IMAT Mathematics [Active learning tutor]
Course Content
[Section-1] Numbers and Algebra
1.1 • Properties of Numbers
1.2 • Fractions, Decimals, Percentages
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iii. Percentage change, profit/loss
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iv. Unit conversions (e.g., mg → g)
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1.3 Algebraic Manipulations
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i. Simplifying expressions
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ii. Factorization, expansion
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iii. Algebraic fractions
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Algebraic Manipulations Full Chapter Test with Step by Step Explanations
1.4 Equations and Inequalities
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i. Linear, quadratic, simultaneous equations
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ii. Absolute value equations/inequalities
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iii. Inequalities (number line graphing)
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Equations and Inequalities Full Chapter Test with Step by Step Explanation
1.5 Exponents and Surds
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i. Laws of exponents
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ii. Simplifying surds, rationalizing denominators
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iii. Logarithms (basic properties)
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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)
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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
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ii. Composite/inverse (basic)
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iii. Piecewise functions
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Functions Full Chapter Test with Step by Step Explanation
2.2 : Graphs
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i. Linear, quadratic, cubic, exponential, reciprocal
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ii. Key features: intercepts, vertices, asymptotes
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iii. Transformations (shifts, reflections)
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iii. Graphical interpretation (e.g., medical data)
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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)
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ii. Congruence, similarity
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iii. Pythagoras, trigonometry (SOHCAHTOA, sine/cosine rules)
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Full Chapter Test with Explanations
3.2 : Coordinate Geometry
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i. Distance, midpoint, gradient
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ii. Equation of a line, intersection points
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iii. 3D coordinates (distance between points)
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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)
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ii. Density/mass/volume problems
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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°)
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ii. Solving right-angled triangles
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iii. sin²θ + cos²θ = 1, tanθ = sinθ/cosθ
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iv. sin/cos/tan graphs (period, amplitude)
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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
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ii. Tangents/normals
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iii. Area under curves (linear/quadratic)
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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
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ii. Standard deviation (conceptual)
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iii. Data interpretation (tables, graphs)
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Statistics Full Chapter Test with Step by Step Explanations
6.2: Probability
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i. Basic rules (addition, multiplication)
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ii. Conditional probability (added)
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iii. Venn diagrams, probability trees
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iii. Combinatorics (nCr, nPr) (rare)
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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
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ii. Truth tables
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Logical Reasoning Full Chapter Test with Explanations
7.2: Word Problems
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i. Medical contexts (dosages, concentrations)
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Word Problems Full Chapter Test with Step by Step Explanations
