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NCERT · Ganita Manjari · Volume 1 · Chapter 2

Introduction to Linear Polynomials

45 videos in this chapter

Expressions and polynomials

7 videos

Chapter 2Build an Algebraic Expression from a Shopping Story3:48Build an Algebraic Expression from a Shopping StoryYou'll learn: Translate quantities, repeated groups and a fixed extra into an expression. Identify terms, variables and constants.Chapter 2Why Do Fencing and Planting Produce Different Terms?3:50Why Do Fencing and Planting Produce Different Terms?You'll learn: Model boundary costs and area costs and compare their algebraic terms.Chapter 2One Wire, Many Rectangles: Express the Area3:48One Wire, Many Rectangles: Express the AreaYou'll learn: Use a fixed perimeter to express width and area using one variable.Chapter 2What Is a Polynomial in One Variable?4:10What Is a Polynomial in One Variable?You'll learn: Distinguish expressions involving one variable from the opening two-variable examples.Chapter 2Find Coefficients, Constant Terms and Missing Terms3:49Find Coefficients, Constant Terms and Missing TermsYou'll learn: Read signed coefficients and recognise an absent power as having coefficient zero.Chapter 2Degree: The Highest Power Tells the Type3:53Degree: The Highest Power Tells the TypeYou'll learn: Identify constant, linear, quadratic and cubic polynomials and construct examples.Chapter 2What Makes a Polynomial Linear?3:50What Makes a Polynomial Linear?You'll learn: Recognise degree-one expressions and distinguish them from quadratic and cubic forms.

Linear rules and equations

5 videos

Chapter 2A Square’s Perimeter Grows at a Constant Rate3:53A Square’s Perimeter Grows at a Constant RateYou'll learn: Connect a change in side length to a constant change in perimeter.Chapter 2Joining Fee Plus Match Fee: Build a Linear Rule3:48Joining Fee Plus Match Fee: Build a Linear RuleYou'll learn: Separate a starting amount from an amount added per match and work backwards from a total.Chapter 2When Does an Expression Become an Equation?3:57

Equations in practical situations

4 videos

Chapter 2How Old Are Salil and His Mother?3:55How Old Are Salil and His Mother?You'll learn: Translate an age relationship and a future total into one equation.Chapter 2Use a Ratio to Split a Total or Difference3:53Use a Ratio to Split a Total or DifferenceYou'll learn: Represent related quantities using one variable and solve.Chapter 2Coin Counts and Coin Values Are Different3:45Coin Counts and Coin Values Are Different

Linear patterns, growth and decay

7 videos

Chapter 2See Why the Tile Pattern Has 2n−1 Tiles3:45See Why the Tile Pattern Has 2n−1 TilesYou'll learn: Connect the growing picture, a value table and a general rule.Chapter 2Find a Distant Stage—or Work Back from the Tile Count3:50Find a Distant Stage—or Work Back from the Tile CountYou'll learn: Use a stage rule in both directions.Chapter 2Pocket Money Can Follow a Decreasing Linear Pattern3:21Pocket Money Can Follow a Decreasing Linear Pattern

Growth and decay practice

2 videos

Chapter 2Model a Growing Plant and a Growing Village3:39Model a Growing Plant and a Growing VillageYou'll learn: Form increasing rules, make tables and predict future values.Chapter 2Model a Phone’s Falling Value and a Prepaid Balance3:35Model a Phone’s Falling Value and a Prepaid BalanceYou'll learn: Form decreasing rules and interpret an exhaustion or depreciation calculation.

Finding linear relationships

3 videos

Chapter 2Find a Fixed Fee and a Per-GB Charge from Two Bills3:36Find a Fixed Fee and a Per-GB Charge from Two BillsYou'll learn: Build two conditions and recover the parameters in y=ax+b.Chapter 2Recover Pricing Rules for Learning Modules and Court Time3:32Recover Pricing Rules for Learning Modules and Court TimeYou'll learn: Transfer the two-observation method to other fixed-fee situations.Chapter 2Build the Celsius–Fahrenheit Relationship3:43

Graphs, slope and intercept

8 videos

Chapter 2Draw a Linear Relationship Using Two Points3:32Draw a Linear Relationship Using Two PointsYou'll learn: Turn an equation into coordinate pairs and draw the corresponding straight line.Chapter 2Does a Point Belong to the Line?3:21Does a Point Belong to the Line?You'll learn: Complete a value table and verify point membership by substitution.Chapter 2Read a Linear Rule from Its Plotted Points3:31Read a Linear Rule from Its Plotted Points

Chapter challenge problems

9 videos

Chapter 2Reverse the Digits and Find the Number3:17Reverse the Digits and Find the NumberYou'll learn: Use place value and two digit conditions to recover a two-digit number.Chapter 2Rearrange an Equation Before Reading Its Slope3:39Rearrange an Equation Before Reading Its SlopeYou'll learn: Rewrite equations in y=ax+b, graph them and identify parallel pairs.Chapter 2Convert Between Kelvin and Fahrenheit3:35Convert Between Kelvin and Fahrenheit

When Does an Expression Become an Equation?

