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🇵🇰 Police Constable Test · subject
Police Constable Test Mathematics Syllabus
Every chapter and topic of Mathematics examined in Police Constable Test — 5 chapters, 21 topics, plus 50 flashcards written against it.
Mathematics syllabus — full chapter and topic list
Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in Police Constable Test, not a summary of it.
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Arithmetic
5 topics- Number System
- HCF and LCM
- Fractions and Decimals
- Simplification
- Square Roots and Cube Roots
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Commercial Mathematics
6 topics- Percentage
- Profit and Loss
- Ratio and Proportion
- Average
- Simple Interest
- Discount
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Time, Distance and Work
3 topics- Time and Work
- Time, Speed and Distance
- Trains and Boats
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Basic Algebra and Geometry
4 topics- Linear Equations
- Perimeter and Area
- Volume and Surface Area
- Angles and Triangles
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Data Interpretation
3 topics- Tables
- Bar Graphs and Pie Charts
- Basic Statistics
Mathematics flashcards for Police Constable Test
21 of 50 cards from the Mathematics deck — real questions with worked answers.
What is a natural number?
A counting number starting from 1: 1, 2, 3, 4, ... (positive integers). The set is denoted N.
What is the difference between whole numbers and natural numbers?
Whole numbers include 0 along with all natural numbers (0, 1, 2, 3, ...), whereas natural numbers begin at 1.
Define a prime number and give the smallest prime.
A prime number has exactly two distinct factors: 1 and itself. The smallest prime is 2, which is also the only even prime.
What is a composite number?
A natural number greater than 1 that has more than two factors (i.e., it is divisible by numbers other than 1 and itself), e.g., 4, 6, 8, 9.
Is 1 prime, composite, or neither?
Neither. 1 has only one factor (itself), so it is neither prime nor composite.
What is the divisibility rule for 3?
A number is divisible by 3 if the sum of its digits is divisible by 3.
What is the divisibility rule for 9?
A number is divisible by 9 if the sum of its digits is divisible by 9.
What is the divisibility rule for 11?
A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11.
What is the divisibility rule for 4 and for 8?
Divisible by 4 if the last two digits form a number divisible by 4; divisible by 8 if the last three digits form a number divisible by 8.
Define HCF (Highest Common Factor).
The HCF (or GCD) of two or more numbers is the largest number that divides each of them exactly without leaving a remainder.
Define LCM (Least Common Multiple).
The LCM of two or more numbers is the smallest number that is exactly divisible by each of them.
What is the relationship between HCF, LCM and two numbers?
Product of two numbers = HCF x LCM. So for numbers a and b: a x b = HCF(a,b) x LCM(a,b).
How do you find HCF and LCM of fractions?
HCF of fractions = HCF of numerators / LCM of denominators. LCM of fractions = LCM of numerators / HCF of denominators.
For two co-prime numbers, what is their HCF and LCM?
Co-prime numbers have HCF = 1, and their LCM equals the product of the two numbers.
What is a proper fraction versus an improper fraction?
A proper fraction has numerator less than denominator (e.g., 3/4); an improper fraction has numerator greater than or equal to denominator (e.g., 5/3).
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/4 = 3 divided by 4 = 0.75.
How do you convert a recurring decimal like 0.333... to a fraction?
For a single repeating digit, the fraction is that digit over 9. So 0.333... = 3/9 = 1/3.
How do you compare two fractions such as 3/5 and 4/7?
Cross-multiply: compare 3x7=21 with 4x5=20. Since 21 > 20, 3/5 > 4/7.
What is the BODMAS / order of operations rule?
Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).
In BODMAS, how are multiplication and division handled?
They have equal priority and are performed from left to right in the order they appear, not multiplication always before division.
What is a perfect square? Give examples.
A number that is the square of an integer, e.g., 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
Planning Mathematics for Police Constable Test
Mathematics is about 17% of the Police Constable Test syllabus by topic count — 21 of 124 topics, spread over 5 chapters. At roughly 45 minutes per topic plus 12 minutes per sub-topic, a first pass runs to about 15 hours.
The heaviest chapters are Commercial Mathematics (6 topics), Arithmetic (5 topics), Basic Algebra and Geometry (4 topics) . Front-load those while your energy is high; the short chapters are better revision filler later.
Work top-down: read the chapter, then tick topics off individually rather than marking the whole chapter done. Sub-topics are where silent gaps hide.
Mathematics (Police Constable Test) FAQ
What is in the Police Constable Test Mathematics syllabus?
Mathematics is split into 5 chapters — Arithmetic, Commercial Mathematics, Time, Distance and Work, Basic Algebra and Geometry and Data Interpretation, containing 21 topics and 0 sub-topics in total.
How is Mathematics structured in the Police Constable Test syllabus?
5 chapters. Mathematics accounts for about 17% of the topics in the whole Police Constable Test syllabus (21 of 124).
How long should I spend on Mathematics for Police Constable Test?
Budget around 15 hours for a first pass through Mathematics — about 45 minutes per topic plus 12 minutes per sub-topic across its 21 topics. Add revision cycles on top.
Are there flashcards for Police Constable Test Mathematics?
Yes — a 50-card Mathematics deck. Sample cards are printed on this page, and the full deck is free in the Examius app with spaced repetition scheduling.