Linear Polynomials Class 9 Maths Worksheet with Quiz and Activities
Find the degree, slope and intercepts, write the nth term of a pattern and draw lines on a graph. On WitKnowLearn you get the Linear Polynomials Class 9 online quiz, online activities and interactive games, a line lab, a virtual lab and a worksheet-style practice sheet for NCERT Ganita Manjari Chapter 2.
Linear Polynomials Class 9 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
Linear Polynomials Class 9 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
Linear Polynomials: the Raju and Rickshaw Story
A short read for Class 9 before you play. These notes follow Chapter 2 of NCERT Ganita Manjari, Part I.
🛍️ Boxes of pens and pencils
Raju buys x red boxes with 4 pens each and y blue boxes with 5 pencils each, plus 3 free pens. The total is 4x + 5y + 3, an algebraic expression with variables and a constant.
📏 Degree and linear polynomials
A polynomial of degree 1 is a linear polynomial. The perimeter 4x of a square and the fee 200 + 50m of a chess club are linear.
🧱 Growing patterns
Tiles and matchsticks grow stage by stage with a fixed difference. Such a pattern has an nth term of the form dn + b.
📈 Growth and decay
A taxi fare grows by a fixed amount per km, while the water in a tank can fall by a fixed amount per minute. The sign of the slope tells which one it is.
📐 Visualising relationships
Plotting the points of a linear relation gives a straight line. Its slope and intercepts tell the whole story.
Linear Polynomials Class 9 Activities
Evaluate, solve and graph on the Number Train. Earn up to 3 stars in every activity.
This page follows NCERT Class 9 Maths Ganita Manjari, Part I, Chapter 2. Students work with degree, linear polynomials, linear patterns, growth and decay, and the graph of y = ax + b with its slope and intercepts.
The activities are pitched at Class 9 level. Students sort polynomials by degree, pop true facts, match terms, fill formula gaps, solve fare and pattern problems, and draw two lines on a graph by plotting points. Explore more Class 9 maths worksheets on WitKnowLearn after this chapter.
Formulas and facts to know
| Line | Slope | y-intercept | Shows |
|---|---|---|---|
| y = 3x - 2 | 3 | -2 | Growth |
| y = 5 - 2x | -2 | 5 | Decay |
| y = x/2 + 8 | 1/2 | 8 | Growth |
How to use this page
- Flip the six cards and try the Line Lab in the Learn tab.
- Play the five games and the five labs to practise each idea.
- Finish the five challenges to collect up to 15 points.
- Plot two lines in the Virtual Lab and find where they meet.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
Slope = 9/3 = 3, and 7 = 3(2) + b gives b = 1, so 3x + 1.
5t = 10, so t = 2 minutes.
d = 4 and 4 + b = 5, so the nth term is 4n + 1.
This Linear Polynomials worksheet for Class 9 maths gives you online activities and interactive games that make algebra and graphs clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: NCERT Class 9 Maths Linear Polynomials Chapter 2
This guide is for Class 9 students, parents and teachers. It covers Chapter 2 of NCERT Ganita Manjari, Part I, and shows how to use the quiz, labs and games on this page.
Introduction to Linear Polynomials
The chapter starts with algebraic expressions in two variables, defines polynomials and their degree, studies linear polynomials and linear patterns, and ends by drawing the graphs of linear relationships.
What is there in this chapter
- Algebraic expressions, terms, coefficients and constants.
- Polynomials and the degree of a polynomial.
- Linear polynomials and their values.
- Linear patterns and the nth term.
- Linear growth and linear decay.
- Linear relationships such as fares and bills.
- Graphs of linear relationships, slope and intercepts.
Learning objectives
- Identify polynomials and find their degree.
- Evaluate a linear polynomial at a given value.
- Write the nth term of a linear pattern.
- Draw a straight-line graph and read slope and intercepts.
- Reason with assertions and case studies.
Learning outcomes
- The student can find that p(3) = 7 when p(x) = 4x - 5.
- The student can write 4n + 1 for the pattern 5, 9, 13, 17.
- The student can find that two fares are equal at 4 km.
- The student can solve a growth and decay case study about two water tanks.
Linear Polynomials Class 9 resources on this page
| Resource | What it gives |
|---|---|
| Online quiz | 20 questions: 10 easy, 5 average and 5 thinking, with assertion and reason and case study questions and a full review |
| Flip cards | 6 picture cards with one-line rules |
| Line Lab | A hands-on lab with 3 rounds |
| Games | 5 interactive games |
| Labs | 5 activity labs |
| Virtual Lab | 2 experiments and a graph-building lab with aim, procedure, observations and conclusion |
| Challenges | 5 challenges, 15 points in all |
| Practice sheet | A worksheet-style sheet with 16 questions, name and date lines and a live score |
Key facts
| Idea | Rule |
|---|---|
| Linear polynomial | ax + b, degree 1 |
| Constant polynomial | A number, degree 0 |
| Slope | Rise divided by run |
| y-intercept | The value of b |
| x-intercept | Put y = 0 and solve |
| Parallel lines | Same slope, different intercepts |
| Growth and decay | Positive and negative slope |
Types of questions you may see
- Find the degree or a coefficient.
