Cambridge O Level Mathematics (Syllabus D) 4024 Flashcards

24 sample cards from the Mathematics (Syllabus D) 4024 deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

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

   a^2 + 2ab + b^2.

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

   (a + b)(a - b).

3. 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).

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

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

5. 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.

6. How do you add or subtract algebraic fractions?

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

7. 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 >).

8. 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.

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

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

10. 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.

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

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

12. 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.

13. 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.

14. 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.

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

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

16. 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.

17. 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).

18. 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.

19. 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).

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

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

21. 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).

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

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

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

    Parallel lines have equal gradients (m1 = m2).

24. 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).

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Mathematics (Syllabus D) 4024 flashcards FAQ