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FAST-NU Entry Test Basic Mathematics Syllabus

The Basic Mathematics syllabus for FAST-NU Entry Test in full: 6 chapters and 21 topics, every one listed below, plus 50 Basic Mathematics flashcards with answers.

6Chapters
21Topics
50Flashcards

Basic Mathematics syllabus: all 6 chapters

Expand any chapter to see its topics and sub-topics.

  1. Arithmetic

     4 topics
    • Number Properties and Divisibility
    • HCF and LCM
    • Fractions, Decimals and Ratios
    • Average and Mixtures

  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. Ratio, Proportion and Variation

     3 topics
    • Direct and Inverse Proportion
    • Partnership Problems
    • Mixture and Alligation

  4. Algebra and Word Problems

     3 topics
    • Linear Equations
    • Age and Number Problems
    • Algebraic Simplification and Exponents

  5. Time, Speed, Distance and Work

     4 topics
    • Speed, Distance and Time
    • Trains, Boats and Streams
    • Time and Work
    • Pipes and Cisterns

  6. Quantitative Reasoning

     3 topics
    • Data Interpretation
    • Number Series and Patterns
    • Basic Mensuration

FAST-NU Entry Test Basic Mathematics flashcards — 50 questions with 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.

Show the other 30 Basic Mathematics flashcards

  1. 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.

  2. 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.

  3. 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.

  4. What is the formula for Profit?

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

  5. What is the formula for Loss?

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

  6. What is the formula for Profit percentage?

    Profit% = (Profit / Cost Price) x 100. Profit and loss percentages are always calculated on the Cost Price.

  7. How do you find Selling Price given Cost Price and Profit%?

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

  8. What is Marked Price (also called List Price)?

    Marked Price (MP) is the price labelled on an item before any discount; the selling price is obtained after subtracting discount from MP.

  9. What is the formula relating Discount, Marked Price, and Selling Price?

    Discount = Marked Price - Selling Price, and Discount% = (Discount / Marked Price) x 100. SP = MP x (100 - Discount%)/100.

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

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

  11. What is the formula for Simple Interest?

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

  12. What is the formula for the Amount under Simple Interest?

    Amount = Principal + Simple Interest = P(1 + RT/100).

  13. What is the formula for Compound Interest (amount), compounded annually?

    Amount = P(1 + R/100)^T, and Compound Interest = Amount - P.

  14. How is the compound interest amount formula adjusted when interest is compounded half-yearly?

    Use Amount = P(1 + R/200)^(2T): halve the rate and double the number of periods.

  15. For the same P, R, and T = 2 years, what is the difference between CI and SI?

    Difference (for 2 years) = P x (R/100)^2.

  16. Define direct proportion.

    Two quantities are in direct proportion if their ratio stays constant: when one increases, the other increases proportionally (x/y = constant, or x ∝ y).

  17. Define inverse proportion.

    Two quantities are in inverse proportion if their product stays constant: when one increases, the other decreases proportionally (xy = constant, or x ∝ 1/y).

  18. Is the number of workers and the time taken to finish a fixed job a direct or inverse proportion?

    Inverse proportion: more workers means less time (workers x time = constant work).

  19. In a simple partnership where capitals are invested for the same time, how is profit shared?

    Profit is shared in the ratio of the capitals invested: Profit ratio = C1 : C2 : C3.

  20. In a compound partnership, how is profit divided when both capital and time differ?

    Profit is divided in the ratio of (Capital x Time) for each partner: (C1 x T1) : (C2 x T2) : ...

  21. What is the difference between a sleeping (dormant) partner and a working partner?

    A working (active) partner manages the business and may receive an additional salary/fee; a sleeping (dormant) partner only invests capital and shares profit by investment ratio.

  22. State the Rule of Alligation.

    (Quantity of cheaper)/(Quantity of dearer) = (Price of dearer - Mean price)/(Mean price - Price of cheaper).

  23. What is the 'mean price' in a mixture (alligation) problem?

    The mean price is the cost price per unit of the resulting mixture obtained by mixing two or more ingredients.

  24. Using alligation, in what ratio must two ingredients costing Rs 60 and Rs 90 be mixed to get a mixture worth Rs 70?

    Ratio cheaper:dearer = (90 - 70):(70 - 60) = 20:10 = 2:1.

  25. What is a linear equation in one variable, and how many solutions does it generally have?

    An equation of the form ax + b = 0 (a ≠ 0) where the variable has degree 1; it has exactly one solution: x = -b/a.

  26. How many solutions does a consistent and independent pair of linear equations in two variables have?

    Exactly one unique solution (the lines intersect at a single point).

  27. For a pair of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0, what condition gives infinitely many solutions?

    a1/a2 = b1/b2 = c1/c2 (the equations are dependent / represent the same line).

  28. For a pair of linear equations, what condition gives no solution (inconsistent)?

    a1/a2 = b1/b2 ≠ c1/c2 (the lines are parallel and distinct).

  29. What is the slope-intercept form of a linear equation and what do its constants represent?

    y = mx + c, where m is the slope (rate of change) and c is the y-intercept (value of y when x = 0).

  30. If the cost price of x articles equals the selling price of y articles, what is the profit/loss percentage?

    Profit/Loss% = [(x - y)/y] x 100. Positive result means profit, negative means loss.

FAST-NU Entry Test Basic Mathematics FAQ

What is in the FAST-NU Entry Test Basic Mathematics syllabus?

FAST-NU Entry Test Basic Mathematics is split into 6 chapters: Arithmetic, Percentages, Profit and Loss, Ratio, Proportion and Variation, Algebra and Word Problems, Time, Speed, Distance and Work and Quantitative Reasoning. Together they contain 21 topics.

How many chapters are in FAST-NU Entry Test Basic Mathematics?

6 chapters, containing 21 topics. The largest chapter is Arithmetic, with 4 topics.

Are there flashcards for FAST-NU Entry Test Basic Mathematics?

Yes — a 50-card Basic Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.