CDS (Combined Defence Services) Exam Elementary Mathematics (IMA, INA and AFA only) Flashcards

24 sample cards from the Elementary Mathematics (IMA, INA and AFA only) deck

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

1. How do you find the LCM of two polynomials?

   Factorise each polynomial; the LCM is the product of all distinct factors taken with the highest powers.

2. What is the condition for a pair of linear equations to have a unique solution?

   For a1x+b1y+c1=0 and a2x+b2y+c2=0, a unique solution exists when a1/a2 != b1/b2.

3. When does a pair of linear equations have no solution or infinitely many solutions?

   No solution when a1/a2 = b1/b2 != c1/c2 (parallel lines). Infinitely many when a1/a2 = b1/b2 = c1/c2 (coincident lines).

4. What is the quadratic formula for ax^2 + bx + c = 0?

   x = (-b +/- sqrt(b^2 - 4ac)) / (2a).

5. What does the discriminant of a quadratic tell you?

   D = b^2 - 4ac. If D>0: two real distinct roots; D=0: two equal real roots; D<0: no real (complex) roots.

6. What are the sum and product of roots of ax^2 + bx + c = 0?

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

7. What happens to an inequality when both sides are multiplied or divided by a negative number?

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

8. State the formula for the number of elements in the union of two sets.

   n(A union B) = n(A) + n(B) - n(A intersection B).

9. State the three basic laws of indices.

   a^m x a^n = a^(m+n); a^m / a^n = a^(m-n); (a^m)^n = a^(mn). Also a^0 = 1 and a^(-n) = 1/a^n.

10. State the key laws of logarithms.

    log(mn) = log m + log n; log(m/n) = log m - log n; log(m^n) = n log m; log_a a = 1; log_a 1 = 0.

11. Define sine, cosine and tangent in a right triangle.

    sin = opposite/hypotenuse; cos = adjacent/hypotenuse; tan = opposite/adjacent.

12. What are the values of sin, cos and tan at 0, 30, 45, 60 and 90 degrees?

    sin: 0, 1/2, 1/sqrt2, sqrt3/2, 1. cos: 1, sqrt3/2, 1/sqrt2, 1/2, 0. tan: 0, 1/sqrt3, 1, sqrt3, undefined.

13. State the three fundamental trigonometric identities.

    sin^2 A + cos^2 A = 1; 1 + tan^2 A = sec^2 A; 1 + cot^2 A = cosec^2 A.

14. What are the complementary angle relations in trigonometry?

    sin(90-A)=cos A; cos(90-A)=sin A; tan(90-A)=cot A; sec(90-A)=cosec A.

15. In heights and distances, what are the angle of elevation and angle of depression?

    Angle of elevation is the angle above the horizontal to an object higher than the observer; angle of depression is the angle below the horizontal to an object lower than the observer.

16. What is the angle sum of a triangle and the exterior angle theorem?

    Angles of a triangle sum to 180 degrees. An exterior angle equals the sum of the two opposite interior angles.

17. State the Pythagoras theorem and its converse.

    In a right triangle, hypotenuse^2 = sum of squares of the other two sides. Converse: if a^2 + b^2 = c^2, the triangle is right-angled.

18. What is the sum of interior angles of a polygon with n sides?

    Sum of interior angles = (n - 2) x 180 degrees. Sum of exterior angles is always 360 degrees.

19. State the relationship between the angle subtended by an arc at the centre and at the circumference.

    The angle at the centre is twice the angle subtended by the same arc at any point on the remaining circumference.

20. What is the angle in a semicircle?

    The angle in a semicircle is a right angle (90 degrees).

21. What is the formula for the area of a triangle and a circle?

    Area of triangle = (1/2) x base x height. Area of circle = pi r^2.

22. State the curved surface area and volume of a sphere and a cylinder.

    Sphere: surface area = 4 pi r^2, volume = (4/3) pi r^3. Cylinder: curved surface area = 2 pi r h, volume = pi r^2 h.

23. What is the volume and total surface area of a cone?

    Volume = (1/3) pi r^2 h; curved surface area = pi r l; total surface area = pi r (l + r), where l is slant height = sqrt(r^2 + h^2).

24. How are mean, median and mode related (empirical relationship)?

    Mode = 3 Median - 2 Mean. The median is the middle value; the mode is the most frequent value; the mean is the arithmetic average.

What this deck covers

Elementary Mathematics (IMA, INA and AFA only) flashcards FAQ