- Evaluate p(a) or find an unknown coefficient.
- Write the nth term of a pattern.
- Find slope and intercepts of a line.
- Assertion and reason questions.
- Case studies on fares, bills and tanks.
Solved examples
4(3) - 5 = 7.
2x + 5 = 0, so (-5/2, 0).
40 + 15d = 25d gives d = 4 km.
At 35 degrees C, F = 95.
11(a + b) = 66, so the digits are 4 and 2: 42 or 24.
They meet at (3, 2) and form a triangle of area 3 sq units with the x-axis.
Common mistakes
| Mistake | Correct idea |
|---|---|
| Calling a constant a linear polynomial. | A non-zero constant has degree 0. |
| Reading the slope from 2y = 4x + 7 as 4. | Divide by 2 first: y = 2x + 3.5, so the slope is 2. |
| Putting x = 0 for the x-intercept. | Put y = 0 for the x-intercept. |
| Calling a negative slope steeper than it is. | Steepness uses the size of the slope, ignoring the sign. |
| Using n instead of n - 1 in the first term. | The nth term is dn + (a - d). |
Linear Polynomials in daily life
Taxi fares, phone plans, gym bills and the cooling of a drink are often linear. Graphs help us compare options and decide when one becomes cheaper than another.
Tips for parents and teachers
- Ask students to write a fare rule for an auto ride and graph it.
- Compare two plans and find where their lines meet.
- Build a matchstick pattern and find its rule.
- Practise one assertion and one case study each week.
Related Class 9 Maths Worksheets
- 🔢Number Systems Class 9 Worksheet
- 🧮Polynomials Class 9 Worksheet
- 📍Coordinate Geometry Class 9 Worksheet
- 📈Linear Equations in Two Variables Class 9
- 📐Introduction to Euclids Geometry Class 9
- 📏Lines and Angles Class 9 Worksheet
- 🔺Triangles Class 9 Worksheet with MCQs
- 🔷Quadrilaterals Class 9 Worksheet
- ⭕Circles Class 9 Worksheet with MCQs
- 🧩Herons Formula Class 9 Worksheet
- 📦Surface Area and Volumes Class 9 Worksheet
- 📊Statistics Class 9 Worksheet
Linear Polynomials Class 9 FAQs
What is Chapter 2 of NCERT Class 9 Maths Ganita Manjari?
Chapter 2 is Introduction to Linear Polynomials. It covers algebraic expressions, linear polynomials, linear patterns, linear growth and decay, linear relationships and how to visualise them as straight-line graphs.
What is a polynomial?
A polynomial is an algebraic expression whose terms are a number times a whole-number power of a variable, such as 3x^2 - 5x + 7. A term like 1/x or the square root of x is not allowed.
What is a linear polynomial?
A linear polynomial is a polynomial of degree 1, such as 4x + 7 or 5 - 3y. It has the form ax + b with a not equal to 0.
What is the degree of a polynomial?
The degree is the highest power of the variable in the polynomial. For 4x + 7 the degree is 1, for x^2 + 1 it is 2, and for a non-zero constant like 8 it is 0.
How do you find the value of a polynomial at a number?
Replace the variable by the number and simplify. If p(x) = 5x - 3, then p(2) = 5 x 2 - 3 = 7.
What is the slope of a line?
The slope tells how steep a line is. It is rise divided by run, the change in y divided by the change in x. In y = ax + b the slope is a.
What is the y-intercept of a line?
The y-intercept is the y-value where the line cuts the y-axis, which is b in y = ax + b. The line passes through the point (0, b).
How do you find where a line cuts the x-axis?
Put y = 0 and solve for x. For y = 3x + 2, 3x + 2 = 0 gives x = -2/3, so the line cuts the x-axis at (-2/3, 0).
What is a linear pattern and how do you find its nth term?
A linear pattern is a sequence with a constant difference between neighbouring terms. If the difference is d and the first term is a, the nth term is dn + (a - d). For 5, 9, 13 the nth term is 4n + 1.
What are linear growth and linear decay?
In linear growth a quantity increases by a fixed amount each step, so the slope is positive. In linear decay it decreases by a fixed amount each step, so the slope is negative.
How do you find where two lines meet?
Set the two expressions equal and solve for x, then find y. The lines y = 2x - 4 and y = -x + 5 meet where 2x - 4 = -x + 5, which gives x = 3 and y = 2.
What can students do on this page?
Students can take a 20-question online quiz with assertion and reason and case study questions, play five games, try five online activities, finish five challenges, run the Line Lab, do two virtual experiments, draw two lines on a graph by plotting points, and fill in a 16-question practice sheet with a Show answers button.
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