Examius

🇵🇰 PMA Graduate Course · subject

PMA Graduate Course Mathematics Syllabus

The Mathematics syllabus for PMA Graduate Course in full: 6 chapters and 17 topics, every one listed below, plus 50 Mathematics flashcards with answers.

6Chapters
17Topics
50Flashcards

Mathematics syllabus: all 6 chapters

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

  1. Arithmetic

     4 topics
    • Number System
    • HCF and LCM
    • Fractions and Decimals
    • Ratio and Proportion

  2. Percentages and Averages

     2 topics
    • Percentage Calculations
    • Averages

  3. Profit, Loss and Interest

     3 topics
    • Profit and Loss
    • Simple Interest
    • Compound Interest

  4. Algebra

     3 topics
    • Linear Equations
    • Algebraic Expressions
    • Factorization

  5. Geometry and Mensuration

     3 topics
    • Angles and Triangles
    • Area and Perimeter
    • Volume of Solids

  6. Time, Speed and Work

     2 topics
    • Time and Distance
    • Time and Work

PMA Graduate Course Mathematics flashcards — 50 questions with answers

  1. What is the difference between a natural number and a whole number?

    Natural numbers are the counting numbers starting from 1 (1, 2, 3, ...). Whole numbers include all natural numbers plus 0 (0, 1, 2, 3, ...).

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

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

  3. What is a composite number?

    A composite number is a natural number greater than 1 that has more than two factors, i.e., it is divisible by numbers other than 1 and itself (e.g., 4, 6, 9).

  4. How do rational numbers differ from irrational numbers?

    A rational number can be written as a fraction p/q where q is not 0 (e.g., 1/2, 0.75). An irrational number cannot be expressed as such a fraction and has a non-terminating, non-repeating decimal (e.g., pi, sqrt(2)).

  5. State the divisibility rule for 3.

    A number is divisible by 3 if the sum of its digits is divisible by 3 (e.g., 123: 1+2+3=6, divisible by 3).

  6. State the divisibility rule for 9.

    A number is divisible by 9 if the sum of its digits is divisible by 9 (e.g., 729: 7+2+9=18, divisible by 9).

  7. State 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.

  8. Define the HCF (Highest Common Factor) of two numbers.

    The HCF (also called GCD) is the largest number that divides each of the given numbers exactly without leaving a remainder.

  9. Define the LCM (Least Common Multiple) of two numbers.

    The LCM is the smallest number that is exactly divisible by each of the given numbers (the smallest common multiple).

  10. What is the relationship between the HCF and LCM of two numbers?

    For two numbers a and b: HCF x LCM = a x b. Thus the product of two numbers equals the product of their HCF and LCM.

  11. How do you find the LCM of fractions?

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

  12. How do you find the HCF of fractions?

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

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

    In a proper fraction the numerator is less than the denominator (value < 1, e.g., 3/5). In an improper fraction the numerator is greater than or equal to the denominator (value >= 1, e.g., 7/4).

  14. How do you convert an improper fraction to a mixed number?

    Divide the numerator by the denominator; the quotient is the whole part, the remainder becomes the new numerator, and the denominator stays the same (e.g., 7/4 = 1 3/4).

  15. How do you multiply two fractions?

    Multiply the numerators together and the denominators together: (a/b) x (c/d) = (a x c)/(b x d), then simplify.

  16. How do you divide one fraction by another?

    Multiply the first fraction by the reciprocal of the second: (a/b) / (c/d) = (a/b) x (d/c).

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

    Divide the numerator by the denominator (e.g., 3/4 = 3 divided by 4 = 0.75).

  18. How do you convert the recurring decimal 0.333... to a fraction?

    0.333... (repeating 3) equals 1/3. A single repeating digit over 9: 0.bar(d) = d/9.

  19. Define a ratio.

    A ratio is a comparison of two quantities of the same kind by division, written as a:b or a/b, showing how many times one quantity contains the other.

  20. What does it mean for four quantities to be in proportion?

    Four quantities a, b, c, d are in proportion (a:b :: c:d) when a/b = c/d, i.e., the two ratios are equal.

