ASI Police Test Mathematics and Intelligence Syllabus

Mathematics and Intelligence syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics and Intelligence in ASI Police Test, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Number System and HCF/LCM
   • Fractions, Decimals and Percentages
   • Ratio, Proportion and Averages
   • Profit, Loss and Interest
2. 2

   Algebra and Geometry

   4 topics

   • Linear Equations
   • Basic Algebraic Expressions
   • Areas and Perimeters
   • Angles and Triangles
3. 3

   Quantitative Aptitude

   3 topics

   • Time, Speed and Distance
   • Time and Work
   • Data Interpretation
4. 4

   Verbal and Logical Reasoning

   4 topics

   • Analogies and Classification
   • Coding and Decoding
   • Blood Relations
   • Series Completion
5. 5

   Non-Verbal Reasoning

   3 topics

   • Figure Series and Patterns
   • Mirror and Water Images
   • Spatial Visualization

Mathematics and Intelligence flashcards for ASI Police Test

23 of 50 cards from the Mathematics and Intelligence deck — real questions with worked answers.

1. What is the difference between an HCF and an LCM of two numbers?

   HCF (Highest Common Factor) is the largest number that divides both numbers exactly; LCM (Least Common Multiple) is the smallest number that both numbers divide into exactly.

2. What is the key relationship between the product of two numbers and their HCF and LCM?

   Product of two numbers = HCF x LCM. So HCF x LCM = first number x second number.

3. How do you classify natural, whole, and integer numbers?

   Natural numbers are counting numbers (1, 2, 3...); whole numbers add zero (0, 1, 2, 3...); integers include negatives (...-2, -1, 0, 1, 2...).

4. What is a prime number, and what is the smallest prime number?

   A prime number has exactly two factors: 1 and itself. The smallest prime number is 2, which is also the only even prime.

5. What is the difference between rational and irrational numbers?

   Rational numbers can be written as a fraction p/q (q not 0), e.g. 1/2 or 0.75; irrational numbers cannot, e.g. the square root of 2 or pi.

6. What is the divisibility rule for 3?

   A number is divisible by 3 if the sum of its digits is divisible by 3.

7. What is the divisibility rule for 9?

   A number is divisible by 9 if the sum of its digits is divisible by 9.

8. 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 even positions is 0 or a multiple of 11.

9. How do you convert a fraction to a percentage?

   Multiply the fraction by 100. For example, 3/4 = (3/4) x 100 = 75%.

10. How do you convert a percentage to a decimal?

    Divide the percentage by 100 (or move the decimal point two places left). For example, 45% = 0.45.

11. What is the formula for finding x% of a number N?

    x% of N = (x / 100) x N.

12. How do you calculate the percentage increase from an old value to a new value?

    Percentage increase = ((New value - Old value) / Old value) x 100.

13. What is the fraction equivalent of the recurring decimal 0.333...?

    0.333... = 1/3.

14. If a value increases by 20% then decreases by 20%, what is the net percentage change?

    A net decrease of 4%. (1.20 x 0.80 = 0.96, so 96% of the original, a 4% loss.)

15. What is the definition of a ratio?

    A ratio is a comparison of two quantities of the same kind by division, written as a:b, showing how many times one quantity contains the other.

16. What does it mean for four quantities to be in proportion?

    Four quantities a, b, c, d are in proportion (a:b :: c:d) when a/b = c/d, i.e. the product of the extremes equals the product of the means (a x d = b x c).

17. What is the formula for the average (arithmetic mean) of a set of numbers?

    Average = (Sum of all values) / (Number of values).

18. How do you divide an amount in the ratio a:b?

    First part = (a / (a+b)) x Total amount; Second part = (b / (a+b)) x Total amount.

19. What is the average of the first n natural numbers?

    Average = (n + 1) / 2.

20. What is the difference between direct and inverse proportion?

    In direct proportion, as one quantity increases the other increases (ratio constant); in inverse proportion, as one increases the other decreases (product constant).

21. What is the formula for profit and for loss?

    Profit = Selling Price - Cost Price (when SP > CP); Loss = Cost Price - Selling Price (when CP > SP).

22. What is the formula for profit percentage?

    Profit % = (Profit / Cost Price) x 100. Profit percentage is always calculated on the cost price.

23. What is the formula for simple interest?

    Simple Interest (SI) = (Principal x Rate x Time) / 100, where rate is per annum and time is in years.

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