You'll learn: Distinguish a polynomial from a statement equating it to a known total.

Chapter 2A Polynomial as an Input-Output Machine3:54A Polynomial as an Input-Output MachineYou'll learn: Explain substitution as a sequence of operations producing an output.

Chapter 2Evaluate Polynomials with Positive, Zero and Negative Inputs3:56Evaluate Polynomials with Positive, Zero and Negative InputsYou'll learn: Substitute carefully and distinguish squaring a negative value from multiplying a signed coefficient.

You'll learn: Represent the number of each coin and build the total-money equation.

Chapter 2Recover a Rectangle’s Dimensions from Its Perimeter3:53Recover a Rectangle’s Dimensions from Its PerimeterYou'll learn: Express length through width and solve the perimeter condition.

You'll learn: Build and interpret a decreasing rule and solve for a target balance.

Chapter 2Why the Auto Fare Rule Starts After the First Two Kilometres3:50Why the Auto Fare Rule Starts After the First Two KilometresYou'll learn: Separate the initial flat fare from later per-kilometre charges.

Chapter 2Can Area and Volume Have Linear Rules?3:40Can Area and Volume Have Linear Rules?You'll learn: Show how fixing other dimensions makes area or volume linear in one changing dimension.

Chapter 2Recognise Linear Growth from Equal Increases3:31Recognise Linear Growth from Equal IncreasesYou'll learn: Read starting value and constant increase from a context and a table.

Chapter 2Recognise Linear Decay from Equal Decreases3:22Recognise Linear Decay from Equal DecreasesYou'll learn: Model a quantity falling by the same amount per time interval.

Build the Celsius–Fahrenheit Relationship

You'll learn: Use two known temperature pairs to determine a and b.

You'll learn: Identify a coordinate relationship from positive and negative input-output pairs.

Chapter 2What Does a Positive Slope Change?3:28What Does a Positive Slope Change?You'll learn: Compare rising lines through the origin and relate coefficient size to steepness.

Chapter 2What Does a Negative Slope Change?3:25What Does a Negative Slope Change?You'll learn: Compare falling lines and explain how coefficient magnitude affects steepness.

Chapter 2Where Does a Line Cross the y-Axis?3:17Where Does a Line Cross the y-Axis?You'll learn: Set x=0 and interpret the signed y-intercept b in y=ax+b.

Chapter 2Change the Constant: Why Do the Lines Stay Parallel?3:19Change the Constant: Why Do the Lines Stay Parallel?You'll learn: Hold a fixed and vary b to compare translated lines.

Chapter 2Read What Changes When a and b Change4:24Read What Changes When a and b ChangeYou'll learn: Compare the five exercise families using graphs and coefficients.

You'll learn: Use a linear temperature formula forwards and backwards.

Chapter 2Work Done as a Linear Graph3:32Work Done as a Linear GraphYou'll learn: Express work as force times distance and interpret the graph.

Chapter 2Recover a Linear Polynomial from Two Points3:19Recover a Linear Polynomial from Two PointsYou'll learn: Find a and b from two graph points, then locate both axis crossings.

Chapter 2Find Two Polynomials from Their Sum and a Graph Condition3:22Find Two Polynomials from Their Sum and a Graph ConditionYou'll learn: Combine p(0), a zero of p−q and the sum identity to recover both rules.

Chapter 2Count Matchsticks in a Growing Chain of Hexagons3:25Count Matchsticks in a Growing Chain of HexagonsYou'll learn: Derive a stage rule using shared sides and test whether a total is possible.

Chapter 2Find a Parallel Line from a Single Point3:29Find a Parallel Line from a Single PointYou'll learn: Find one linear rule from two points, then use its slope to recover a parallel rule.

Chapter 2What Do All Lines y=ax+a Have in Common?3:30What Do All Lines y=ax+a Have in Common?You'll learn: Factor a(x+1) and discover common graphical features.