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ASI Police Test Mathematics and Intelligence Syllabus

The Mathematics and Intelligence syllabus for ASI Police Test in full: 5 chapters and 18 topics, every one listed below, plus 50 Mathematics and Intelligence flashcards with answers.

5Chapters
18Topics
50Flashcards

Mathematics and Intelligence syllabus: all 5 chapters

Expand any chapter to see its topics and sub-topics.

  1. Arithmetic

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

  2. Algebra and Geometry

     4 topics
    • Linear Equations
    • Basic Algebraic Expressions
    • Areas and Perimeters
    • Angles and Triangles

  3. Quantitative Aptitude

     3 topics
    • Time, Speed and Distance
    • Time and Work
    • Data Interpretation

  4. Verbal and Logical Reasoning

     4 topics
    • Analogies and Classification
    • Coding and Decoding
    • Blood Relations
    • Series Completion

  5. Non-Verbal Reasoning

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

ASI Police Test Mathematics and Intelligence flashcards — 50 questions with 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).

Show the other 30 Mathematics and Intelligence flashcards

  1. 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).

  2. What is the formula for profit percentage?

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

  3. 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.

  4. What is the formula for the amount under compound interest?

    Amount = Principal x (1 + R/100)^T, where R is the annual rate and T is the time in years. Compound Interest = Amount - Principal.

  5. How do you find the Selling Price when Cost Price and profit percentage are known?

    Selling Price = Cost Price x (100 + Profit%) / 100.

  6. What is discount and how is discount percentage calculated?

    Discount = Marked Price - Selling Price. Discount % = (Discount / Marked Price) x 100. Discount is calculated on the marked price.

  7. What is a linear equation in one variable?

    An equation of the form ax + b = 0 (a not 0), where the highest power of the variable is 1; it has exactly one solution: x = -b/a.

  8. How do you solve the linear equation 2x + 5 = 15?

    Subtract 5 from both sides: 2x = 10, then divide by 2: x = 5.

  9. What methods can be used to solve a pair of simultaneous linear equations?

    Substitution, elimination, and cross-multiplication (and graphically as the point of intersection of two lines).

  10. What is the standard form of a linear equation in two variables?

    ax + by + c = 0, where a and b are not both zero; its graph is a straight line.

  11. What is the identity for (a + b) squared?

    (a + b)^2 = a^2 + 2ab + b^2.

  12. What is the identity for (a - b) squared?

    (a - b)^2 = a^2 - 2ab + b^2.

  13. What is the identity for a squared minus b squared?

    a^2 - b^2 = (a + b)(a - b).

  14. In algebra, what is the difference between a monomial, binomial, and trinomial?

    A monomial has one term (e.g. 3x); a binomial has two terms (e.g. x + 2); a trinomial has three terms (e.g. x^2 + 3x + 2).

  15. What is the difference between a coefficient and a constant in an algebraic expression?

    A coefficient is the numerical factor multiplying a variable (the 5 in 5x); a constant is a fixed number with no variable (the 7 in 5x + 7).

  16. What is the formula for the area and perimeter of a rectangle?

    Area = length x breadth; Perimeter = 2 x (length + breadth).

  17. What is the formula for the area and perimeter of a square?

    Area = side^2; Perimeter = 4 x side.

  18. What are the formulas for the area and circumference of a circle?

    Area = pi x r^2; Circumference = 2 x pi x r, where r is the radius and pi is approximately 22/7 or 3.14.

  19. What is the formula for the area of a triangle given base and height?

    Area = (1/2) x base x height.

  20. What is the area of a triangle by Heron's formula?

    Area = sqrt(s(s-a)(s-b)(s-c)), where a, b, c are the sides and s = (a+b+c)/2 is the semi-perimeter.

  21. What is the sum of the interior angles of a triangle?

    The sum of the interior angles of any triangle is 180 degrees.

  22. How are angles classified as acute, right, obtuse, and reflex?

    Acute is less than 90 degrees; right is exactly 90 degrees; obtuse is between 90 and 180 degrees; reflex is between 180 and 360 degrees.

  23. What is the difference between complementary and supplementary angles?

    Complementary angles add up to 90 degrees; supplementary angles add up to 180 degrees.

  24. What does the Pythagorean theorem state for a right-angled triangle?

    The square of the hypotenuse equals the sum of the squares of the other two sides: hypotenuse^2 = base^2 + perpendicular^2.

  25. What is the basic formula relating speed, distance, and time?

    Speed = Distance / Time. Therefore Distance = Speed x Time and Time = Distance / Speed.

  26. How do you convert a speed from km/h to m/s?

    Multiply by 5/18. For example, 36 km/h = 36 x 5/18 = 10 m/s.

  27. What is the formula for relative speed of two objects moving in the same and opposite directions?

    Same direction: relative speed = difference of speeds; Opposite directions: relative speed = sum of speeds.

  28. How do you find the combined time for two people to finish a job working together?

    If one does it in x days and the other in y days, together they take (x x y) / (x + y) days; their combined one-day work is 1/x + 1/y.

  29. In data interpretation, what does each component of a pie chart represent and how do you find the angle for a category?

    Each sector represents a category's share of the whole; angle of a category = (category value / total) x 360 degrees.

  30. In an analogy or classification reasoning question, what is the task in each type?

    In an analogy, find a pair related the same way as a given pair (A:B :: C:?); in classification (odd-one-out), identify the item that does not share the common property of the group.

ASI Police Test Mathematics and Intelligence FAQ

What is in the ASI Police Test Mathematics and Intelligence syllabus?

ASI Police Test Mathematics and Intelligence is split into 5 chapters: Arithmetic, Algebra and Geometry, Quantitative Aptitude, Verbal and Logical Reasoning and Non-Verbal Reasoning. Together they contain 18 topics.

How many chapters are in ASI Police Test Mathematics and Intelligence?

5 chapters, containing 18 topics. The largest chapter is Arithmetic, with 4 topics.

Are there flashcards for ASI Police Test Mathematics and Intelligence?

Yes — a 50-card Mathematics and Intelligence deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.