IPMAT Quantitative Ability Syllabus

Quantitative Ability syllabus — full chapter and topic list

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

1. 1

   Number System

   4 topics

   • Integers
   • Fractions
   • Decimals
   • Factors and Multiples
2. 2

   Algebra

   4 topics

   • Linear Equations
   • Quadratic Equations
   • Inequalities
   • Polynomials
3. 3

   Geometry

   4 topics

   • Lines and Angles
   • Triangles
   • Circles
   • Coordinate Geometry
4. 4

   Mensuration

   3 topics

   • Area and Perimeter
   • Volume and Surface Area
   • 2D and 3D Shapes
5. 5

   Probability and Statistics

   3 topics

   • Mean, Median, Mode
   • Standard Deviation
   • Basic Probability

Quantitative Ability flashcards for IPMAT

25 of 52 cards from the Quantitative Ability deck — real questions with worked answers.

1. What are integers?

   The set of whole numbers and their negatives, including zero: {..., -3, -2, -1, 0, 1, 2, 3, ...}. They have no fractional or decimal part.

2. State the rules for the sign of a product/quotient of two integers.

   Same signs give a positive result; different signs give a negative result. (+ x + = +, - x - = +, + x - = -, - x + = -)

3. What is the result of dividing any non-zero integer by zero, and zero by a non-zero integer?

   Division by zero is undefined. Zero divided by any non-zero integer equals 0.

4. What is a proper fraction versus an improper fraction?

   A proper fraction has numerator smaller than denominator (value < 1), e.g. 3/4. An improper fraction has numerator greater than or equal to denominator (value >= 1), e.g. 7/4.

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

   Find the least common denominator (LCM of the denominators), convert each fraction to an equivalent fraction with that denominator, then add or subtract the numerators and keep the common denominator.

6. 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) = ad/bc.

7. How do you convert a fraction to a decimal, and what makes a decimal terminating?

   Divide the numerator by the denominator. A fraction (in lowest terms) gives a terminating decimal only if its denominator's prime factors are only 2s and/or 5s; otherwise the decimal is recurring.

8. What is the place value of each digit after the decimal point (first three places)?

   First place = tenths (1/10), second = hundredths (1/100), third = thousandths (1/1000).

9. How do you multiply two decimals?

   Multiply the numbers ignoring the decimal points, then place the decimal point in the product so it has as many decimal places as the total number of decimal places in the two factors combined.

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

    A factor of n divides n exactly (with no remainder); a multiple of n is the product of n with an integer. E.g. for 12, factors include 1,2,3,4,6,12; multiples include 12,24,36,...

11. What is a prime number and what is the smallest prime?

    A prime number is a natural number greater than 1 with exactly two factors: 1 and itself. The smallest prime is 2, which is also the only even prime.

12. What is the relationship between HCF (GCD) and LCM of two numbers a and b?

    HCF(a,b) x LCM(a,b) = a x b. The product of the two numbers equals the product of their HCF and LCM.

13. How do you find the HCF and LCM using prime factorisation?

    HCF = product of the lowest powers of the common prime factors. LCM = product of the highest powers of all prime factors appearing in any number.

14. How many factors does a number have if its prime factorisation is p^a x q^b x r^c?

    Total number of factors = (a+1)(b+1)(c+1).

15. What is the standard form and the solution of a linear equation in one variable ax + b = 0?

    Standard form: ax + b = 0 with a ≠ 0. Its unique solution is x = -b/a.

16. Give the methods for solving a pair of linear equations in two variables.

    Substitution, elimination (addition/subtraction), and cross-multiplication; graphically, the solution is the point where the two lines intersect.

17. For a pair of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0, what conditions give unique, no, or infinitely many solutions?

    Unique solution: a1/a2 ≠ b1/b2. No solution (parallel): a1/a2 = b1/b2 ≠ c1/c2. Infinitely many (coincident): a1/a2 = b1/b2 = c1/c2.

18. What is the general (standard) form of a quadratic equation?

    ax^2 + bx + c = 0, where a, b, c are constants and a ≠ 0.

19. State the quadratic formula for the roots of ax^2 + bx + c = 0.

    x = [-b ± sqrt(b^2 - 4ac)] / (2a).

20. What is the discriminant of a quadratic, and what does its value tell you about the roots?

    Discriminant D = b^2 - 4ac. If D > 0 there are two distinct real roots; if D = 0 there are two equal real roots; if D < 0 the roots are complex (no real roots).

21. For ax^2 + bx + c = 0, what are the sum and product of the roots?

    Sum of roots = -b/a; product of roots = c/a.

22. What happens to an inequality when you multiply or divide both sides by a negative number?

    The direction of the inequality sign reverses (e.g. < becomes >).

23. How do you represent the solution set of an inequality such as x > 3 on a number line?

    Draw an open circle at 3 (value not included) and shade the line to the right toward larger values; use a closed/filled circle if the inequality is >= (value included).

24. What is a polynomial, and what is its degree?

    A polynomial is an expression of the form a_n x^n + ... + a_1 x + a_0 with non-negative integer exponents and real coefficients. Its degree is the highest power of the variable with a non-zero coefficient.

25. Name polynomials of degree 0, 1, 2, and 3.

    Degree 0 = constant; degree 1 = linear; degree 2 = quadratic; degree 3 = cubic.

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