Functions and Limit

Maths, HSSC-KPK Second Year. This chapter is split into 67 topics and has 1,589 practice questions. The topics covered are listed below, followed by 10 free sample questions from the chapter.

Topics in this chapter

1. Types of real numbers 22 questions
2. Composition of polynomial functions 22 questions
3. Limit of a sequence and convergence 29 questions
4. Definition of continuity at a point and on an interval 21 questions
5. Finding the inverse of a linear function 21 questions
6. Important limits - (a^x - 1)/x and ((1+x)^n - 1)/x 27 questions
7. Trigonometric limit sin x / x 26 questions
8. Laws of exponents 30 questions
9. Functions with and without inverses 20 questions
10. Interval notation and types of intervals 23 questions
11. Other trigonometric limits 23 questions
12. Composition of rational radical and trigonometric functions 21 questions
13. Function definition and variables 23 questions
14. Polynomial functions - degree and coefficients 24 questions
15. Logarithmic model for sales 20 questions
16. Vertical and horizontal asymptotes 25 questions
17. Graphs of logarithmic functions 23 questions
18. Exercise 1.4 - sales function and continuity tests 21 questions
19. Inverse function - definition and properties 21 questions
20. Composition of functions - definition and notation 20 questions
21. Solving exponential equations using logarithms 21 questions
22. Solving logarithmic equations 21 questions
23. Domain of a function 26 questions
24. Limits of rational functions by substitution 23 questions
25. Evaluating polynomial functions 27 questions
26. Parametric equations of curves 29 questions
27. Important limits - (x-a)/(sqrt x - sqrt a) and (x^n - a^n)/(x-a) 25 questions
28. Testing continuity at a point 25 questions
29. Exponential function - definition and properties 22 questions
30. Graphs of exponential functions 26 questions
31. Theorems (rules) on limits of functions 29 questions
32. Solving exponential equations 24 questions
33. Explicit and implicit functions 21 questions
34. Important limits involving the number e 21 questions
35. Evaluating and checking inverse functions 24 questions
36. Definition of limit - drug concentration example 22 questions
37. Range of a function 22 questions
38. Compound (piecewise) functions 25 questions
39. Domain and range from algebraic and graphical examples 23 questions
40. Limits at infinity 26 questions
41. Converting between logarithmic and exponential forms 24 questions
42. Graph of a piecewise function (Example 1.5.7) 22 questions
43. Approximation to significant figures and real number inequalities 26 questions
44. Evaluating composite functions at a point 25 questions
45. Sequences - nth term and functional notation 27 questions
46. Graphs of intervals on the real number line 21 questions
47. One-to-one and many-to-one functions 21 questions
48. Meaning of x tends to 0, a and infinity 23 questions
49. Evaluating rational radical and piecewise functions 30 questions
50. Absolute value function and its graph 23 questions
51. Hyperbolic functions 28 questions
52. Estimating limits from a graph (Example 1.8.4) 21 questions
53. Applications of function evaluation 24 questions
54. Finding constants that make a function continuous 25 questions
55. Inverse of a composition of functions 22 questions
56. Algebraic and transcendental functions 20 questions
57. One-sided continuity and the postage function 25 questions
58. Limits of polynomial functions by substitution 27 questions
59. The number e and exponential growth 24 questions
60. Existence of limits and infinite limits 20 questions
61. Evaluating logarithms without a calculator 27 questions
62. Left-hand and right-hand limits 24 questions
63. Limits by rationalisation 25 questions
64. Properties of logarithms 21 questions
65. Logarithmic functions - definition and notation 23 questions
66. Continuity of standard classes of functions 22 questions
67. Limits by factorisation (indeterminate form 0/0) 25 questions