FAST-NU Entry Test Basic Mathematics Syllabus

Basic Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Basic Mathematics in FAST-NU Entry Test, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Number Properties and Divisibility
   • HCF and LCM
   • Fractions, Decimals and Ratios
   • Average and Mixtures
2. 2

   Percentages, Profit and Loss

   4 topics

   • Percentage Increase and Decrease
   • Cost Price, Selling Price and Profit
   • Discount and Marked Price
   • Simple and Compound Interest
3. 3

   Ratio, Proportion and Variation

   3 topics

   • Direct and Inverse Proportion
   • Partnership Problems
   • Mixture and Alligation
4. 4

   Algebra and Word Problems

   3 topics

   • Linear Equations
   • Age and Number Problems
   • Algebraic Simplification and Exponents
5. 5

   Time, Speed, Distance and Work

   4 topics

   • Speed, Distance and Time
   • Trains, Boats and Streams
   • Time and Work
   • Pipes and Cisterns
6. 6

   Quantitative Reasoning

   3 topics

   • Data Interpretation
   • Number Series and Patterns
   • Basic Mensuration

Basic Mathematics flashcards for FAST-NU Entry Test

24 of 50 cards from the Basic Mathematics deck — real questions with worked answers.

1. What is the divisibility rule for 3?

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

2. What is the divisibility rule for 4?

   A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

3. What is the divisibility rule for 8?

   A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

4. What is the divisibility rule for 9?

   A number is 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. Define a prime number and give the smallest one.

   A prime number is a natural number greater than 1 having exactly two factors: 1 and itself. The smallest prime is 2 (and it is the only even prime).

7. How many factors does a number with prime factorization p^a x q^b have?

   The number of factors is (a+1)(b+1). In general, multiply (exponent+1) for each prime factor.

8. What is the relationship between HCF, LCM, and two numbers a and b?

   HCF(a,b) x LCM(a,b) = a x b (the product of the two numbers).

9. How do you find the HCF and LCM of two numbers using prime factorization?

   HCF = product of common prime factors with the lowest powers. LCM = product of all prime factors with the highest powers.

10. What is the LCM of fractions formula?

    LCM of fractions = LCM of numerators / HCF of denominators.

11. What is the HCF of fractions formula?

    HCF of fractions = HCF of numerators / LCM of denominators.

12. How do you convert a recurring decimal like 0.̅3 (0.333...) to a fraction?

    A single repeating digit equals that digit over 9, so 0.333... = 3/9 = 1/3. For two repeating digits, divide by 99, etc.

13. If a:b = 2:3 and b:c = 4:5, what is a:b:c?

    Make b common: a:b = 8:12, b:c = 12:15, so a:b:c = 8:12:15.

14. How do you compare two fractions a/b and c/d without converting to decimals?

    Cross-multiply: compare a x d with c x b. If a x d > c x b then a/b > c/d (for positive denominators).

15. What is the formula for the average (arithmetic mean) of n numbers?

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

16. The average of the first n natural numbers is what?

    Average = (n + 1) / 2.

17. In a mixture/replacement problem, if a vessel has x litres and y litres are removed and replaced with water n times, what fraction of original liquid remains?

    Remaining liquid = x x (1 - y/x)^n. The amount of original liquid after n operations is x(1 - y/x)^n.

18. If the average of a group changes when one member is added/removed, how do you find the new member's value?

    New value = (New total) - (Old total), where totals = average x count. Equivalently, value = new average +/- (change in average x affected count).

19. What is the formula for percentage increase?

    Percentage increase = (Increase / Original value) x 100.

20. What is the formula for percentage decrease?

    Percentage decrease = (Decrease / Original value) x 100.

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

    There is a net decrease of (x^2 / 100)%. The original value is never fully restored.

22. If A is x% more than B, by what percentage is B less than A?

    B is less than A by [x / (100 + x)] x 100 percent.

23. What does 'x% of y equals y% of x' illustrate?

    Percentage is commutative: x% of y = (x/100) x y = (y/100) x x = y% of x.

24. What is the formula for Profit?

    Profit = Selling Price (SP) - Cost Price (CP), valid when SP > CP.

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