13.5 hours: (8:30-10am)
Date: 30 Sep-4 Oct and 8-11 Oct 2024
Dr Amir presents online, in a lecture format, to a group of approved registered participants. Dr Amir designs the questions presented in this session based on Dr Amir's understanding of HSC and Mathematics Advanced and Dr Amir's Pedagogy. The materials presented are subject to Copy Right and can not be saved or copied or distributed in any format. Dr Amir presents from a selection of the following topics:
Let’s embark on a mathematical odyssey through the realms of high school mathematics, guided by the sagacious Dr. Amir. Brace yourself for a comprehensive exploration of these captivating topics:
Algebra, the magical art of balancing equations and deciphering unknowns, awaits! Dr. Amir will introduce you to algebraic expressions, equations, and inequalities. You’ll dance with linear functions, quadratic polynomials, and systems of equations. Algebra is like a symphony of symbols, where variables harmonize to reveal hidden truths.
Functions are mathematical machines that transform inputs into outputs. Dr. Amir will guide you through function notation, domain, range, and composition. Graphs will come alive—lines, parabolas, and exponential curves. Transformations will twist and stretch these graphs, revealing their secrets.
Imagine stretching or compressing a graph horizontally or vertically. Dr. Amir will show you how dilation affects functions. You’ll encounter scaling factors, amplitude, and phase shifts. It’s like adjusting a cosmic telescope to explore mathematical constellations.
Functions love to slide! Dr. Amir will teach you the art of translation. Shifting left or right (horizontal) or up and down (vertical) changes the game. You’ll explore intercepts, asymptotes, and intercepting aliens in the Cartesian plane.
Why settle for one transformation when you can have a party? Dr. Amir will combine dilation, translation, and reflection. Functions will twist, flip, and pirouette. It’s like choreographing a mathematical ballet.
Triangles and angles unite! Dr. Amir will introduce sine, cosine, and tangent. You’ll sail the unit circle, decode radians, and unravel periodicity. Trig functions oscillate like cosmic waves—prepare for a celestial voyage.
Dr. Amir’s treasure trove includes Pythagorean identities, sum and difference formulas, and double-angle magic. You’ll solve trig equations, prove identities, and navigate the mysterious world of trigonometry.
Exponential growth and decay await! Dr. Amir will reveal the secrets of base e. You’ll explore compound interest, radioactive decay, and population explosions. Exponential functions are like wildfire—spreading knowledge across mathematical landscapes.
Logarithms—the inverse of exponentials—hold mystical powers. Dr. Amir will guide you through logarithmic properties, change of base, and solving logarithmic equations. It’s like decoding ancient scrolls with a mathematical Rosetta Stone.
Calculus time! Dr. Amir will introduce derivatives—the slopes of curves. You’ll find rates of change, tangents, and critical points. Anti-derivatives (indefinite integrals) are like unraveling time-travel equations. Hold on tight!
Dr. Amir loves hills and valleys! You’ll explore concavity, inflection points, and stationary curves. Increasing or decreasing—functions reveal their secrets. It’s like hiking through mathematical landscapes.
Real-world puzzles await! Dr. Amir will tackle optimization—maximizing areas, minimizing costs, and optimizing rocket trajectories. Calculus becomes a compass for navigating life’s challenges.
Dr. Amir’s canvas is the Cartesian plane. You’ll sketch curves using derivatives—finding intercepts, asymptotes, and turning points. It’s like painting with mathematical brushes.
Beyond the basics lies a universe of calculus. Dr. Amir will delve into parametric equations, polar coordinates, and vectors. Calculus becomes a cosmic adventure.
Anti-derivatives meet definite integrals. Dr. Amir will calculate areas under curves, volumes of revolution, and centroids. Imagine finding the area enclosed by a dragon-shaped curve—it’s like mathematical origami.
Numerical integration enters the scene. Dr. Amir will use trapezoids to estimate areas. Definite integrals become your mathematical GPS—navigating through mathematical landscapes.
Uncertainty meets data. Dr. Amir will display and interpret data. You’ll explore correlation, regression, and the line of best fit. Standard deviation and variance become your statistical companions.
Probability density functions (PDFs) and cumulative distribution functions (CDFs) await. Dr. Amir will introduce quartiles, z-scores, and the normal distribution. Probability becomes a cosmic dice game.
Probability Density Functions (PDFs):
Cumulative Distribution Functions (CDFs):
Quantile/Percentile:
Z-scores:
Normal Distribution:
In summary, these concepts provide the foundation for understanding continuous random variables, their distributions, and how to analyze and interpret data. Dr. Amir’s tutoring has equipped you with essential tools for tackling real-world problems involving uncertainty and variability.
