Gd 11 Math

📅 Term 1: Sequences, Surds, Matrices, & Financial Math

Unit 1: Sequences & Series (3 Weeks)

• Arithmetic Progression (A.P.): Derive and apply formulas for the nth term and the sum of the first n terms of an A.P.

• Geometric Progression (G.P.): Derive and apply formulas for the nth term and the sum of the first n terms of a G.P.

Unit 2: Surds & Theory of Logarithms (3 Weeks)

• Surds: Simplify, add, subtract, and multiply surds. Rationalize denominators involving binomial surds.

• Logarithms: Solve advanced logarithmic equations. Apply changes of base rules without using tables.

Unit 3: Matrices & Determinants (2 Weeks)

• Matrix Operations: Master addition, subtraction, and scalar multiplication of matrices up to 2 × 2.

• Determinants & Inverses: Calculate the determinant and inverse of a 2 × 2 matrix. Solve simultaneous linear equations using Cramer's rule or matrix inversion.

Unit 4: Commercial Mathematics (2 Weeks)

• Depreciation & Annuities: Calculate reducing balance depreciation, simple compound interest, and basic annuities.

• Taxation & Exchange Rates: Compute value-added tax (VAT), income tax bands, and currency conversions using contemporary West African rates.

📅 Term 2: Coordinate Geometry, Circle Theorems, & Calculus

Unit 5: Linear Inequalities & Graphs (2 Weeks)

• Linear Programming: Graph systems of linear inequalities in two variables. Determine maximum and minimum values within a feasible region.

Unit 6: Circle Geometry (3 Weeks)

• Circle Theorems: Prove and apply the 8 core WAEC circle theorems (e.g., angles at the center, angles in the same segment, cyclic quadrilaterals, alternate segment theorem).

• Tangents & Chords: Calculate lengths of tangents, chords, and angles formed by intersecting chords.

Unit 7: Advanced Trigonometry (3 Weeks)

• The Sine and Cosine Rules: Apply these rules to solve acute and obtuse non-right-angled triangles.

• Bearings & Distances: Solve 3-point navigation and surveying word problems using bearings (true and compass) and trigonometry.

Unit 8: Introductory Calculus (2 Weeks)

• Differentiation: Understand the concept of limit and rate of change. Differentiate basic algebraic functions using the power rule nxn-1.

• Application: Determine the gradient of a curve at a given point and find turning points (local maxima/minima).

📅 Term 3: Vectors, Advanced Statistics, & Probability

Unit 9: Vectors in a Plane (2 Weeks)

• Vector Mechanics: Define vectors as directed line segments. Express vectors in component form .yx.

• Operations: Perform vector addition, scalar multiplication, and calculate the magnitude and direction of a resultant vector.

Unit 10: Advanced Statistics & Dispersion (4 Weeks)

• Measures of Dispersion: Calculate the range, variance, and standard deviation for both ungrouped and grouped data populations.

• Data Interpretation: Analyze curves, percentile values, and quartiles from cumulative frequency graphs (Ogives).

Unit 11: Advanced Probability (2 Weeks)

• Laws of Probability: Apply the addition law for mutually exclusive events and the multiplication law for independent events.

• Outcome Trees: Construct tree diagrams to solve complex, multi-stage conditional probability problems without replacement.