Unit C34 paper in Mathematics. After completing this session, you will be able to sketch the graph of a curve given its parametric equation, use the parametric equation of a curve to solve various problems including the intersection of a line with the curve, convert the parametric equation to a Cartesian form, as well as find the area under a curve whose equation is expressed in parametric form.
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6. Chapter 6 Differentiation (C34) In this session, you will learn about Differentiation, one of the 9 topics you need to be knowledgeable in to master the Unit C34 paper in Mathematics. After completing this session, you will be able to differentiate a composite function using the chain rule, differentiate functions that are multiplied together by using the product rule, differentiate rational functions using the quotient rule, differentiate variations on the functions of $$e^x$$ and $$ln(x)$$, differentiate variations on the functions $$sinx, cosx$$ and $$tanx$$, find the gradient of a curve whose equation is expressed in a parametric form, differentiate implicit relationships, differentiate power functions such as $$a^x$$, use the chain rule to connect the rates of change of two variables, as well as set up simple differential equations from information given in context.
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7. Chapter 7 Integration (C34) In this session, you will learn about Integration, one of the 9 topics you need to be knowledgeable in to master the Unit C34 paper in Mathematics. After completing the session, you will be able to integrate the following: a number of standard mathematical functions, using the reverse of the chain rule, using trigonometrical identities, using partial fractions, by substitution, by parts, to find areas and volumes, to solve differential equations. You will also be able to use the trapezium rule to approximate their value for functions that are too difficult to integrate. Furthermore, you will be able to add and subtract two or more fractions, convert an expression with linear factors in the denominator into partial fractions, convert an expression with repeated linear factors in the denominator into partial fractions, as well as convert an improper fraction into partial fraction form.
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8. Chapter 8 Numerical Methods (C34) In this session, you will learn about Numerical Methods, one of the 9 topics you need to be knowledgeable in to master the Unit C34 paper in Mathematics. After completing this session, you will be able to use a graphical method to find the number of roots of the equation $$f(x) = 0$$, prove that a root lies within a given interval $$[a, b]$$, use iteration to find an approximation to the root of the equation $$f(x) = 0$$, as well as express your answer to an appropriate degree of accuracy.
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9. Chapter 9 Vectors (C34) In this session, you will learn about Vectors, one of the 9 topics you need to be knowledgeable in to master the Unit C34 paper in Mathematics. After completing this session, you will be able to know the difference between a scalar and a vector quantity, draw vector diagrams, perform simple vector arithmetic and know the definition of a unit vector, use position vectors to describe points in two or three dimensions, use Cartesian coordinates in three dimensions, including finding the distance between two points, find a scalar product and know how it can be used to find the angle between two vectors, write down the equation of a line in vector form, determine whether or not two given straight lines intersect (if they do intersect, you should be able to find the point of intersection), as well as find the angle between two intersecting lines.
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### 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