AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Introduction to Linear Polynomials

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
If p(x) = −6x, then p(2) is:
  1. 12
  2. −4
  3. −13
  4. −12
2.
The zero of 9x + 5 is:
  1. −5/9
  2. 5/9
  3. −1 4/5
  4. 5
3.
A linear polynomial has degree:
  1. 3
  2. 2
  3. 1
  4. 0
4.
The graph of y = −5x − 1 crosses the y-axis at:
  1. (0, −5)
  2. (−5, −1)
  3. (−1, 0)
  4. (0, −1)
5.
A line passes through (5, 40) and (8, 61). Its slope is:
  1. 7
  2. 1/7
  3. 21
  4. −7
6.
Which point lies on the line y = −x − 1?
  1. (1, −3)
  2. (1, −1)
  3. (2, −2)
  4. (1, −2)
7.
The line y = −2x + 6 crosses the x-axis at:
  1. (6, 0)
  2. (−3, 0)
  3. (0, 6)
  4. (3, 0)
8.
A delivery costs Rs 56 plus Rs 19 per km. Which polynomial gives the cost for x km?
  1. 56 + 19x
  2. 56x − 19
  3. 75x
  4. 19 + 56x
Section B — Short answer8 × 2 = 16 marks
9.
Find the values of p(x) = −9x + 3 at x = −1, 1, 3. By how much does p(x) change each time x goes up by 1?
10.
Find the zero of −7x + 11 and check it.
11.
A line passes through (−1, 4) and (0, 7). Find its slope and its equation in the form y = mx + c.
12.
Where does the line y = x + 6 cross each axis?
13.
A gym charges a joining fee of Rs 106 and Rs 19 per visit. Write the cost for x visits as a linear polynomial and find it for 28 visits.
14.
A candle 53 cm tall burns 3 cm every hour. Write its height after t hours, find it after 15 hours, and find when it burns out.
15.
Are the lines y = 4x + 7 and y = 4x + 15 parallel? Do they meet?
16.
For which x is 2x − 8 equal to 16?
Section C — Word problems4 × 4 = 16 marks
17.
Plan A costs Rs 83 plus Rs 8 per hour; plan B costs Rs 66 plus Rs 10 per hour. Write each as a linear polynomial. After how many hours do they cost the same, and which is cheaper for longer use?
18.
Isha has Rs 310 and saves Rs 417 every week. Write the savings after w weeks as a linear polynomial. After how many weeks will Isha have Rs 6,982?
19.
A tank has 30 litres of water and a pipe adds 4 litres a minute. Write the amount after t minutes. How much is there after 18 minutes, and what is the slope of the graph?
20.
Temperature in °F is a linear polynomial of °C: F = 1.8C + 32. Find F when C = 4. What is the slope, and what does it mean?
AmbifulWorksheets
Practice that never repeats
CBSE · Class 9 · Mathematics

Answer key

Introduction to Linear Polynomials · AW-9M-LPO-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) −12−6 × 2 + 0
2(a) −5/99x + 5 = 0 → x = −5/9
3(c) 1the highest power of x is 1
4(d) (0, −1)put x = 0
5(a) 7(61 − 40) ÷ (8 − 5)
6(d) (1, −2)−1 × 1 − 1 = −2
7(d) (3, 0)−2x + 6 = 0
8(a) 56 + 19x—
912, −6, −24; by −9down by 9 each step
101 4/7−7x + 11 = 0 → −7x = −11 → x = 1 4/7
11slope 3; y = 3x + 7slope 3 ÷ 1 = 3; then c = 4 − 3 × (−1) = 7
12y-axis (0, 6); x-axis (−6, 0)x = 0 gives y = 6; y = 0 gives x = −6
13106 + 19x; Rs 638106 + 19 × 28
1453 − 3t; 8 cm; after 17 2/3 hours53 − 3t = 0 → t = 17 2/3
15parallel; they never meetsame slope 4, different y-intercepts 7 and 15
16122x = 16 − (−8) = 24
17A: 83 + 8h; B: 66 + 10h; equal at h = 8 1/2; A is cheaper after that83 + 8h = 66 + 10h → 2h = 17
18310 + 417w; 16 weeks310 + 417w = 6982
1930 + 4t; 102 litres; slope 4 litres per minute30 + 4 × 18
2039.2; 1.8: each 1 °C rise is a 1.8 °F rise1.8 × 4 + 32