Cambridge O Level Mathematics (Syllabus D) 4024 Syllabus

Mathematics (Syllabus D) 4024 syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics (Syllabus D) 4024 in Cambridge O Level, not a summary of it.

1. 1

   Number

   5 topics

   • Types of Number and Sets
   • The Four Operations and Order
   • Indices and Standard Form
   • Ratio, Proportion and Percentages
   • Applied Number
2. 2

   Algebra and Graphs

   5 topics

   • Algebraic Manipulation
   • Equations and Inequalities
   • Sequences
   • Variation
   • Graphs of Functions
3. 3

   Coordinate Geometry

   2 topics

   • Points and Lines
   • Parallel and Perpendicular Lines
4. 4

   Geometry

   5 topics

   • Geometrical Terms and Constructions
   • Angles
   • Similarity and Congruence
   • Symmetry
   • Circle Theorems
5. 5

   Mensuration

   3 topics

   • Perimeter and Area
   • Volume and Surface Area
   • Arcs and Sectors
6. 6

   Trigonometry

   3 topics

   • Right-Angled Triangles
   • Non-Right-Angled Triangles
   • Bearings and 3D Problems
7. 7

   Transformations and Vectors

   2 topics

   • Transformations
   • Vectors in Two Dimensions
8. 8

   Probability and Statistics

   3 topics

   • Probability
   • Data Representation
   • Averages and Spread

Mathematics (Syllabus D) 4024 flashcards for Cambridge O Level

19 of 50 cards from the Mathematics (Syllabus D) 4024 deck — real questions with worked answers.

1. What is a natural number?

   A positive whole number used for counting: 1, 2, 3, 4, ... (sometimes 0 is included).

2. Define a prime number and give the smallest one.

   A number with exactly two distinct factors: 1 and itself. The smallest prime is 2 (the only even prime).

3. What is a rational number?

   Any number that can be written as a fraction p/q where p and q are integers and q is not 0 (includes terminating and recurring decimals).

4. What is an irrational number? Give an example.

   A number that cannot be written as a fraction p/q; its decimal is non-terminating and non-recurring. Examples: pi, sqrt(2).

5. In set notation, what do the symbols union (U) and intersection do?

   A U B is the union: all elements in A or B (or both). A intersection B is the intersection: only elements in both A and B.

6. What does the symbol n(A) mean, and what is the empty set symbol?

   n(A) is the number of elements in set A (its cardinality). The empty set (containing no elements) is written {} or the symbol with a slashed circle.

7. What is the difference between a subset and a proper subset?

   A is a subset of B if every element of A is in B (A can equal B). A is a proper subset if A is contained in B but A is not equal to B.

8. What is the order of operations (BODMAS/BIDMAS)?

   Brackets, Orders (indices/powers), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

9. How do you find the HCF (Highest Common Factor) of two numbers using prime factorisation?

   Write each number as a product of primes, then multiply the common prime factors using the lowest power of each.

10. How do you find the LCM (Lowest Common Multiple) using prime factorisation?

    Write each number as a product of primes, then multiply every prime factor that appears, using the highest power of each.

11. State the index laws for multiplication and division of powers with the same base.

    a^m x a^n = a^(m+n); a^m / a^n = a^(m-n).

12. State the index law for a power raised to a power.

    (a^m)^n = a^(mn).

13. What do a^0 and a^(-n) equal?

    a^0 = 1 (for a not 0); a^(-n) = 1/a^n.

14. What does a^(1/n) mean, and what does a^(m/n) mean?

    a^(1/n) = the n-th root of a; a^(m/n) = the n-th root of a, all raised to the power m (= (n-th root of a)^m).

15. What is the standard form (scientific notation) of a number?

    Writing a number as A x 10^n, where 1 <= A < 10 and n is an integer.

16. Write 0.00046 in standard form.

    4.6 x 10^(-4).

17. How do you multiply numbers in standard form, e.g. (3 x 10^4)(2 x 10^3)?

    Multiply the A-values and add the powers of 10: 6 x 10^7.

18. What is the difference between a ratio and a proportion?

    A ratio compares two or more quantities (e.g. 3:2). A proportion is a statement that two ratios are equal (e.g. 3:2 = 6:4).

19. How do you divide a quantity in a given ratio, e.g. share $60 in ratio 2:3?

    Add the parts (2+3=5), divide the total by the number of parts (60/5=12), then multiply each part: $24 and $36.

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