MAT Mathematical Skills Syllabus

Mathematical Skills syllabus — full chapter and topic list

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

1. 1

   Arithmetic

   6 topics

   • Number System
     • Factors, multiples, HCF and LCM
     • Divisibility rules
     • Unit digit and remainders
   • Percentage, Profit and Loss
     • Percentage change and successive changes
     • Profit, loss and discount
     • Marked price and cost price relations
   • Ratio, Proportion and Variation
     • Direct and inverse proportion
     • Partnership
     • Mixtures and alligation
   • Interest
     • Simple interest
     • Compound interest
   • Time, Speed and Distance
     • Relative speed and trains
     • Boats and streams
     • Time and work, pipes and cisterns
   • Averages
     • Simple and weighted averages
2. 2

   Algebra

   4 topics

   • Linear and Quadratic Equations
     • Simultaneous linear equations
     • Roots and nature of quadratic equations
   • Inequalities
     • Linear inequalities
     • Modulus and absolute value
   • Progressions
     • Arithmetic progression
     • Geometric progression
   • Functions and Logarithms
     • Basic functions
     • Laws of logarithms
3. 3

   Geometry and Mensuration

   4 topics

   • Lines, Angles and Triangles
     • Triangle properties and similarity
     • Pythagoras theorem
   • Polygons and Circles
     • Quadrilaterals
     • Circle theorems, tangents and chords
   • Coordinate Geometry
     • Distance and section formula
     • Straight lines and slope
   • Mensuration
     • Areas of 2D figures
     • Surface area and volume of solids
4. 4

   Modern Mathematics

   3 topics

   • Permutation and Combination
     • Arrangements and selections
     • Circular permutations
   • Probability
     • Classical probability
     • Addition and multiplication rules
   • Set Theory
     • Venn diagram applications
     • Union, intersection and complement

Mathematical Skills flashcards for MAT

20 of 51 cards from the Mathematical Skills deck — real questions with worked answers.

1. What is the difference between rational and irrational numbers?

   A rational number can be expressed as p/q where p and q are integers and q is not zero (its decimal terminates or repeats). An irrational number cannot be written as a ratio of integers (its decimal is non-terminating and non-repeating), e.g. sqrt(2), pi.

2. State the divisibility rules for 3, 9, and 11.

   Divisible by 3 if the digit sum is divisible by 3; by 9 if the digit sum is divisible by 9; by 11 if the difference between the sum of digits in odd positions and even positions is 0 or a multiple of 11.

3. How are LCM and HCF of two numbers related to the numbers themselves?

   For any two numbers a and b: LCM(a,b) x HCF(a,b) = a x b.

4. What is the unit digit cyclicity of powers of 2, 3, 7, and 8?

   Each repeats in a cycle of 4. 2: 2,4,8,6; 3: 3,9,7,1; 7: 7,9,3,1; 8: 8,4,2,6. Find the unit digit by taking the power modulo 4.

5. How do you find the number of factors of a number from its prime factorization?

   If N = p^a x q^b x r^c, the number of factors = (a+1)(b+1)(c+1).

6. What is the formula to convert a fraction or decimal into a percentage and vice versa?

   To get a percentage, multiply the fraction/decimal by 100. To convert a percentage to a fraction, divide by 100 (e.g. 25% = 25/100 = 1/4).

7. How do you compute percentage change between an old value and a new value?

   Percentage change = ((New value - Old value) / Old value) x 100. A positive result is an increase, negative is a decrease.

8. In Profit and Loss, how are Profit%, Loss%, Cost Price (CP) and Selling Price (SP) related?

   Profit% = (SP - CP)/CP x 100; Loss% = (CP - SP)/CP x 100. SP = CP x (1 + Profit%/100) or CP x (1 - Loss%/100).

9. How do Marked Price (MP), Discount, and Selling Price relate?

   SP = MP x (1 - Discount%/100). Discount is always calculated on the Marked Price, while profit/loss is calculated on the Cost Price.

10. What is the net effect of two successive percentage changes a% and b%?

    Net change = a + b + (ab/100) percent. Use the same formula for successive discounts (with negative signs) or successive increases.

11. In Profit and Loss, what is the result of selling two items at the same price, one at x% profit and the other at x% loss?

    There is always an overall loss of (x/10)^2 percent = (x^2/100)%.

12. What is the difference between ratio and proportion?

    A ratio compares two quantities (a:b). A proportion is a statement that two ratios are equal (a:b = c:d), where the product of means equals the product of extremes: bc = ad.

13. Define direct, inverse, and joint variation.

    Direct: y = kx (y increases as x increases). Inverse: y = k/x (y decreases as x increases). Joint: y = kxz (y varies with the product of two or more variables).

14. What is the formula for the mean proportional (geometric mean) between two numbers a and b?

    Mean proportional = sqrt(a x b). In the proportion a:x = x:b, x is the mean proportional.

15. How do you divide a quantity in the ratio a:b:c?

    Give each part as a/(a+b+c), b/(a+b+c), c/(a+b+c) of the total. Each share = (its ratio term / sum of terms) x total.

16. What is the formula for Simple Interest?

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

17. What is the formula for Compound Interest (compounded annually)?

    Amount = P x (1 + R/100)^T; Compound Interest = Amount - P, where P = principal, R = rate% per annum, T = time in years.

18. How do you adjust the compound interest formula when interest is compounded n times per year?

    Amount = P x (1 + R/(100n))^(nT). For half-yearly use n=2 (rate halved, periods doubled); for quarterly use n=4.

19. For the same principal, rate and time, how do SI and CI compare, and what is the 2-year difference?

    CI is always greater than or equal to SI (equal only for 1 year). The difference for 2 years = P x (R/100)^2.

20. What is the basic relationship between speed, distance, and time?

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

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