LAT 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 LAT, not a summary of it.

1. 1

   Arithmetic

   4 topics

   • Number Operations
   • Fractions and Decimals
   • HCF and LCM
   • Average
2. 2

   Percentages and Ratios

   3 topics

   • Percentage
   • Ratio and Proportion
   • Profit and Loss
3. 3

   Basic Algebra

   2 topics

   • Simple Equations
   • Algebraic Expressions
4. 4

   Word Problems and Reasoning

   4 topics

   • Time, Speed and Distance
   • Time and Work
   • Simple Interest
   • Basic Logical Reasoning

Mathematics flashcards for LAT

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

1. What are the four basic operations in arithmetic and in what order are they performed (operator precedence)?

   The four basic operations are addition (+), subtraction (-), multiplication (×) and division (÷). Order of operations follows BODMAS/PEMDAS: Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

2. What is the difference between a factor and a multiple of a number?

   A factor of a number divides it exactly with no remainder (e.g. factors of 12 are 1,2,3,4,6,12). A multiple is the product of that number with an integer (e.g. multiples of 12 are 12,24,36,...). A number is a factor of its multiples.

3. What is the divisibility rule for 3 and for 9?

   A number is divisible by 3 if the sum of its digits is divisible by 3. A number is divisible by 9 if the sum of its digits is divisible by 9. Example: 252 → 2+5+2=9, divisible by both 3 and 9.

4. What are prime numbers and composite numbers?

   A prime number has exactly two factors: 1 and itself (e.g. 2,3,5,7,11). A composite number has more than two factors (e.g. 4,6,8,9). The number 1 is neither prime nor composite.

5. What is the result of any number multiplied by 0, and of dividing a number by 0?

   Any number multiplied by 0 equals 0. Division by 0 is undefined (not allowed). Also, 0 divided by any non-zero number equals 0.

6. What is a proper fraction, an improper fraction and a mixed number?

   In a proper fraction the numerator is less than the denominator (e.g. 3/4). In an improper fraction the numerator is greater than or equal to the denominator (e.g. 7/4). A mixed number combines a whole number and a proper fraction (e.g. 1¾).

7. How do you add or subtract two fractions with different denominators?

   Find the LCM of the denominators to get a common denominator, convert each fraction to an equivalent fraction with that denominator, then add or subtract the numerators while keeping the denominator the same. Finally simplify.

8. How do you multiply and how do you divide two fractions?

   To multiply: multiply numerators together and denominators together (a/b × c/d = ac/bd). To divide: multiply the first fraction by the reciprocal of the second (a/b ÷ c/d = a/b × d/c).

9. How do you convert a fraction to a decimal and a decimal to a fraction?

   To convert a fraction to a decimal, divide the numerator by the denominator. To convert a terminating decimal to a fraction, write the digits over the appropriate power of 10 and simplify (e.g. 0.75 = 75/100 = 3/4).

10. What is the rule for the number of decimal places when multiplying two decimals?

    Multiply the numbers ignoring the decimal points, then place the decimal point in the product so that it has as many decimal places as the total number of decimal places in the two factors combined. Example: 0.3 × 0.02 = 0.006 (3 decimal places).

11. 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 leaving a remainder. Example: HCF of 12 and 18 is 6.

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

    The LCM is the smallest positive number that is a multiple of (i.e. exactly divisible by) each of the given numbers. Example: LCM of 4 and 6 is 12.

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

    For any two numbers, Product of the two numbers = HCF × LCM. So HCF × LCM = a × b. This lets you find one quantity if the other three are known.

14. How do you find the LCM and HCF using the prime factorization method?

    Express each number as a product of primes. For the HCF, multiply the common prime factors taken to their lowest powers. For the LCM, multiply all prime factors taken to their highest powers.

15. When are HCF and LCM typically used in word problems?

    HCF is used to split things into smaller equal groups or find the largest size (e.g. largest tile, maximum equal distribution). LCM is used to find when events coincide or repeat together (e.g. bells ringing together, smallest common quantity).

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

    Average = (Sum of all observations) ÷ (Number of observations). Rearranged: Sum = Average × Number of observations.

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

    Total sum = Average × number of items = A × n. This is the key relationship used to add or remove items and recompute the average.

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

    The average of the first n natural numbers (1,2,3,...,n) is (n+1)/2. For example, the average of 1 to 10 is (10+1)/2 = 5.5.

19. How does the average change when a new value is added to a set?

    Compute the new sum (old sum + new value) and divide by the new count (old count + 1). If the new value is above the old average, the average rises; if below, it falls; if equal, it stays the same.

20. What is the average speed for a whole journey covering different distances at different speeds?

    Average speed = Total distance ÷ Total time (NOT the simple average of the speeds). Only when equal distances are covered does it equal the harmonic mean of the speeds.

21. What does percentage mean and how do you convert a fraction to a percentage?

    Percentage means 'per hundred' (out of 100). To convert a fraction or decimal to a percentage, multiply it by 100 and add the % sign. Example: 3/4 = 0.75 × 100 = 75%.

See more Mathematics flashcards →

Planning Mathematics for LAT

Mathematics (LAT) FAQ