Cadet College Entry Test 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 Cadet College Entry Test, not a summary of it.

1. 1

   Sets

   3 topics

   • Concept and Types of Sets
   • Operations on Sets
   • Venn Diagrams
2. 2

   Number System and Direct Numbers

   3 topics

   • Whole Numbers and Integers
   • Direct (Signed) Numbers
   • Factors and Multiples
3. 3

   Rational Numbers and Fractions

   3 topics

   • Operations on Rational Numbers
   • Fractions
   • Decimals
4. 4

   Squares and Square Roots

   3 topics

   • Squares of Numbers
   • Square Roots
   • Cubes and Cube Roots
5. 5

   Ratio, Proportion and Percentage

   4 topics

   • Ratio and Proportion
   • Percentage
   • Profit, Loss and Discount
   • Unitary Method
6. 6

   Algebra

   4 topics

   • Algebraic Expressions
   • Algebraic Formulas and Identities
   • Factorization
   • Linear Equations
7. 7

   Geometry

   5 topics

   • Lines and Angles
   • Triangles
   • Quadrilaterals and Polygons
   • Construction of Figures
   • Circles
8. 8

   Mensuration

   2 topics

   • Perimeter and Area
   • Surface Area and Volume
9. 9

   Information Handling

   3 topics

   • Data Representation
   • Bar Graphs and Pie Charts
   • Average (Mean)

Mathematics flashcards for Cadet College Entry Test

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

1. What is a set in mathematics?

   A set is a well-defined collection of distinct objects, called its elements or members. 'Well-defined' means it can be decided clearly whether any given object belongs to the set or not.

2. What is the difference between a finite set and an infinite set?

   A finite set has a countable (limited) number of elements that comes to an end, e.g. {1, 2, 3}. An infinite set has an unlimited (never-ending) number of elements, e.g. the set of natural numbers {1, 2, 3, ...}.

3. What is an empty (null) set and how is it written?

   An empty or null set is a set that contains no elements. It is denoted by { } or by the symbol Ø. Note that {0} and {Ø} are NOT empty sets because they each contain one element.

4. What is a singleton set?

   A singleton (or unit) set is a set that contains exactly one element, for example {5} or {a}.

5. When are two sets said to be equal, and when are they equivalent?

   Two sets are equal if they contain exactly the same elements. Two sets are equivalent if they have the same number of elements (same cardinality), even if the elements differ. Equal sets are always equivalent, but equivalent sets are not always equal.

6. What is a subset, and what is a proper subset?

   Set A is a subset of B (A ⊆ B) if every element of A is also in B. A is a proper subset of B (A ⊂ B) if A is a subset of B but A is not equal to B (B has at least one element not in A).

7. What is the universal set?

   The universal set, denoted U, is the set that contains all the elements under consideration for a particular discussion or problem; every other set in that context is a subset of U.

8. How many subsets does a set with n elements have?

   A set with n elements has 2^n subsets in total, and 2^n − 1 proper subsets.

9. Define the union of two sets A and B.

   The union A ∪ B is the set of all elements that belong to A, or to B, or to both. Common elements are written only once.

10. Define the intersection of two sets A and B.

    The intersection A ∩ B is the set of all elements that belong to both A and B (the common elements).

11. What does the difference of sets A − B mean?

    A − B (the difference) is the set of elements that are in A but NOT in B. In general A − B is not equal to B − A.

12. What is the complement of a set A?

    The complement of A, written A' or A^c, is the set of all elements in the universal set U that are NOT in A. Thus A' = U − A.

13. What are disjoint sets?

    Two sets are disjoint if they have no elements in common, i.e. their intersection is the empty set: A ∩ B = Ø.

14. State the commutative laws for union and intersection of sets.

    Union and intersection are commutative: A ∪ B = B ∪ A and A ∩ B = B ∩ A.

15. State De Morgan's laws for sets.

    De Morgan's laws state: (A ∪ B)' = A' ∩ B' and (A ∩ B)' = A' ∪ B'.

16. What is a Venn diagram?

    A Venn diagram is a pictorial representation of sets and their relationships, using a rectangle for the universal set and overlapping circles for the individual sets.

17. In a Venn diagram, how are A ∩ B and A ∪ B shown?

    A ∩ B is shown by the overlapping (common) region of the two circles. A ∪ B is shown by the entire region covered by both circles together (everything inside either circle).

18. State the formula for n(A ∪ B) using a Venn diagram.

    n(A ∪ B) = n(A) + n(B) − n(A ∩ B), where n(X) denotes the number of elements in set X.

19. What are whole numbers?

    Whole numbers are the set of natural numbers (counting numbers) together with zero: {0, 1, 2, 3, 4, ...}.

20. What are integers?

    Integers are the set of whole numbers together with their negatives: {..., −3, −2, −1, 0, 1, 2, 3, ...}. They include positive integers, negative integers, and zero.

21. Is zero positive, negative, even, or odd?

    Zero is neither positive nor negative, but it IS an even number and it is an integer and a whole number.

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