Show the other 30 Mathematics flashcards

  1. State the rule of cross-multiplication in a proportion a:b = c:d.

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

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

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

  3. What is direct proportion versus inverse proportion?

    In direct proportion, as one quantity increases the other increases at the same rate (y = kx). In inverse proportion, as one increases the other decreases (xy = k).

  4. How do you convert a fraction or decimal into a percentage?

    Multiply the fraction or decimal by 100 and add the % sign (e.g., 0.45 x 100 = 45%; 1/4 x 100 = 25%).

  5. How do you find x% of a quantity N?

    x% of N = (x/100) x N (e.g., 20% of 150 = (20/100) x 150 = 30).

  6. What is the formula for percentage increase?

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

  7. If a number is increased by 25%, by what fraction does it become?

    It becomes 125/100 = 5/4 of the original number (i.e., multiplied by 1.25).

  8. Define the average (arithmetic mean) of a set of numbers.

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

  9. If the average of n numbers is A, what is their total sum?

    Sum = Average x Number of observations = A x n.

  10. What is the average of the first n natural numbers?

    Average of first n natural numbers = (n + 1) / 2.

  11. How does adding a new value affect an average if the new value equals the old average?

    If the new value equals the existing average, the average stays unchanged.

  12. Define Cost Price (CP) and Selling Price (SP).

    Cost Price (CP) is the price at which an article is bought. Selling Price (SP) is the price at which it is sold.

  13. When is there a profit and when is there a loss?

    Profit occurs when SP > CP (Profit = SP - CP). Loss occurs when CP > SP (Loss = CP - SP).

  14. What is the formula for Profit Percentage?

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

  15. What is the formula for Loss Percentage?

    Loss% = (Loss / Cost Price) x 100.

  16. How do you find SP when CP and Profit% are known?

    SP = CP x (100 + Profit%) / 100.

  17. What is discount and on what is it calculated?

    Discount is a reduction on the Marked Price (List Price). Discount = Marked Price - Selling Price, and Discount% is calculated on the Marked Price.

  18. State 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.

  19. What is the Amount in simple interest?

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

  20. In simple interest, how is the principal found if SI, R, and T are known?

    P = (SI x 100) / (R x T).

  21. State the formula for Compound Interest (Amount).

    Amount = P(1 + R/100)^T, where P = Principal, R = rate% per annum, T = time in years. Then CI = Amount - P.

  22. How does compound interest differ from simple interest?

    In simple interest, interest is calculated only on the original principal each year. In compound interest, interest is calculated on the principal plus accumulated interest, so the base grows each period.

  23. What is the compound interest formula when interest is compounded half-yearly?

    Amount = P(1 + (R/2)/100)^(2T), i.e., halve the rate and double the number of periods.

  24. What is the difference between CI and SI for 2 years at the same rate?

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

  25. Define a linear equation in one variable.

    A linear equation in one variable is an equation of the form ax + b = 0 (a not 0), where the highest power of the variable is 1; it has exactly one solution: x = -b/a.

  26. What is the solution of the linear equation 3x + 6 = 0?

    3x = -6, so x = -2.

  27. What does the term 'coefficient' mean in an algebraic expression?

    A coefficient is the numerical factor multiplying a variable in a term (e.g., in 5x, the coefficient is 5).

  28. What is the difference between a monomial, binomial, and trinomial?

    A monomial has one term (e.g., 3x), a binomial has two terms (e.g., x + 2), and a trinomial has three terms (e.g., x^2 + 3x + 2).

  29. What is the factorization of a^2 - b^2?

    a^2 - b^2 = (a + b)(a - b), the difference of two squares.

  30. Factorize x^2 + 5x + 6.

    Find two numbers that multiply to 6 and add to 5 (2 and 3): x^2 + 5x + 6 = (x + 2)(x + 3).

PMA Graduate Course Mathematics FAQ

What is in the PMA Graduate Course Mathematics syllabus?

PMA Graduate Course Mathematics is split into 6 chapters: Arithmetic, Percentages and Averages, Profit, Loss and Interest, Algebra, Geometry and Mensuration and Time, Speed and Work. Together they contain 17 topics.

How many chapters are in PMA Graduate Course Mathematics?

6 chapters, containing 17 topics. The largest chapter is Arithmetic, with 4 topics.

Are there flashcards for PMA Graduate Course Mathematics?

Yes — a 50-card 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.