Course Content

[Section-1] Numbers and Algebra

1.1 • Properties of Numbers

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i. Natural, integers, rational/irrational

ii. Prime numbers, LCM, GCD

iii. Scientific notation, significant figures

iv. Absolute value

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1.2 • Fractions, Decimals, Percentages

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ii. Conversions, ratios, proportions

iii. Percentage change, profit/loss

iv. Unit conversions (e.g., mg → g)

Fractions, Decimals, Percentages Full Chapter Test with Step by Step Explanations

1.3 Algebraic Manipulations

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i. Simplifying expressions

ii. Factorization, expansion

iii. Algebraic fractions

Algebraic Manipulations Full Chapter Test with Step by Step Explanations

1.4 Equations and Inequalities

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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

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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

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i. Arithmetic/geometric sequences (simple problems)

Sequences & Series Full Chapter Test with step by step Explanation

[Section-2] Functions and Graphs

2.1 : Functions

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i. Domain, range, notation

ii. Composite/inverse (basic)

iii. Piecewise functions

Functions Full Chapter Test with Step by Step Explanation

2.2 : Graphs

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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

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

ii. Congruence, similarity

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

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3.2 : Coordinate Geometry

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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

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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

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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

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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

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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

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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

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i. Deduction, number sequences

ii. Truth tables

Logical Reasoning Full Chapter Test with Explanations

7.2: Word Problems

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i. Medical contexts (dosages, concentrations)

Word Problems Full Chapter Test with Step by Step Explanations

IMAT Mathematics [Active learning tutor]

IMAT Math Preparation - Properties of Numbers

IMAT Math Preparation

Topic: Properties of Numbers

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