Worksheet with Solutions: Introduction to Linear Polynomials - 1

Q1: Which of the following is a linear polynomial?
 (a) x2+3x+2
 (b) 5x−7
 (c) x3−1
 (d) 4

Q2: In the polynomial p(x)=7x+3, the coefficient of x is:
 (a) 3
 (b) 7x
 (c) 7
 (d) 1

Q3: A linear pattern has consecutive terms: 5, 9, 13, 17, … What is the general term Tn?
 (a) Tn=4n+1
 (b) Tn=5n
 (c) Tn=3n+2
 (d) Tn=4n−3

Q4: The graph of y=−3x+6 represents:
 (a) Linear growth with y-intercept 6
 (b) Linear decay with y-intercept 6
 (c) Linear growth with y-intercept −3
 (d) Linear decay with y-intercept −3

Q5: Two lines y=5x+2 and y=5x−4 are:
 (a) Intersecting at the origin
 (b) The same line
 (c) Parallel to each other
 (d) Perpendicular to each other

Q6:  State whether the following statement is True or False:
 “The polynomial p(x)=9 is a linear polynomial because it has only one term.”

Q7:  State whether the following statement is True or False:
 “In a linear pattern, the difference between any two consecutive terms is always constant.”

Q8:  State whether the following statement is True or False:
 “The point (3,11) lies on the line y=4x−1.”

Q9:  The degree of the polynomial p(x)=6x+11 is __________, and this polynomial is called a __________ polynomial.

Q10:  In the linear relationship y=ax+b, the value of b is called the __________, and it represents the point where the line crosses the __________.

Q11:  The square-tile pattern 1, 3, 5, 7, 9, … is a linear pattern. The constant difference between consecutive terms is __________, and the general term is Tn= __________.

Q12:  If the slope of a linear polynomial y=ax+b is negative, the graph shows linear __________, and as x increases, the value of y __________.

Q13:  A gym charges a one-time registration fee of ₹500 and an additional ₹150 per day for use of its facilities. Write a linear polynomial p(x) representing the total amount paid (in ₹) after x days. Complete the table below, and find:
 (i) The total amount paid after 7 days.
 (ii) The number of days after which the total amount reaches ₹2000.

Days $(x)$	0	1	2	3	4
Amount ₹ $(y)$	?	?	?	?	?

Q14:  A square-tile pattern at each stage n has Tn tiles. The pattern at Stage 1 has 4 tiles and at Stage 2 has 7 tiles, and it follows a linear pattern.(i) Find the general term Tn. (ii) How many tiles are there at Stage 10? (iii) At which stage will the number of tiles be 49?

Q15 :Consider the linear polynomial y=2x−4.
 (a) Find at least three coordinate pairs (x,y) that satisfy the equation by substituting x=0,2,4.
 (b) Plot these points on graph paper and draw the straight line through them.
 (c) What is the y-intercept of the line?
 (d) Does the line show linear growth or linear decay?
 (e) Does the point (3,2) lie on the line? Verify by substituting into the equation.
 (f) At what value of x does y=0? Mark this point on your graph.