PAF GD Pilot Mathematics Syllabus

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 PAF GD Pilot, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Number System
   • Fractions and Decimals
   • Percentages
   • Ratio and Proportion
2. 2

   Commercial Mathematics

   3 topics

   • Profit and Loss
   • Simple and Compound Interest
   • Discount and Markup
3. 3

   Algebra

   4 topics

   • Algebraic Expressions and Factorization
   • Linear Equations
   • Quadratic Equations
   • Algebraic Identities
4. 4

   Geometry

   4 topics

   • Lines and Angles
   • Triangles and Their Properties
   • Circles
   • Polygons
5. 5

   Mensuration

   2 topics

   • Area and Perimeter
   • Surface Area and Volume
6. 6

   Trigonometry

   3 topics

   • Trigonometric Ratios
   • Heights and Distances
   • Trigonometric Identities
7. 7

   Time, Speed and Work

   3 topics

   • Time and Distance
   • Time and Work
   • Average, Age and Mixtures
8. 8

   Data Interpretation

   3 topics

   • Tables and Bar Graphs
   • Pie Charts and Line Graphs
   • Basic Probability and Statistics

Mathematics flashcards for PAF GD Pilot

21 of 56 cards from the Mathematics deck — real questions with worked answers.

1. What is a natural number? Give the set.

   Counting numbers starting from 1: {1, 2, 3, 4, ...}. They do not include 0, negatives, or fractions.

2. What are whole numbers and how do they differ from natural numbers?

   Whole numbers are {0, 1, 2, 3, ...}. They are the natural numbers together with 0 — the only difference is the inclusion of 0.

3. Define an integer and give the set.

   Integers are positive and negative whole numbers and zero: {..., -3, -2, -1, 0, 1, 2, 3, ...}. No fractions or decimals.

4. What is a rational number?

   A number that can be written as p/q where p and q are integers and q ≠ 0. Its decimal form either terminates or repeats. Example: 3/4, 0.75, -5.

5. What is an irrational number? Give two examples.

   A number that cannot be written as p/q; its decimal is non-terminating and non-repeating. Examples: √2 and π.

6. Define a prime number and give the smallest prime.

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

7. What is a composite number?

   A natural number greater than 1 that has more than two factors (i.e., it has at least one factor besides 1 and itself). Example: 4, 6, 9.

8. Is 1 prime, composite, or neither? Why?

   Neither. It has only one factor (itself), not the two required for prime, and it is not composite.

9. State the divisibility rule for 3.

   A number is divisible by 3 if the sum of its digits is divisible by 3. Example: 372 → 3+7+2 = 12, which is divisible by 3, so 372 is divisible by 3.

10. State the divisibility rules for 4 and 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.

11. State the divisibility rule for 9 and for 11.

    By 9: the digit sum is divisible by 9. By 11: the difference between the sum of digits in odd places and even places is 0 or a multiple of 11.

12. What is the difference between HCF (GCD) and LCM?

    HCF is the largest number that divides two or more numbers exactly. LCM is the smallest number that is a multiple of those numbers. For two numbers a and b: HCF × LCM = a × b.

13. How do you convert a fraction to a decimal?

    Divide the numerator by the denominator. Example: 3/8 = 3 ÷ 8 = 0.375.

14. How do you convert a terminating decimal to a fraction?

    Write the decimal over a power of 10 equal to the number of decimal places, then simplify. Example: 0.75 = 75/100 = 3/4.

15. How do you add two fractions with different denominators?

    Find the LCM of the denominators, convert each fraction to that common denominator, add the numerators, and simplify. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.

16. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal of the second (invert and multiply). Example: (2/3) ÷ (4/5) = (2/3) × (5/4) = 10/12 = 5/6.

17. What is the difference between a proper and an improper fraction?

    A proper fraction has numerator smaller than denominator (value < 1), e.g. 3/5. An improper fraction has numerator ≥ denominator (value ≥ 1), e.g. 7/4.

18. How do you convert a percentage to a fraction and to a decimal?

    To a fraction: write it over 100 and simplify (e.g. 40% = 40/100 = 2/5). To a decimal: divide by 100 (e.g. 40% = 0.40).

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

    Multiply the fraction by 100. Example: 3/4 × 100 = 75%.

20. How do you find what percentage one number is of another?

    Percentage = (part ÷ whole) × 100. Example: 15 out of 60 = (15/60) × 100 = 25%.

21. Give the formula for percentage increase and percentage decrease.

    % increase = (increase ÷ original) × 100. % decrease = (decrease ÷ original) × 100, where increase/decrease is the change from the original value.

See more Mathematics flashcards →

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