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Cambridge O Level Mathematics (Syllabus D) 4024 Syllabus

The Mathematics (Syllabus D) 4024 syllabus for Cambridge O Level in full: 8 chapters and 28 topics, every one listed below, plus 50 Mathematics (Syllabus D) 4024 flashcards with answers.

8Chapters
28Topics
50Flashcards

Mathematics (Syllabus D) 4024 syllabus: all 8 chapters

Expand any chapter to see its topics and sub-topics.

  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. Algebra and Graphs

     5 topics
    • Algebraic Manipulation
    • Equations and Inequalities
    • Sequences
    • Variation
    • Graphs of Functions

  3. Coordinate Geometry

     2 topics
    • Points and Lines
    • Parallel and Perpendicular Lines

  4. Geometry

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

  5. Mensuration

     3 topics
    • Perimeter and Area
    • Volume and Surface Area
    • Arcs and Sectors

  6. Trigonometry

     3 topics
    • Right-Angled Triangles
    • Non-Right-Angled Triangles
    • Bearings and 3D Problems

  7. Transformations and Vectors

     2 topics
    • Transformations
    • Vectors in Two Dimensions

  8. Probability and Statistics

     3 topics
    • Probability
    • Data Representation
    • Averages and Spread

Cambridge O Level Mathematics (Syllabus D) 4024 flashcards — 50 questions with 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.

  20. What is the difference between direct and inverse proportion?

    Direct: as one quantity increases, the other increases at the same rate (y = kx). Inverse: as one increases, the other decreases (y = k/x; their product is constant).

Show the other 30 Mathematics (Syllabus D) 4024 flashcards

  1. How do you find a percentage increase or decrease?

    Percentage change = (change / original amount) x 100%.

  2. How do you find the original amount before a percentage change (reverse percentage)?

    Treat the new amount as the changed percentage of the original, then divide. E.g. after a 20% increase, divide the new value by 1.2.

  3. State the simple interest formula.

    I = (P x R x T) / 100, where P = principal, R = rate per year (%), T = time in years.

  4. State the compound interest formula for the total amount.

    A = P(1 + R/100)^n, where P = principal, R = rate per period (%), n = number of periods.

  5. How is speed related to distance and time?

    Speed = Distance / Time. Therefore Distance = Speed x Time and Time = Distance / Speed.

  6. What is the formula linking density, mass and volume?

    Density = Mass / Volume.

  7. Expand and simplify (a + b)^2.

    a^2 + 2ab + b^2.

  8. Factorise the difference of two squares a^2 - b^2.

    (a + b)(a - b).

  9. How do you factorise a quadratic of the form x^2 + bx + c?

    Find two numbers that multiply to give c and add to give b; write as (x + p)(x + q).

  10. State the quadratic formula for ax^2 + bx + c = 0.

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

  11. What does the discriminant b^2 - 4ac tell you about the roots of a quadratic?

    If > 0: two distinct real roots; if = 0: one repeated real root; if < 0: no real roots.

  12. How do you add or subtract algebraic fractions?

    Find a common denominator, rewrite each fraction over it, then add or subtract the numerators.

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

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

  14. How do you solve a pair of simultaneous linear equations by elimination?

    Make the coefficients of one variable equal (by multiplying), add or subtract the equations to eliminate it, solve for the remaining variable, then back-substitute.

  15. What is the nth term of an arithmetic sequence with first term a and common difference d?

    nth term = a + (n - 1)d.

  16. How do you find the common difference of an arithmetic (linear) sequence?

    Subtract any term from the next term; the difference between consecutive terms is constant.

  17. What is the nth term of a geometric sequence with first term a and common ratio r?

    nth term = a r^(n-1).

  18. How do you find the nth term of a sequence whose second differences are constant (quadratic sequence)?

    It has the form an^2 + bn + c; the coefficient a = (constant second difference) / 2, then solve for b and c using known terms.

  19. What does it mean to say y varies directly as x, and how do you write it?

    y is directly proportional to x: y = kx for a constant k; doubling x doubles y.

  20. What does it mean to say y varies inversely as x, and how do you write it?

    y is inversely proportional to x: y = k/x; doubling x halves y.

  21. How do you find the constant of variation k?

    Substitute a known pair of values into the variation equation and solve for k.

  22. What is the general shape of the graph of y = x^2, and what is it called?

    A parabola: a U-shaped curve symmetrical about the y-axis with a minimum at the origin.

  23. What does the graph of a reciprocal function y = k/x (k > 0) look like?

    A hyperbola: two curves in opposite quadrants, never touching the x- or y-axes (the axes are asymptotes).

  24. For an exponential graph y = a^x (a > 1), describe its key features.

    It passes through (0, 1), rises steeply for positive x, and approaches (but never touches) the x-axis for negative x.

  25. How do you estimate the gradient of a curve at a point from its graph?

    Draw a tangent to the curve at that point, then calculate the gradient of the tangent (change in y / change in x).

  26. What is the formula for the gradient of a line through points (x1, y1) and (x2, y2)?

    Gradient m = (y2 - y1) / (x2 - x1).

  27. State the equation of a straight line in gradient-intercept form and what each letter means.

    y = mx + c, where m is the gradient and c is the y-intercept (where the line crosses the y-axis).

  28. What is the formula for the midpoint of the segment joining (x1, y1) and (x2, y2)?

    Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

  29. What is the relationship between the gradients of two parallel lines?

    Parallel lines have equal gradients (m1 = m2).

  30. What is the relationship between the gradients of two perpendicular lines?

    The product of their gradients is -1; each gradient is the negative reciprocal of the other (m1 x m2 = -1).

Cambridge O Level Mathematics (Syllabus D) 4024 FAQ

What is in the Cambridge O Level Mathematics (Syllabus D) 4024 syllabus?

Cambridge O Level Mathematics (Syllabus D) 4024 is split into 8 chapters: Number, Algebra and Graphs, Coordinate Geometry, Geometry, Mensuration, Trigonometry, Transformations and Vectors and Probability and Statistics. Together they contain 28 topics.

How many chapters are in Cambridge O Level Mathematics (Syllabus D) 4024?

8 chapters, containing 28 topics. The largest chapter is Number, with 5 topics.

Are there flashcards for Cambridge O Level Mathematics (Syllabus D) 4024?

Yes — a 50-card Mathematics (Syllabus D) 4024 deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.