CSEC Mathematics 2025: Complete Formula and Concept Guide
Question 1: Numeracy / Consumer Arithmetic
- Simple Interest: I = (P R T) / 100
- Compound Interest: A = P(1 + r/100)^n
- Percentage Change:
- Increase: ((New - Old)/Old) 100
- Decrease: ((Old - New)/Old) 100
- Profit/Loss:
- Profit = Selling Price - Cost Price
- Loss = Cost Price - Selling Price
- Profit/Loss % = (Profit or Loss / Cost Price) 100
- Discount = Marked Price - Selling Price
- VAT/GCT = Price (Rate/100)
Question 2: Algebra
- Expanding:
- (a + b)^2 = a^2 + 2ab + b^2
- (a - b)^2 = a^2 - 2ab + b^2
- (a + b)(a - b) = a^2 - b^2
- Factorising:
- Common Factor: ab + ac = a(b + c)
- Quadratic: ax^2 + bx + c (px + q)(rx + s)
- Laws of Indices:
- a^m * a^n = a^(m+n)
- a^m / a^n = a^(m-n)
- (a^m)^n = a^(mn)
- a^0 = 1, a^-n = 1/a^n
- Transposition of Formulae
- Inequalities
Question 3: Geometry / Trigonometry / Transformations
- Pythagoras Theorem: a^2 + b^2 = c^2
- Trigonometric Ratios:
- sin = opposite/hypotenuse
- cos = adjacent/hypotenuse
- tan = opposite/adjacent
- Area of Triangle: A = 1/2 ab sin C
- Sine Rule: a/sin A = b/sin B = c/sin C
- Cosine Rule: c^2 = a^2 + b^2 - 2ab cos C
- Transformations: Reflection, Rotation, Translation, Enlargement
Question 4: Straight Lines / Functions
- Gradient: m = (y2 - y1)/(x2 - x1)
- Equation of Line: y = mx + c, or y - y1 = m(x - x1)
- Parallel Lines: same gradient
- Perpendicular Lines: product of gradients = -1
- Function Notation: f(x), composite f(g(x)), inverse f^-1(x)
Question 5: Statistics
- Mean = x/n
- Median = middle value
- Mode = most frequent value
- Range = Max - Min
- Estimated Mean (Grouped Data): fx / f
- Cumulative Frequency
Question 6: Measurement
- Area:
- Triangle: 1/2 bh
- Rectangle: lw
- Parallelogram: bh
- Trapezium: 1/2(a + b)h
- Circle: r^2
- Circumference: 2r
- Volume:
- Cube: a^3
- Cuboid: lwh
- Cylinder: r^2h
- Cone: 1/3r^2h
- Sphere: 4/3r^3
- Surface Area: based on shape formulas
Question 7: Patterns
- Linear: Tn = a + (n - 1)d
- Geometric: Tn = ar^(n-1)
- Recursive: Tn = Tn-1 + Tn-2
Question 8: Quadratics / Linear Programming
- Quadratic Equation Standard: ax^2 + bx + c = 0
- Methods: Factorising, Completing the Square, Quadratic Formula
- Nature of Roots: b^2 - 4ac
- Graph:
- Axis of symmetry: x = -b/2a
- Vertex: (-b/2a, f(-b/2a))
- Linear Programming: Inequalities, feasible region, objective function
Question 9: Trigonometry
- Ratios: sin, cos, tan
- Use sine and cosine rules
- Solve triangles
Question 10: Vectors
- Vector: x, y or [x, y]
- Addition: a1 + b1, a2 + b2
- Scalar Multiplication: ka1, a2
- Magnitude: (a1^2 + a2^2)
- Direction: tan(y/x)
- Displacement and position vectors