Pure Mathematics

Solve problems similar to those that appear in exams

Created byYasir Amir

Last updated 7/2023

English

English [Auto],

What you'll learn

Will be able to understand A Levels Pure Mathematics 1 Exam like problems
Will be able analyze A level Pure Mathematics 1 Exam like problems
Will be able solve problems from A level Pure Mathematics 1 Text Book
Will develop ability to work with problems logically and systematically

Course content

2 sections • 15 lectures • 3h 30m total length

Introduction1:44
Explore pure mathematics through drills and worked problems in this boot camp designed for exam practice. Maintain a notebook, try textbook exercises, and access one-to-one lessons to deepen understanding.
Lecture 18:09
This pure mathematics bootcamp guides you through exam-style problems and past paper questions. It demonstrates polynomial expansion and proves that the coefficient of x^2 is zero.
Lecture 211:15
Derive original function from derivative 3x^2 − 7 with f(3) = 5, yielding f(x) = x^3 − 7x − 1, and solve sin^{-1}(4x^4 + x^2) = π/6 to get x = ±1/2.
Lecture 319:46
Solve a trig equation by substituting x = sin θ to form a quadratic, apply the quadratic formula, and extract θ in 0 to 360 degrees, getting two solutions.
Lecture 411:12
Compute the first and second derivatives of y = 8/x + 2x, yielding dy/dx = -8/x^2 + 2 and d2y/dx2 = 16/x^3, and identify stationary points at (2,8) and (-2,-8).
Lecture 519:21
Identify the bigger and smaller circle radii, centers, and key distances; plan to approximate the shaded region as the semicircle minus two triangle areas, yielding a segment area.
Lecture 616:43
Solve progression problems by identifying arithmetic sequences through common difference and quadratic relations, then apply geometric progression sums to find missing terms.
Lecture 724:35
Explore a real-world problem in pure mathematics, analyze its magnitude, and plan collaborative study to find a solution and secure funding.
Lecture 812:06
we differentiate the curve y = sqrt(1+4x) to find the tangent slope at B(6,5) as 2/5, then form the normal with slope -5/2 through B and verify perpendicularity.

Lecture 0913:20
Pure mathematics lecture nine covers quadratic equations, written in standard form ax^2+bx+c=0 with a≠0, and solving by factoring—splitting the middle term to find the roots, illustrated with x=5/2 and x=1/3.
Lecture 1014:30
Learn the completing the square technique to solve quadratic equations, derive the quadratic formula, and apply these methods to exercises, including a projectile range problem.
Lecture 1113:51
Apply the quadratic formula to solve quadratics, find intersection points of a line and a parabola, and identify stationary turning points and the symmetry line to locate parabola minimum point.
Lecture 1214:31
Explore how functions map elements between sets, define domain and range, and determine inverses, using a one-to-one example like f(x)=5-(x-2)^2 with x in [2,6].
Lecture 1313:20
Master differentiation and integration by locating stationary, turning, maximum, minimum, and inflection points with first and second derivatives, and compute volumes of solids of revolution via the disk method.
Lecture 1416:15
This lecture analyzes arc length and perimeter in an isosceles triangle with a circle, then computes the area of a square-circle shaded region using sectors and triangles.

Requirements

O Levels Math

Description

This course offers targeted preparation for high school level Pure Mathematics exams, focusing on efficient problem-solving techniques. Pure mathematics delves into the fundamental concepts and structures underpinning the entire field, seeking a deeper understanding of mathematics itself. While often abstract and challenging, mastering these concepts is crucial for advanced mathematical studies. Like the renowned Archimedes, whose discoveries laid the groundwork for much of modern mathematics, success in this field requires dedication and consistent practice. Many students find the increasing complexity of advanced mathematics demanding, requiring extra effort to fully grasp abstract concepts. This course is designed to provide that extra support.

We assume prior familiarity with PM1-level material and an understanding of core mathematical principles. This course is not designed to teach foundational concepts from scratch. Instead, it focuses on refining problem-solving skills and exam preparation strategies. Through focused practice and dedicated effort in this course, you can significantly improve your exam performance.

This course is ideally suited for A-Level/High School students aiming to boost their grades and seeking a time-efficient study solution. We understand the pressures of exam preparation and have tailored this course to maximize learning in a concise format. While this course concentrates on exam-relevant problem-solving, we encourage students to explore related areas like logic, number theory, complex analysis, and applied mathematics. These and other advanced topics will be covered in future courses, expanding your mathematical horizons. We believe that a strong foundation in pure mathematics opens doors to a wide range of exciting and challenging fields.

Who this course is for:

Teachers and Parents teaching and guiding High School Cambridge Students as teaching aid.

Pure Mathematics

What you'll learn

Explore related topics

Course content

Introduction9 lectures • 2hr 5min

Drill 026 lectures • 1hr 26min

Requirements

Description

Who this course is for: