## Pearson Edexcel IAL – P3: Pure Mathematics 3 (WMA13 010) – Samir Sha’lan

- Course Duration: 1H 16M

From: 100,00 $ / month

#### Available courses

#### Samir Sha'lan

High school Mathematics teacher

Course Type |
Full Course |
---|---|

Program | |

Level |
Pearson Edexcel IAL (A2) |

Subject |
Mathematics |

## Course Curriculum

**General**- Announcements

**1- Algebraic Methods**- 1.1 Arithmetic operations with algebraic fractions
- 1.2 Improper Fractions

**2- Functions and Graphs**- 2.1 The Modulus Function
- 2.2 Functions and Mapping
- 2.3 Composite Functions
- 2.4 Inverse Functions
- 2.5 y = |f(x)| and y = f(|x|)
- 2.6 Combining Transformations
- 2.7 Solving Modulus Problems

**3-Trigonometric Functions**- 3.1 Secant, Cosecant, and Cotangent
- 3.2 Graphs of sec(x), cosec(x), cot(x)
- 3.3 Using sec(x), cosec(x), and cot(x)
- 3.4 Trigonometric Identities
- 3.5 Inverse Trigonometric Functions

**4-Trigonometric Addition Functions**- 4.1 Addition Formulae
- 4.2 Using the Angle Addition Formulae
- 4.3 Double-Angle Formulae
- 4.4 Solving Trigonometric Equations
- 4.5 Simplifying a cos(x) ± b sin(x)
- 4.6 Proving Trigonometric Identities

**5- Exponentials and Logarithms**- 5.1 Exponential Functions
- 5.2 y = e^(ax+b) + c
- 5.3 Natural Logarithms
- 5.4 Logarithms and Non-Linear Data
- 5.5 Exponential Modelling

**6- Differentiation**- 6.1 Differentiating sin(x) and cos(x)
- 6.2 Differentiating Exponentials and Logarithms

## About Course

P3: Pure Mathematics 3
(WMA13 010) is a continuation of the foundational studies in mathematics,
designed to deepen students’ understanding of advanced mathematical concepts.
This course builds upon the principles introduced in Pure Mathematics 1 and 2,
focusing on further development of algebra, calculus, and mathematical
reasoning. It is tailored for students preparing for higher education in
mathematics or related disciplines.

## What you'll learn?

## Material Includes

– Simplification of rational expressions including

factorizing and cancelling, and algebraic division definition of a function.

Domain and range of functions. Composition of functions. Inverse functions and

their graphs, the modulus function, and Combinations of the transformations

– Knowledge of secant, cosecant and cotangent and of arc sin,

arc cos and arctan. Their relationships to sine, cosine and tangent.

Understanding of their graphs and appropriate restricted domains, Knowledge and

use of sec2 θ = 1 + tan2 θ and cosec2 θ = 1 + cot2 θ, Knowledge and use of

double angle formulae; use of formulae for sin (A ± B), cos(A ± B) and tan (A ±

B) and of expressions for a cos θ + b sin θ in the equivalent forms of r cos(θ

± a) or rsin (θ ± a).

– The function ex and its graph, The function ln x and its

graph; ln x as the inverse function of e^{x}, and Use logarithmic

graphs to estimate parameters in relationships of the form y = ax^{n}

and y = kb^{x}

– Differentiation of e^{kx}, ln kx, sin kx, cos kx,

tan kx and their sums and differences

– Differentiation using the product rule, the quotient rule

and the chain rule, and understand and use exponential growth and decay

– Integration of e^{kx}, 1 / x , sin kx, cos kx and

their sums and differences, in addition to Integration by recognition of known

derivatives.

– Location of roots of f(x) = 0 by considering changes of

sign of f(x) in an interval of x in which f(x) is continuous, and Approximate

solution of equations using simple iterative methods, including recurrence

relations of the form x^{n} + 1 = f(x^{n})

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