Class 10 Mathematics Chapter 4 Full Unit Test 2027 | Functions and Graphs | Punjab Boards Paper Pattern
Class 10 Math Chapter 4 Full unit Test
Class 10 Mathematics Chapter 4 Full Unit Test 2027 is designed for students preparing for the Punjab Boards examinations according to the latest paper pattern. This Functions and Graphs test covers important short-answer and long-answer questions, including functions, composition of functions, inverse functions, absolute value functions, graphs, domain and range, one-to-one and bijective functions, and related problem-solving questions. It is useful for Class 10 Mathematics exam preparation, chapter-wise practice, school tests, and Punjab Board 2027 preparation.
Here is Subjective part of Paper.
(Part-I)
(i) If f(x) = x2 + 3x + 1, then evaluate f(x + 1).
(ii) Let f(x) = 5x + 2, g(x) = x2 − 3. Find f(x) − g(x).
(iii) Find the domain and range of f(x) = (x + 1)2.
(iv) Let f(x) = 2x + 3 and g(x) = x2 + x + 1. Add f(x) and g(x).
(v) If f(x) = 2x2 + 5x then find f(x + 2).
(vi) Let f(x) = x + 1, g(x) = 2x − 3, find f(x) · g(x).
(vii) Let f(x) = x2 − 4, g(x) = x + 2. Find f g (x), where x ≠ −2.
(viii) Define Composition of Function.
(ix) Let f(x) = 2x + 3, g(x) = x2, then find (gof)(x).
(i) Define Bijective Function.
(ii) Define Horizontal Line Test.
(iii) Define One to One function.
(iv) Plot graph for the following absolute valued functions: f(x) = |x − 2|
(v) Solve and express the solution on number line: |6x + 18| ≤ 24
(vi) Find f−1(x), if f(x) = 5 x − 1 , x ≠ 1.
(vii) Find the value of k, such that (fog)(x) = (gof)(x), where f(x) = 3x + 2, g(x) = 6x − k.
(viii) Find f−1(x) in each of the following: f(x) = 2x − 3.
(ix) Without finding f−1(x), find domain and range of f−1(x): f(x) = 12x − 3.
(i) Plot the graph of the following functions: g(x) = |x − 3|
(ii) Solve |2x − 3| = 16 and express the solution on number line.
(iii) Solve and express the solution on number line: |5x + 8| ≤ 3.
(iv) Let E(n) = 1,500n is the total earning (in Rs.) function, where n is the number of days. If labourer works 10 days, find his earning.
(v) Solve and express the solution on number line: |x − 2| = 6.
(vi) The cost of manufacturing fancy sofa set would be fixed charges Rs. 5500 which is modeled as f(n) = 5500n, where n is the number of sofa sets. Find the cost of 50 sofa sets.
(vii) A function f(k) = 150 + 20k represents the total fare (in rupees) for after k kilometres. How much will the fare be for a 12 kilometres ride?
(viii) If f(x) = x3 and g(x) = 14 + 2x, then find: (fog)(x).
(ix) Plot graph for the following absolute valued functions: f(x) = 7|x|.
5:(a) For the function f and g, find (a) (fog)(x), (b) (gof)(x), (c) (fof)(x) and (d) (gog)(x)
Where: f(x) = 2x + 3 ; g(x) = x3
(b) If f(x) = x3, find f−1(x). Also verify that (f−1(x)) = (f−1(x)) = x.
6:(a) Find f−1(x) in each of the following: (iv) f(x) = x + 1 3x − 2 , x ≠ 2 3
(b) Plot graph for the following absolute valued functions: f(x) = 2|x + 4| − 3
7:(a) Solve and express the solution on number line: |1 − 2 3 2 x − 5| > −3
(b) A company charges Rs. 100 for an encoding work. In addition, the company charges Rs. 5 per page of printed output. The model of function f(x) = 100 + 5x, where x represents the number of pages printed out. How much will company charge for 55 page encoding and printing work?
8:(a) Solve and express the solution on number line: |6x + 1| = 9
(b) A GPS system is considered accurate if the actual position differs from the reported position by no more than 6 metres. If the actual location is at point x = 100, the allowed range is defined as: |x − r| ≤ 6, where r is the reported location. What is the range of acceptable reported locations?
9:(a) Plot the graph of the following functions: g(x) = |x − 3|
(b) Express the solution of 40|2x − 5| + 1 > 201 on number line.