So, dear student, sharpen your pencils, ignite your curiosity, and let Dr. Amir’s mathematical lantern guide you through this enchanting labyrinth
Registration is required by 27-Sep-2024.
13.5 hours: (10-11:30am)
Date: 30 Sep-4 Oct and 8-11 Oct 2024
Dr Amir presents online, in a lecture format, to a group of approved registered participants. Dr Amir designs the questions presented in this session based on Dr Amir's understanding of HSC and Mathematics Standard and Dr Amir's Pedagogy. The materials presented are subject to Copy Right and can not be saved or copied or distributed in any format. Dr Amir presents from a selection of the following topics:
Let’s explore these topics in depth:
Financial mathematics deals with managing money, investments, and financial transactions. Key concepts include interest rates, present value, and future value. Here are some essential components:
Understanding taxation is crucial for financial planning. Topics include income tax, deductions, credits, and tax brackets.
Investments involve allocating funds to assets (stocks, bonds, real estate) to generate returns. Concepts include risk, diversification, and portfolio management.
Depreciation accounts for the decrease in value of assets over time. Methods include straight-line depreciation and declining balance.
Loans involve borrowing money with interest. Types include personal loans, mortgages, and student loans.
Inflation reduces the purchasing power of money. Appreciation refers to an asset’s increase in value, while depreciation is its decrease.
Shares (stocks) represent ownership in a company. Understanding stock markets, dividends, and stock valuation is essential.
Credit cards allow borrowing against a credit limit. Managing credit card debt and interest rates is crucial.
Used for calculating depreciation, this method allocates more depreciation in the early years of an asset’s life.
Annuities involve regular payments over time. Examples include retirement pensions and insurance policies.
Calculating the value of annuity payments at a future or present date.
Understanding loan amortization and repayment schedules.
Creating and managing a budget to allocate income effectively.
Solving systems of equations with multiple variables.
Determining the point at which costs equal revenue.
Understanding rates of change and comparing quantities.
Used in navigation and land surveying.
Examining relationships between two variables.
Measures the strength and direction of linear association between two variables.
Used in regression analysis to model data trends.
Standardizing data for comparison.
Estimating values within or beyond a given data range.
Understanding probability distributions, sampling, and hypothesis testing.
Used in probability calculations.
The bell-shaped curve and Z-scores.
Visualizing data distributions and outliers.
In project management, identifies the longest path for completing tasks.
Graph theory concept related to network flow.
Understanding functions, domain, range, and graphing.
Registration is required by 27-Sep-2024.
13.5 hours: (12-1:30pm)
Date: 30 Sep-4 Oct and 8-11 Oct 2024
Dr Amir presents online, in a lecture format, to a group of approved registered participants. Dr Amir designs the questions presented in this session based on Dr Amir's understanding of HSC and Mathematics Extension 1 and Dr Amir's Pedagogy. The materials presented are subject to Copy Right and can not be saved or copied or distributed in any format. Dr Amir presents from a selection of the following topics:
Dr. Amir’s Mathematics Tutoring: Unlocking Potential for High School Students in Extension 1 Mathematics
Dr. Amir, an experienced online mathematics tutor, is committed to helping high school students excel in their mathematical journey. His personalised approach, deep subject knowledge, and effective teaching methods make him a sought-after mentor. Let’s delve into the quality tutoring Dr. Amir provides across various topics:
In summary, Dr. Amir’s tutoring transcends rote learning. He fosters critical thinking, problem-solving, and mathematical intuition. With Dr. Amir, students not only conquer topics but also develop a lifelong love for mathematics.
Registration is required by 27-Sep-2024.
13.5 hours: (2-3:30pm)
Date: 30 Sep-4 Oct and 8-11 Oct 2024
Dr Amir presents online, in a lecture format, to a group of approved registered participants. Dr Amir designs the questions presented in this session based on Dr Amir's understanding of HSC and Mathematics Extension 2 and Dr Amir's Pedagogy. The materials presented are subject to Copy Right and can not be saved or copied or distributed in any format. Dr Amir presents from a selection of the following topics:
Dr. Amir’s Mathematics Tutoring Services: Unlocking Potential for High School Students
Are you a high school student seeking expert guidance in mathematics? Look no further! Dr. Amir’s Mathematics Tutoring offers exceptional services designed to empower students, enhance their understanding, and boost their academic performance. Let’s delve into the comprehensive topics covered by Dr. Amir’s tutoring:
Dr. Amir’s mission is clear: unleash every student’s potential. With personalized lessons, expert guidance, and a passion for teaching, Dr. Amir transforms mathematical challenges into triumphs. Whether you’re preparing for exams or seeking deeper understanding, Dr. Amir’s Mathematics Tutoring is your compass to success!
Registration is required by 27-Sep-2024.
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