IGCSE & DSAT Math Specialist - Parshwa M

The IGCSE Mathematics course is designed to build a strong foundation in mathematical concepts, reasoning, and problem-solving. While specific details vary slightly by exam board (Cambridge vs. Edexcel), the core syllabus is largely consistent.

The syllabus is divided into four major domain areas.

A. Number

Foundational arithmetic and numerical fluency.

• Integers, Decimals, & Fractions: Order of operations (BODMAS), directed numbers, converting between forms.

• Number Theory: Prime numbers, factors, multiples (HCF/LCM), square/cube roots.

• Set Notation: Venn diagrams, union, intersection, complement.

• Ratios & Proportions: Map scales, direct and inverse proportion, dividing quantities in ratios.

• Percentages: Simple and compound interest, reverse percentages, percentage increase/decrease.

• Standard Form: Writing and calculating with large/small numbers.

• Estimation & Limits: Significant figures, decimal places, upper and lower bounds.

B. Algebra

Manipulation of symbols and solving equations.

• Expressions: Expanding brackets, factorizing (common factors, difference of two squares, quadratics), algebraic fractions.

• Equations: Linear equations, simultaneous equations (linear & non-linear), quadratic equations (factorization, formula, completing the square).

• Formulas: Substituting values, rearranging subject of a formula.

• Inequalities: Solving linear/quadratic inequalities and representing them on number lines/graphs.

• Sequences: Arithmetic and geometric progressions, $n$-th term formulas.

• Indices (Exponents): Laws of indices, negative and fractional indices.

• Functions: Notation f(x), inverse functions, composite functions.

• Graphs: Linear (y=mx+c), quadratic, cubic, reciprocal, and exponential graphs. Gradients and area under curves (specific to Higher tier).

C. Shape, Space & Measures (Geometry)

Visualizing and calculating with 2D/3D shapes.

• Euclidean Geometry: Angles, parallel lines, polygons (interior/exterior angles).

• Mensuration: Perimeter, area (circles, trapeziums, triangles), volume and surface area (cylinders, spheres, cones, pyramids).

• Co-ordinate Geometry: Midpoints, distance between points, equation of a line.

• Trigonometry: Pythagoras' theorem, SOH CAH TOA, Sine and Cosine rules, Area of a triangle formula, 3D trigonometry.

• Transformations: Reflection, Rotation, Translation (vectors), Enlargement (scale factors).

• Vectors: Column vectors, vector addition/subtraction, geometric proofs.

• Circle Theorems: Tangents, chords, alternate segment theorem, cyclic quadrilaterals.

D. Probability & Statistics

Handling data and chance.

• Data Representation: Bar charts, pie charts, histograms (frequency density), scatter diagrams (correlation), stem-and-leaf plots.

• Measures of Central Tendency: Mean, median, mode, and range.

• Cumulative Frequency: Box-and-whisker plots, quartiles, interquartile range (IQR).

• Probability: Tree diagrams, conditional probability, mutually exclusive/independent events.

A highly passionate and results-driven Mathematics Professional with a proven track record of guiding students to achieve exceptional scores in IGCSE and SAT Math. With X years of experience (or "extensive experience"), I specialize in demystifying complex mathematical concepts, fostering strong problem-solving skills, and building student confidence.

My approach combines in-depth curriculum knowledge with personalized teaching methodologies, ensuring each student receives tailored support to meet their individual learning styles and academic goals. I am adept at identifying learning gaps and developing targeted strategies to transform challenges into triumphs.

I am committed to empowering students not just to pass exams, but to develop a genuine understanding and appreciation for mathematics, setting them up for long-term academic and career success.

Key Skills:

• IGCSE Mathematics (Core & Extended)

• SAT Math (Algebra, Problem Solving & Data Analysis, Passport to Advanced Math, Geometry, Trigonometry)

• Test Preparation Strategies

• Curriculum Development

• Personalized Tutoring

• Differentiated Instruction

• Problem-Solving

• Critical Thinking

• Student Engagement

• Performance Analysis & Feedback

• Online & In-Person Instruction