16 pages
TKA SMP
Arithmetic with Real Numbers
Order of operations with powers and roots, sign rules for negative numbers, and the −3² versus (−3)² trap.
5 worked examples · 10 practice problems · answer key
Free PDF modules
Free PDF modules for exam preparation
Selected modules on the most frequently tested topics in TKA Mathematics SMP, UTBK, and CPNS SKD. Each module has a concept summary, worked examples, graded practice, and an answer key that has been checked again.
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Sign in or sign upTKA Mathematics SMP
16 pages
TKA SMP
Systems of Two Linear Equations
Substitution and elimination, choosing the faster method, and word problems about prices and ages.
5 worked examples · 10 practice problems · answer key
16 pages
TKA SMP
The Pythagorean Theorem
Finding the hypotenuse and the legs, Pythagorean triples, and word problems about ladders, diagonals, and distances.
5 worked examples · 10 practice problems · answer key
16 pages
TKA SMP
Mean, Median, Mode, and Range
Four data measures, medians of odd and even data sets, the effect of outliers, and choosing the most representative measure.
5 worked examples · 10 practice problems · answer key
UTBK (SNBT)
20 pages
UTBK · Quantitative Knowledge
Direct Proportion
Constant of proportionality, unit price, proportions, map scales, and testing whether a relationship is truly proportional.
5 worked examples · 10 practice problems · answer key
20 pages
UTBK · Quantitative Knowledge
Profit, Loss, Discounts, and Tax
Percent bases, multipliers, stacked discounts, tax after discount, and working back to the original price.
5 worked examples · 10 practice problems · answer key
22 pages
UTBK · Mathematical Reasoning
Turning Context into a Mathematical Model
Separating information and constraints, defining variables with their domains, building the model, and auditing a flawed one.
5 worked examples · 10 practice problems · answer key
CPNS SKD
84 pages
CPNS SKD · TIU
CPNS TIU 2026 Complete Module
All the General Intelligence Test (TIU) material for the CPNS SKD: verbal, arithmetic, number series, quantitative comparison, word problems, and figural reasoning, with quick strategies and a target time per question.
6 chapters · 52 worked examples · 60 SKD-format practice problems · answer key with explanations
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