ISSB Academic and Initial Tests Syllabus

Academic and Initial Tests syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Academic and Initial Tests in ISSB, not a summary of it.

1. 1

   Mathematics

   5 topics

   • Arithmetic and Percentages
   • Ratio, Proportion and Averages
   • Algebra Basics
   • Geometry and Mensuration
   • Profit, Loss and Interest
2. 2

   English

   5 topics

   • Grammar and Tenses
   • Vocabulary and Idioms
   • Comprehension
   • Sentence Correction
   • Synonyms and Antonyms
3. 3

   General Knowledge

   5 topics

   • Pakistan Studies
   • Islamic Studies
   • Current Affairs
   • World Geography and History
   • Defense and Armed Forces Knowledge
4. 4

   Basic Science

   4 topics

   • Everyday Physics
   • Basic Chemistry
   • Biology and Human Body
   • Computer Fundamentals

Academic and Initial Tests flashcards for ISSB

25 of 50 cards from the Academic and Initial Tests deck — real questions with worked answers.

1. What is the formula to express a number X as a percentage of a number Y?

   (X / Y) × 100. For example, 30 as a percentage of 150 = (30/150) × 100 = 20%.

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

   Percentage increase = ((New value − Old value) / Old value) × 100.

3. If a quantity is increased by 20% and then decreased by 20%, what is the net percentage change?

   A net decrease of 4%. (Successive change = a + b + ab/100 = 20 − 20 + (20×−20)/100 = −4%.)

4. How do you find the original value when a final value and the percentage change are known (reverse percentage)?

   Original = Final value ÷ (1 ± rate/100). For a 25% increase giving 250: Original = 250 ÷ 1.25 = 200.

5. What is the formula relating a ratio a:b to two actual quantities sharing a total T?

   Each share = (ratio part / sum of ratio parts) × Total. For a:b sharing T, first = a/(a+b) × T, second = b/(a+b) × T.

6. In a proportion a:b = c:d, what is the key cross-multiplication rule?

   The product of the means equals the product of the extremes: b × c = a × d.

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

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

8. If the average of 5 numbers is 20 and one number is removed leaving an average of 18 for 4 numbers, what was the removed number?

   28. (Total of 5 = 100; total of 4 = 72; removed = 100 − 72 = 28.)

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

   In direct proportion, as one quantity increases the other increases at the same rate (x/y constant). In inverse proportion, as one increases the other decreases (x × y constant).

10. What is the formula for combined (weighted) average when two groups of sizes n1 and n2 have averages A1 and A2?

    Combined average = (n1·A1 + n2·A2) / (n1 + n2).

11. What does the algebraic identity (a + b)² expand to?

    (a + b)² = a² + 2ab + b².

12. What does the identity (a − b)² expand to?

    (a − b)² = a² − 2ab + b².

13. What is the factorisation of a² − b² (difference of two squares)?

    a² − b² = (a + b)(a − b).

14. What is the quadratic formula for solving ax² + bx + c = 0?

    x = [−b ± √(b² − 4ac)] / (2a).

15. In a quadratic ax² + bx + c = 0, what does the discriminant b² − 4ac tell you?

    If > 0, two distinct real roots; if = 0, one repeated real root; if < 0, no real roots (complex roots).

16. How do you solve a linear equation such as 3x + 5 = 20?

    Isolate x: subtract 5 from both sides (3x = 15), then divide by 3 (x = 5).

17. What is the sum of the interior angles of a triangle, and of a quadrilateral?

    A triangle's interior angles sum to 180°; a quadrilateral's interior angles sum to 360°.

18. State the Pythagorean theorem for a right-angled triangle.

    In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c² = a² + b².

19. What are the formulas for the area and circumference of a circle of radius r?

    Area = πr²; Circumference = 2πr (or πd, where d is the diameter).

20. What is the formula for the area of a triangle given base b and height h?

    Area = ½ × base × height = ½ × b × h.

21. What are the formulas for the volume and total surface area of a cube of side a?

    Volume = a³; Total surface area = 6a².

22. What is the formula for the volume of a cylinder with radius r and height h?

    Volume = πr²h.

23. What is the formula for profit percentage in terms of cost price (CP) and selling price (SP)?

    Profit% = ((SP − CP) / CP) × 100, where Profit = SP − CP.

24. How do you find the selling price when cost price and a desired profit percentage are known?

    SP = CP × (1 + Profit%/100). For CP = 200 at 15% profit: SP = 200 × 1.15 = 230.

25. What is the formula for simple interest (SI)?

    SI = (P × R × T) / 100, where P = principal, R = rate per annum, T = time in years.

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