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IMAT Mathematics [Active learning tutor]

📊 What to Focus On? Priority Topics High Algebra, percentages, probability, geometry, basic trig Medium Functions, exponents, inequalities, sequences Low Calculus, vectors, logarithms 🗑️ Topics to Skip (Not in IMAT) Complex numbers Matrices Advanced calculus (chain rule, integration by parts) Advanced trig (double-angle identities) Proof by induction

Instructor naveedhameed55533

Updated August 12, 2025

Course Content

[Section-1] Numbers and Algebra

1.1 • Properties of Numbers

1.2 • Fractions, Decimals, Percentages

1.3 Algebraic Manipulations

1.4 Equations and Inequalities

1.5 Exponents and Surds

1.6 Sequences & Series

[Section-2] Functions and Graphs

2.1 : Functions

2.2 : Graphs

[Section-3] Geometry and Mensuration

3.1 : Lines and Angles AND Plain Geometry

3.2 : Coordinate Geometry

3.3 : Mensuration

[Section-4] Trigonometry

4.1 : Trigonometric Ratios, Identities & Graphs

[Section-5] Calculus (Basic) (Low priority)

5.1: Differentiation AND Integration

[Section-6] Probability and Statistics

6.1: Statistics

6.2: Probability

[Section-7] Logic and Problem Solving

7.1: Logical Reasoning

7.2: Word Problems

IMAT Mathematics [Active learning tutor]

Course Content

[Section-1] Numbers and Algebra

1.1 • Properties of Numbers

1.2 • Fractions, Decimals, Percentages

iii. Percentage change, profit/loss

iv. Unit conversions (e.g., mg → g)

1.3 Algebraic Manipulations

i. Simplifying expressions

ii. Factorization, expansion

iii. Algebraic fractions

Algebraic Manipulations Full Chapter Test with Step by Step Explanations

1.4 Equations and Inequalities

i. Linear, quadratic, simultaneous equations

ii. Absolute value equations/inequalities

iii. Inequalities (number line graphing)

Equations and Inequalities Full Chapter Test with Step by Step Explanation

1.5 Exponents and Surds

i. Laws of exponents

ii. Simplifying surds, rationalizing denominators

iii. Logarithms (basic properties)

Exponents and Surds Full Chapter Test with Step by Step Explanations

1.6 Sequences & Series

i. Arithmetic/geometric sequences (simple problems)

Sequences & Series Full Chapter Test with step by step Explanation

[Section-2] Functions and Graphs

2.1 : Functions

i. Domain, range, notation

ii. Composite/inverse (basic)

iii. Piecewise functions

Functions Full Chapter Test with Step by Step Explanation

2.2 : Graphs

i. Linear, quadratic, cubic, exponential, reciprocal

ii. Key features: intercepts, vertices, asymptotes

iii. Transformations (shifts, reflections)

iii. Graphical interpretation (e.g., medical data)

Graphs Full Chapter Test with Step by Step Explanations

[Section-3] Geometry and Mensuration

3.1 : Lines and Angles AND Plain Geometry

i. Parallel lines, polygons, circle theorems (basic)

ii. Congruence, similarity

iii. Pythagoras, trigonometry (SOHCAHTOA, sine/cosine rules)

Full Chapter Test with Explanations

3.2 : Coordinate Geometry

i. Distance, midpoint, gradient

ii. Equation of a line, intersection points

iii. 3D coordinates (distance between points)

Coordinate Geometry Full Chapter Test with Step by Step Explanations

3.3 : Mensuration

i. Area/perimeter (2D), surface area/volume (3D)

ii. Density/mass/volume problems

Mensuration Full Chapter Test with Step By Step Explanations

[Section-4] Trigonometry

4.1 : Trigonometric Ratios, Identities & Graphs

i. sin, cos, tan (standard angles: 0°, 30°, 45°, 60°, 90°)

ii. Solving right-angled triangles

iii. sin²θ + cos²θ = 1, tanθ = sinθ/cosθ

iv. sin/cos/tan graphs (period, amplitude)

Full Chapter test with Step by Step Explanations

[Section-5] Calculus (Basic) (Low priority)

5.1: Differentiation AND Integration

i. Derivatives of polynomials

ii. Tangents/normals

iii. Area under curves (linear/quadratic)

Differentiation AND Integration Test with Step by Step Explanations

[Section-6] Probability and Statistics

6.1: Statistics

i. Mean, median, mode, range

ii. Standard deviation (conceptual)

iii. Data interpretation (tables, graphs)

Statistics Full Chapter Test with Step by Step Explanations

6.2: Probability

i. Basic rules (addition, multiplication)

ii. Conditional probability (added)

iii. Venn diagrams, probability trees

iii. Combinatorics (nCr, nPr) (rare)

Probability Full Chapter Test with Step by Step Explanations

[Section-7] Logic and Problem Solving

7.1: Logical Reasoning

i. Deduction, number sequences