PMA Long Course Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in PMA Long Course, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Percentages
   • Ratio and Proportion
   • Profit and Loss
   • Average
2. 2

   Number System

   3 topics

   • HCF and LCM
   • Factors and Multiples
   • Fractions and Decimals
3. 3

   Algebra

   3 topics

   • Linear Equations
   • Quadratic Equations
   • Algebraic Expressions and Factorization
4. 4

   Geometry

   4 topics

   • Lines and Angles
   • Triangles
   • Circles
   • Area and Perimeter
5. 5

   Mensuration

   2 topics

   • Surface Area
   • Volume of Solids
6. 6

   Time, Speed and Distance

   3 topics

   • Speed and Distance
   • Time and Work
   • Trains and Boats
7. 7

   Simple and Compound Interest

   2 topics

   • Simple Interest
   • Compound Interest

Mathematics flashcards for PMA Long Course

21 of 51 cards from the Mathematics deck — real questions with worked answers.

1. What is the formula to convert a fraction into a percentage?

   Percentage = (Value / Total) x 100. To express any fraction as a percentage, multiply it by 100 and add the % sign.

2. How do you find x% of a number N?

   x% of N = (x/100) x N.

3. If a quantity increases from A to B, what is the percentage increase?

   Percentage increase = [(B - A) / A] x 100, where A is the original value.

4. A number is first increased by 20% and then decreased by 20%. What is the net percentage change?

   A net decrease of 4%. (Successive change formula: a + b + ab/100 = 20 - 20 + (20 x -20)/100 = -4%.)

5. What is the formula for successive percentage changes of a% and b%?

   Net % change = a + b + (ab/100), using signs (+ for increase, - for decrease).

6. What is a ratio, and how is the ratio a:b expressed as a fraction?

   A ratio is a comparison of two quantities of the same kind by division. The ratio a:b equals the fraction a/b, where a is the antecedent and b is the consequent.

7. What is a proportion, and what is the rule of the means and extremes?

   A proportion states two ratios are equal: a:b = c:d. The product of the extremes equals the product of the means, i.e., a x d = b x c (cross multiplication).

8. In the proportion a:b = c:d, what is the 'mean proportional' between two numbers a and b?

   The mean proportional between a and b is the square root of (a x b), i.e., the value x where a:x = x:b, so x = sqrt(ab).

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

   a:b:c = 8:12:15. (Make b common: multiply first ratio by 4 and second by 3 to get b = 12.)

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

    In direct proportion, two quantities increase or decrease together (x/y = constant). In inverse proportion, one increases as the other decreases (x x y = constant).

11. How is profit (gain) calculated, and on what is profit percentage based?

    Profit = Selling Price (SP) - Cost Price (CP). Profit percentage is always calculated on the Cost Price: Profit% = (Profit / CP) x 100.

12. How is loss calculated, and how is loss percentage found?

    Loss = Cost Price (CP) - Selling Price (SP). Loss% = (Loss / CP) x 100, calculated on the Cost Price.

13. What is the formula for Selling Price in terms of Cost Price and gain percentage?

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

14. What is the formula for Cost Price given the Selling Price and profit percentage?

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

15. If an article is sold at a discount, what do 'marked price' and 'discount' mean?

    Marked Price (MP) is the listed/labeled price before reduction. Discount is the reduction on the marked price: SP = MP - Discount, and Discount% = (Discount / MP) x 100.

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

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

17. How do you find the total sum if you know the average and the count?

    Sum = Average x Number of observations.

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

    The average of the first n natural numbers is (n + 1)/2.

19. The average of 5 numbers is 20. If one number is removed and the average of the remaining 4 becomes 18, what was the removed number?

    28. (Original sum = 5 x 20 = 100; new sum = 4 x 18 = 72; removed number = 100 - 72 = 28.)

20. What is the HCF (Highest Common Factor) of two or more numbers?

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

21. What is the LCM (Least Common Multiple) of two or more numbers?

    The LCM is the smallest number that is exactly divisible by each of the given numbers.

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