[ Keynote Live ]

Works Zone

Runtime Revision Sessions (R2S)

[ Upload ]

R2S LEGACY TUTORIALS

• Keynotes - All Archived!

V-REC FILES

• All Archived!

HOMEWORK

• SW.01 - R & Logic
• SW.02 -  Proofs
• SW.03 - Surd_Sigm

DATE

09.18

09.23

09.30

FEEDBACK

• RS.01
• RS.02
• RS.03

Computational Intellegence

Scroll for Reports!

R2S ADD MATH (P1; 20XX)

• [12S]  [12]    [13]     [14]    
• [15]     [16]    [17]     [18]    
• [19]     [20]    [21]     [22[

C.I. TOOLS

GUIDES & REPORTS

Quick Glance

• Course Outline
• Course Compass
• 2-Page Syllabus

————————

R2S REPORTS

*********************

Tue., June 27, 2022

Finals of 2021-2022 CAPE Pure Mathematics, Unit 1.  

Fri., June 24, 2022

No Unit 1 student was present. The class was cancelled.

Mon., June 20, 2022

Today, we completed, 2020, 2019, 2018, 2017, 2016, 2015 and Modules 1 and 2 of 2017S.

Much emphases were placed in addressing the following:

• General Problem Understanding!
• “What if?” Scenarios (the key to complete revision!)
• Solutions with the aid of curve sketching
• Strategies to Minimize Time & Efforts
• Identifying “Distractors” in MCQs!
• In-question revision for non-Paper 2 topics!
• Afternoon Speed and Accuracy drills (solving any paper in less than 30 mins!)
• Optimal handing and care with any repeated questions!

Mon., May 09, 2022

We completed day-3 solutions for all new questions in P2.2016.

 

For all additional Q&A, if and when requested, all further solutions will be posted online.

Please continue to practice and revise, relentlessly.

Thu., May 05, 2022

We completed day-2 solutions for P2.2009*, P2.2010, P2.2012 and P2.2013 while working in “Semi-Tutorial Mode,” which afforded us the chance to review deeply as we went along. The meant giving maximum attention to non-I.A. type questions.

Many of the questions required computational skills in  (1) solutions of simultaneous equations, (2) roots of polynomials, (3) Viete’s Formulae and (4) algebraic operations and use of identities.

We noticed the evolution of Paper 2’s over the years, which, as expected, flowed with the syllabus. The 2013 paper was the least challenging test seen thus far.

Next week, we will continue working on all recent years of practice papers but primarily solving the “R2S solutions for the missing years” first.

The R2S Syndicate will post the detailed solutions for past papers in the coming 3 days.

Wed., May 04, 2022

We developed in-house solutions for P2.2008.May, P2.2008.June and P2.2009* while working in “Semi-Tutorial Mode,” which afforded us the chance to review deeply as we went along.

Much emphases were placed on topics which included but not limited to:

• Trigonometry - Solutions to equations giving rise to (a) domain-restricted solutions or (b) General Solutions; Use of Identities; and Direct Proofs.
• Coordinate Geometry - Intersection of Lines and Curves, Tangents and Normals; and Parametric Equations.
• Early Vectors (2D) - Position and Displacement vectors, Dot (Scalar) Product, Angle between 2 vectors.
• Limits - Evaluations of limits, Continuity and Discontinuity of of functions
• Differential Calculus - Chain, Product  and Quotient rules, Critical Points, Parametric Equations, Curve Sketching, Max/Min Modeling Problems, and several Geometric Questions.  
• Integral Calculus - Indefinite and Definite integrals, Integration by Inspection (aka recognition), Integration by Substitution, Properties of the integral operator, Areas under the curve(s) and Simple Differential Equations.

 R2S 2023 FINALS

• R2S CAPE P1
• R2S CAPE P2
• R2S CAPE P3

Mathematica™ Online

MATLAB™ Online

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek patterns, formulate new conjectures, and establish truth by rigorous proofs from axioms, definitions and laws.

This science of quantities, change and space is either abstract concepts (Pure Mathematics) or extensions to other disciplines such as physics and engineering (Applied Mathematics).

Works Zone

ARCHIVES

BASIC ALGEBRA & FUNCTIONS

TRIGONOMETRY, COORDINATE GEOMETRY & VECTORS

CALCULUS I (Limits, Differentiation and Integration)

Universal Worksheets (UWS) for Greek Groups

SIMULATORS & TOOLS

Contents of R2S Explorations

MODULE 1

REASONING AND LOGIC

• Intro: Informal, Formal and Symbolic Logic
• Statements, Truth Tables, Laws & Mathematical Proofs

REAL NUMBER SYSTEM, R

• Classification and Definitions of Field & Order Axiom
• Binary Operations
• Surds, Sigma Notation and Mathematical Proofs by Induction

ALGEBRAIC OPERATIONS

• The Remainder Theorem and the Factor Theorem
• Algebra of Polynomials

EXPONENTIAL & LOGARITHMIC FUNCTIONS

• The Laws of Indices (review)
• The Exponential Function and its properties
• The Laws of Logarithms.
• Naperian (Natural) and Common logarithms

FUNCTIONS

• Definition and Classification of Functions
• Injective, Surjective and Bijective tests
• Inverse and Composite Functions

THE MODULUS FUNCTIONS

• The Classic Definitions
• Properties of the Modulus Function
• Handling Quadratics and Inequalities.

CUBIC FUNCTIONS & EQUATIONS

• Review of Quadratic Equations
• François Viète’s  formulae

[EOM 1]

MODULE 2

TRIGONOMETRY

• Review of Definitions and the Radian Measure
• Conversions between the angular displacement units of degrees and radians
• Length of an Arc and Area of a Sector revisited
• The Unit Circle
• The “Pretty Angles”
• Pythagorean, Compound, Double Angle Identities, S2P and P2S Identities
• Mathematical Proofs
• Principal and General Solutions
• Graphical Analyses

COORDINATE GEOMETRY

• The Cartesian plane
• Equation of a Line
• The Conic Sections
• Case Study: Circles & Parabolae
• Intersection of Curves and Lines
• Parametric Equations
• Modelling Problems

VECTORS

• Definitions and Notations
• The R3 Cartesian Space
• Algebraic Operations
• Parallel, Antiparallel and Equal Vectors
• The Scalar Product of Vector Projections
• Angle between 2 vectors
• Equations of Lines and Planes (Cartesian, Parametric and Vector forms)
• Modelling Problems

[EOM 2]

MODULE 3

LIMITS

• Introduction to Infinitesimals
• Limit of Functions and Special Theorems
• Special Limits (Results)
• Continuity and Discontinuity Lemmas

DIFFERENTIATION I

• The concept of the Derivative
• Differentiation from First Principles
• Product, Quotient and Chain Rules
• Differentiation of LIATE Functions
• Differentiation by Substitution
• Parametric Equations
• Convex Optimization and Saddle Point analysis
• Critical Points on a Curve
• Rate of Change problems and general understanding of curves

INTEGRATION I

• The Fundamental Theorem of Calculus (FTC 1) and the antiderivative
• Integration of Basic LIATE Functions
• The “Family of Curves”
• The Fundamental Theorem of Calculus (FTC 2)
• Special Properties of the Integral Operator
• Integration Techniques
• Applications of Integration (Areas and Volumes)
• Solutions to Rate of Change problems with or without initial boundary conditions.
• Introduction to Ordinary Differential Equations
• Modeling and Realtime Applications

[EOM 3]