AILET Quantitative Techniques Syllabus

Quantitative Techniques syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Techniques in AILET, not a summary of it.

1. 1

   Data Interpretation

   3 topics

   • Tabular and Graphical Data
     • Tables and data charts
     • Bar graphs and line graphs
     • Pie charts and combined data sets
   • Calculations from Data
     • Computing ratios, shares and totals
     • Comparisons and growth rates
   • Caselet and Mixed Data
     • Interpreting data presented in passages
     • Drawing conclusions from data sets
2. 2

   Arithmetic

   4 topics

   • Ratio, Proportion and Percentage
     • Ratios and proportions
     • Percentage increase and decrease
   • Profit, Loss and Interest
     • Profit, loss and discount
     • Simple and compound interest
   • Averages, Mixtures and Allegation
     • Averages and weighted averages
     • Mixtures and allegation
   • Time, Speed and Work
     • Time, speed and distance
     • Time and work
3. 3

   Numbers and Algebra

   3 topics

   • Number System
     • Properties of numbers, factors and multiples
     • HCF and LCM
   • Basic Algebra
     • Linear equations
     • Simplification and approximation
   • Sequences and Operations
     • Arithmetic progressions
     • Order of operations and surds
4. 4

   Mensuration and Basic Geometry

   3 topics

   • Areas and Perimeters
     • Area and perimeter of plane figures
     • Surface area and volume of solids
   • Elementary Probability and Statistics
     • Basic probability
     • Mean, median and mode
   • Lines, Angles and Triangles
     • Properties of triangles and angles
     • Basic coordinate geometry

Quantitative Techniques flashcards for AILET

24 of 51 cards from the Quantitative Techniques deck — real questions with worked answers.

1. In a frequency table, what is the difference between 'frequency' and 'cumulative frequency'?

   Frequency is the count of observations in a single class; cumulative frequency is the running total of frequencies up to and including that class.

2. Which graph type is best for showing how a whole is divided into parts (percentage shares), and how is each slice's angle calculated?

   A pie chart. Each slice angle = (component value / total) x 360 degrees.

3. On a bar graph versus a histogram, what is the key structural difference?

   Bar graphs have gaps between bars and represent categorical data; histograms have no gaps (bars touch) and represent continuous/grouped data, with area proportional to frequency.

4. In a line graph showing a trend over time, how do you read the rate of change between two points?

   Rate of change = (change in y-value) / (change in x-value), i.e., the slope of the line segment between the two points.

5. When data is given in a table, how do you compute the percentage change of a value from year A to year B?

   Percentage change = ((Value_B - Value_A) / Value_A) x 100.

6. From a data table, how do you find what percentage one category contributes to the total?

   Contribution % = (category value / sum of all categories) x 100.

7. In a 'caselet' (paragraph-style data) question, what is the first step before calculating?

   Translate the prose into a structured table or set of equations, extracting each given quantity and the relationship between them, before computing.

8. What does 'mixed data' (combination charts) typically require you to do, e.g., a table plus a graph together?

   Cross-reference both sources: use values from one (table/graph) to fill gaps or verify the other, since neither alone gives the full answer.

9. Define a ratio and state the basic property of an equivalent ratio.

   A ratio compares two quantities (a:b = a/b). An equivalent ratio is obtained by multiplying or dividing both terms by the same non-zero number, e.g., 2:3 = 4:6.

10. What is a proportion, and what is the rule of cross-multiplication?

    A proportion states two ratios are equal: a:b = c:d. Cross-multiplication gives a x d = b x c (product of extremes = product of means).

11. How do you convert a fraction or decimal to a percentage, and a percentage to a fraction?

    Multiply a fraction/decimal by 100 to get a percentage; divide a percentage by 100 to get a fraction/decimal.

12. If a quantity increases by x% then decreases by x%, what is the net percentage change?

    A net decrease of (x^2/100)%. The result is always lower than the original value.

13. In a ratio a:b:c, how do you split a total amount T among three parts?

    Each share = (its ratio term / (a+b+c)) x T. E.g., first part = a/(a+b+c) x T.

14. Define Profit, Loss, and the formula for Profit Percent (Gain %).

    Profit = SP - CP (when SP > CP); Loss = CP - SP (when CP > SP). Profit % = (Profit / CP) x 100, computed on cost price.

15. Write the formula for Simple Interest and the amount.

    SI = (P x R x T) / 100, where P=principal, R=rate% per annum, T=time in years. Amount = P + SI.

16. Write the Compound Interest amount formula (compounded annually) and the CI formula.

    Amount A = P(1 + R/100)^T. Compound Interest = A - P = P[(1 + R/100)^T - 1].

17. How do you find Selling Price from Cost Price given a profit percentage?

    SP = CP x (1 + Profit%/100). For a loss, SP = CP x (1 - Loss%/100).

18. What is the difference between marked price, discount, and selling price?

    Marked price (MP) is the listed/tag price; discount is a reduction on MP; Selling Price = MP - Discount = MP x (1 - Discount%/100).

19. Define the arithmetic mean (average) of n numbers.

    Average = (sum of all observations) / (number of observations) = Total / n.

20. If the average of n values is A, how do you find the new average when one value is added or removed?

    New average = (old sum +/- changed value) / (new count). Always recompute the total first, then divide by the updated number of items.

21. State the rule of alligation for mixing two ingredients of different values.

    (Quantity of cheaper)/(Quantity of dearer) = (Price of dearer - Mean price)/(Mean price - Price of cheaper). It gives the ratio in which two items are mixed to reach a mean value.

22. In a mixture, if x litres are drawn out and replaced by water n times from an initial V litres, what is the remaining pure quantity?

    Remaining pure quantity = V x (1 - x/V)^n.

23. State the relationship between speed, distance, and time.

    Speed = Distance / Time; Distance = Speed x Time; Time = Distance / Speed.

24. How do you convert km/hr to m/s and vice versa?

    km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5.

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