Mathematics
14 topics · 4 sections · Numbers, Algebra, Measurement, Statistics & Probability
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Your Maths Progress
Complete all 14 topics. Each topic has worked examples, key formulas, and 8 MCQs.
Topics
A — Numbers & Operations
A1. Multiples & Factors
HCF × LCM = a × bA2. Prime & Composite Numbers
2, 3, 5, 7, 11, 13, 17, 19A3. Ratio, Rate & Percentage
% = (Part / Whole) × 100A4. Simple & Compound Interest
SI = PRT/100A5. Financial Arithmetic
Profit% on CP · Discount% on MPB — Algebra
B1. Algebraic Expressions
(a+b)² = a²+2ab+b²B2. Equations & Inequalities
x = [−b ± √(b²−4ac)] / 2aB3. Coordinate Geometry
m = (y₂−y₁) / (x₂−x₁)B4. Patterns & Sequences
aₙ = a + (n−1)dC — Measurement
C1. Surface Area & Volume
V = πr²h · V = (4/3)πr³C2. Time & Speed
S = D/T · D = S×T · T = D/SC3. Unit Conversion
1 km = 1000 m · 1 kg = 1000 gD — Statistics & Probability
Formula Reference Sheet
HCF & LCM
HCF × LCM = a × bProduct of the two numbers
Simple Interest
SI = PRT / 100P=Principal · R=Rate · T=Time(yrs)
Compound Interest
A = P(1 + R/100)ⁿCI = A − P
% Change
% = (Change / Original) × 100Always divide by ORIGINAL
Quadratic Formula
x = [−b ± √(b²−4ac)] / 2aD=b²−4ac: >0 two roots, =0 one, <0 none
Slope
m = (y₂−y₁) / (x₂−x₁)Parallel: equal slopes · Perp: m₁×m₂=−1
Distance
d = √[(x₂−x₁)² + (y₂−y₁)²]From Pythagoras theorem
Arithmetic nth Term
aₙ = a + (n−1)da = first term · d = common difference
Sum 1…n
Sₙ = n(n+1) / 2Sum of first n natural numbers
Cylinder
V = πr²h · TSA = 2πr(r+h)π ≈ 22/7 or 3.14159
Sphere & Cone
V = (4/3)πr³ · V = (1/3)πr²hBoth cone and pyramid use ⅓
Key Identities
(a+b)² = a²+2ab+b²a²−b² = (a+b)(a−b)
Mean (freq. table)
Mean = Σfx / Σff = frequency · x = value
Probability
P(A') = 1 − P(A)P ranges: 0 (impossible) → 1 (certain)