Estimate the gradient of a curve
In this lesson, we will estimate the gradient of a curve by drawing a tangent to it. We will learn how to draw tangents to curves.
Unit Overview: Further graphs (Gradients/Area of curves)
Lessons:
4 lessons
Estimate and interpret the gradient of a curve
In this lesson, we will estimate and interpret a gradient for a given curve using triangles.
Find the area under a straight line
In this lesson, we will find the area under a straight line by forming quadrilaterals from the x axis.
Estimate the area under a curve
In this lesson, we will estimate the area under a curve by forming trapeziums from the x axis.
Units in Maths
- Simplifying Surds
- Adding surds
- Multiplying Surds
- Dividing and Rationalising surds
- Solving equations 2 (Simple algebraic fractions)
- Algebraic Fractions
- Factorise and solve a quadratic (a=1)
- Factorise and solve quadratics (a > 1)
- Substitution and Rearranging formulae
- Further Algebra (Change the subject/Binomial expansion)
- Similarity
- Trigonometry 1
- Trigonometry 2
- Trigonometry 3
- Types of Numbers and Rules of Indices
- Negative and Fractional Indices
- Recurring decimals
- Upper and Lower Bounds
- Straight Line Graphs (y=mx+C)
- Straight Line Graphs 2 (Parallel Lines)
- Higher Straight lines (Perpendicular Lines)
- Simultaneous Equations (Linear)
- Scatter Diagrams & Frequency Trees & Averages
- Higher Data 1 (CF and Box Plots)
- Probability 2 (Sample space, Venn diagrams and experimental)
- Higher Probability (Conditional and Further Set Notation)
- Further Quadratic equations
- Quadratic Graphs 1 (a=1)
- Quadratic Graphs 2 (a>1)
- Quadratic sequences
- One linear and one quadratic simultaneous equations
- Parts of a Circle 1 & 2
- Volume and Surface Area 1 (Prisms)
- Volume 2
- Surface Area 2
- Volume and Surface Area 2
- Advanced Trigonometry 1
- Advanced Trigonometry 2
- Advanced Trigonometry 3
- Directed Numbers
- Rules of indices (numbers)
- Standard Form (Writing and converting)
- Standard Form 4 Operations
- Collecting, Indices, Expand and Simplify, Solving Equations 1
- Adding and Subtracting Fractions
- Rotation and Enlargement
- Pythagoras Theorem 1
- Pythagoras Theorem 2
- Factors Multiple and Primes
- Venn Diagrams
- HCF and LCM
- Rounding and Estimating
- Simple Graphs
- Scatter diagrams and Frequency trees
- Averages (From a list and tables, Stem and Leaf)
- Ratio 1 & 2
- Percentage increase and decrease
- Repeated Percentage Change
- Fractions 1, 2, and Fractional Change
- Parts of circles 1 (Semi and quarter circles)
- Parts of circles 2 (Arcs and Sectors)
- Cylinders
- Area and Perimeter
- 4 Rules of Number
- Types of numbers
- Collecting like terms, simplifying
- Expand and simplify brackets
- Rules of Indices
- Solving equations 1 (One step, Two Step and Brackets)
- Reflection
- Factorising (single bracket)
- Solve Inequalities and Represent on Number Line
- Linear Sequences
- Fraction equivalents
- Fractions 1 (adding and subtracting)
- Fractions 2 (multiplying and dividing)
- Fraction Change
- Percentages
- FDP Equivalents
- Decimals
- Ratio 1
- Circles
- Revise - Angles, Polygons, Bearings
- Circle Theorems 1
- Circle Theorems 2
- Functions
- Revise - Simultaneous Equations
- Charts and Tables (Pie Chart and Two way tables)
- Revise - Data (Mean Table, CF Charts)
- Probability 3 (Tree diagrams)
- Histograms
- Cubic and Reciprocal Graphs
- Travel Graphs
- Graphs of Inequalities
- Compound measures
- Volume and Surface Area 1 & 2
- Translate and Vectors 1
- Vectors 2
- Constructions
- Loci
- Angle Facts
- Parallel Lines and Polygons 1
- Polygons 2 (Interior and Exterior)
- Ratio 2 (Ratio and Fractions/Direct Proportion/Best Buy)
- Revise - Solving Equations
- Frequency charts (Data Collection, Bar and Pictograms)
- Probability 1 (Scale and equally likely events)
- Bearings
- Views and Maps
- Constructions & Loci
- Solve equations numerically (Iteration)
- Direct and Inverse Proportion
- Further Algebraic Fractions
- Algebraic Proof
- Circle Graphs
- Data Collection Higher
- Revise - Linear and Quadratic Graphs
- Other Graphs (Trig, Exponetial and Transformations)
- Further graphs (Gradients/Area of curves)
- Volume and Surface Area Higher 3
- Higher Vectors 1
- Higher Vectors 2 and Congruent Triangles
- Enlargement and Similarity
- Algebraic Fractions
- Other Graphs (Trig, Exponetial and Transformations)
- Cubic and Reciprocal Graphs
- Further Algebraic Fractions
- Rules of Indices
- Graphs of Inequalities
- Simultaneous Equations (Linear)
- Expand and simplify brackets
- Quadratic sequences
- Direct and Inverse Proportion
- Functions
- Further graphs (Gradients/Area of curves)
- Revise - Linear and Quadratic Graphs
- Substitution and Rearranging formulae
- Quadratic Graphs 1 (a=1)
- Solving equations 2 (Simple algebraic fractions)
- Solve Inequalities and Represent on Number Line
- Linear Sequences
- Further Quadratic equations
- Solve equations numerically (Iteration)
- Compound measures
- Higher Straight lines (Perpendicular Lines)
- Quadratic Graphs 2 (a>1)
- Straight Line Graphs 2 (Parallel Lines)
- Circle Graphs
- Algebraic Proof
- One linear and one quadratic simultaneous equations
- Revise - Simultaneous Equations
- Simple Graphs
- Travel Graphs
- Factorise and solve quadratics (a > 1)
- Factorise and solve a quadratic (a=1)
- Collecting like terms, simplifying
- Straight Line Graphs (y=mx+C)
- Factorising (single bracket)
- Solving equations 1 (One step, Two Step and Brackets)
- Further Algebra (Change the subject/Binomial expansion)