PPSC Assistant Director Test Mathematics and Analytical Reasoning Syllabus

Mathematics and Analytical Reasoning 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 Analytical Reasoning in PPSC Assistant Director Test, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Number System and Simplification
   • Ratio, Proportion and Percentage
   • Profit, Loss and Discount
   • Average, Time and Work
2. 2

   Algebra and Basic Mathematics

   3 topics

   • Equations and Expressions
   • HCF and LCM
   • Powers, Roots and Indices
3. 3

   Logical and Analytical Reasoning

   4 topics

   • Series and Sequences
   • Coding and Decoding
   • Blood Relations and Directions
   • Analogies and Classification
4. 4

   Data Interpretation

   3 topics

   • Tables and Graphs
   • Data Sufficiency
   • Puzzles and Arrangements

Mathematics and Analytical Reasoning flashcards for PPSC Assistant Director Test

19 of 50 cards from the Mathematics and Analytical Reasoning deck — real questions with worked answers.

1. What is the difference between a rational and an irrational number?

   A rational number can be expressed as a fraction p/q where q is not zero (e.g., 3/4, 0.25); an irrational number cannot be written as such a fraction and has a non-terminating, non-repeating decimal (e.g., pi, square root of 2).

2. State the BODMAS/BIDMAS order of operations used in simplification.

   Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

3. What are prime numbers, and what is the only even prime number?

   Prime numbers have exactly two distinct factors, 1 and themselves. The only even prime number is 2.

4. What is the divisibility rule for 3 and for 9?

   A number is divisible by 3 if the sum of its digits is divisible by 3; divisible by 9 if the sum of its digits is divisible by 9.

5. 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.

6. What is the sum of the first n natural numbers?

   n(n + 1) / 2.

7. What is the sum of the squares of the first n natural numbers?

   n(n + 1)(2n + 1) / 6.

8. Define a ratio and explain what the terms 'antecedent' and 'consequent' mean.

   A ratio a:b compares two quantities by division. The first term, a, is the antecedent and the second term, b, is the consequent.

9. What is a proportion, and what relationship holds in a:b = c:d?

   A proportion states two ratios are equal. In a:b = c:d, the product of the means equals the product of the extremes: b times c = a times d.

10. How do you convert a fraction to a percentage and vice versa?

    Multiply a fraction by 100 to get a percentage; divide a percentage by 100 to get a fraction (e.g., 3/5 = 60%; 40% = 0.4).

11. If a quantity increases from A to B, how is the percentage increase calculated?

    Percentage increase = ((B - A) / A) x 100.

12. What is the formula for the mean proportional (geometric mean) between a and b?

    Mean proportional = square root of (a x b).

13. Define direct proportion versus inverse proportion.

    In direct proportion, two quantities increase or decrease together (x/y constant). In inverse proportion, one increases as the other decreases (x times y constant).

14. What is the formula for profit and the profit percentage?

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

15. What is the formula for loss and the loss percentage?

    Loss = Cost Price - Selling Price. Loss % = (Loss / Cost Price) x 100.

16. What is discount, and on what value is it calculated?

    Discount is a reduction on the marked (list) price. Discount = Marked Price - Selling Price, and discount % is calculated on the Marked Price.

17. Give the formula for Selling Price in terms of Cost Price and profit percentage.

    SP = CP x (100 + Profit %) / 100. For a loss: SP = CP x (100 - Loss %) / 100.

18. If two successive discounts of x% and y% are given, what is the single equivalent discount?

    Equivalent discount % = x + y - (xy / 100).

19. What is the formula for the average (arithmetic mean) of a set of values?

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

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