Co-Ordinate Geometry

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AS Maths – Pure – y=mx+c

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (Up to 7:26)

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5A Slides (Courtesy of Owen134866)

Dr Frost Video

KS5 – Straight Line Equations

Whole Topic Section (Up to 3:27)

Key Skill – Find the gradient of a straight line which is drawn.

K396: Find the Gradient of a Straight Line Which is Drawn.

Key Skill – Find the gradient of a line given two coordinates.

K397: Find the Gradient of a Line Given Two Coordinates.

Bicen Maths Live Lesson

Straight Line Graphs 1 • y=mx+c and Gradient • P1 Ex5A/B • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (Up to 25:00)

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• Dr Frost Slides 1-10✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 270e: Determine the gradient of a straight line which is drawn on axes with scale in ones.
• 270f: Determine the gradient of a straight line which is drawn on axes with unusual scale.
• 270g: Determine the gradient of a line given a sketch of two points on the axes (not to scale).
• 270h: Determine the gradient of a line given two pairs of coordinates, where all coordinates are positive.
• 270i: Determine the gradient of a line given two pairs of coordinates, where 1 or 2 coordinates are negative.
• 270j: Determine the gradient of a line given two pairs of coordinates, where 3 or 4 coordinates are negative.
• 270k: Determine the unknown x or y coordinate given two points and the value of the gradient.
• 270l: Determine an algebraic expression for the gradient of a line given two points.
• 270m: Determine whether three points are collinear.
• 270n: Determine the unknown x or y coordinate given three points which lie on a straight line.
• 270: Exam Practice: Gradient of a line

Other Videos

Finding the gradient of a line

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Slope

Activities

• PhET Graphing Lines

Worksheets

• Kuta Software Worksheets
  • Finding Slope
  • Finding Slope from a Graph
  • Finding Slope from Two Points
• MadAsMaths (T. Madas)
  • Line Coordinate Geometry Exam Questions Basic Q30; Standard Q4 (difficulty 3 of 5)

AS Maths – Pure – y=mx+c

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (From 7:26)

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5B Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video (From 3:27 to 4:50)
• 172 Draw a line from its equation when the gradient is positive. Key Skill Video (GCSE)
• 173 Draw a line from its equation when the gradient is negative. Key Skill Video (GCSE)
• 174 Draw a line from its equation when the gradient is a fraction. Key Skill Video (GCSE)
• 196 Find the gradient of a straight line which is drawn. Key Skill Video (GCSE)
• 198 Find the y-intercept of a straight line which is drawn. Key Skill Video (GCSE)
• 200 Find an equation of a straight line which is drawn. Key Skill Video (GCSE)

Bicen Maths Live Lesson

Straight Line Graphs 1 • y=mx+c and Gradient • P1 Ex5A/B • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (From 25:00)

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 11-16✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 268a: Determine whether a point lies on a line given its equation in the form y = mx + c
• 268b: Determine whether a point lies on a line given its equation in the form ax + by = c
• 268c: Determine the missing x or y coordinate given the equation of a straight line.
• 269a: Determine the x or y intercept of a straight line which is drawn.
• 269b: Determine the x or y intercept of a straight line given an equation by substitution of 0.
• 271a: Write the equation of a line in the form y=mx+c given a gradient and y-intercept.
• 271b: Determine the gradient or y-intercept of a line given its equation in the form y = mx + c
• 271c: Write the equation of a line in the form ax+by=c given a gradient and y-intercept.
• 271d: Determine the gradient or y-intercept of a line given its equation in the form ax + by = c or ax + by + c = 0
• 271e: Determine the steepest line from a set of equations.
• 272a: Determine the equation of a straight line given in the form x=a, y=b, y=x or y=-x
• 272b: Determine the equation of a straight line in y=mx+c form which is drawn, where m is a positive integer.
• 272c: Determine the equation of a straight line in y=mx+c form which is drawn, where m is a negative integer.
• 272d: Determine the equation of a straight line in y=mx+c form which is drawn, where m is fractional.
• 272e: Determine the equation of a straight line in ax+by=c form which is drawn.
• 273a: Draw a line from its equation given in the form y=mx+c when the gradient is positive.
• 273b: Draw a line from its equation given in the form y=mx+c when the gradient is negative.
• 273c: Draw a line from its equation given in the form y=mx+c when the gradient is a fraction.
• 273d: Draw a line with an equation given in the form x+y=a
• 273e: Draw a line with an equation given in the form ax+by=c
• 268: Exam Practice: Relationship between a line and its equation
• 269: Exam Practice: x and y intercepts of a line
• 271: Exam Practice: Understanding the equation of a straight line in slope-intercept form (y=mx+c) or standard form (ax + by = c)
• 272: Exam Practice: Determining the equation of a straight line in slope-intercept or standard form
• 273: Exam Practice: Drawing a line from its equation

Other Videos

The Equation of a Line 2

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Forms of Linear Equations

Activities

• PhET Graphing Lines
• Math = Love (Sarah Carter)
  • ax+by=c Cut & Paste
  • ax+by=c Foldable

• PhET Graphing Slope Intercept

• Median Don Steward Venn Activity✦

Worksheets

• kutasoftware Worksheets
  • Graphing Lines Using Slope-Intercept Form
  • Graphing Lines Using Standard Form
  • Writing Linear Equations
  • Finding Slope from an Equation
  • Graphing Lines Using Slope-Intercept Form
  • Graphing Lines Using Standard Form
• MathedUp
  • Linear graphs: Questions · Challenge · Answers
• MadAsMaths (T. Madas)
  • Line Coordinate Geometry Exam Questions Basic Q16 (difficulty 2 of 5)
  • Line Coordinate Geometry Practice Gradients & Intercepts Q1–2

AS Maths – Pure – Straight Line Graphs

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (Up to 5:40)

Download Blank Notes

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5C Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video (From 4:50 to 10:44)

Bicen Maths Live Lesson

Straight Line Graphs 2 • Equations of Lines using the 'new' formula • P1 Ex5C • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 17-21✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 272f: Determine the equation of a straight line in y=mx+c form given its gradient and a point, where the gradient is an integer.
• 272g: Determine the equation of a straight line in y=mx+c form given a non-integer gradient and a point.
• 272h: Determine the equation of a straight line in ax+by=c form given a gradient and a point.
• 272i: Determine the equation of a straight line in the form y=mx+c given two points.
• 272j: Determine the equation of a straight line in the form ax + by = c given two points.
• 495a: Determine an equation of a straight line given the gradient and one point using y-y₁=m(x-x₁)
• 495c: Determine an equation of a straight line, in the form ax + by = c, given two points using y-y₁=m(x-x₁)
• 272: Exam Practice: Determining the equation of a straight line in slope-intercept or standard form
• 495: Exam Practice: Determining the equation of a straight line in point-slope form (y-y₁ = m(x-x₁))

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• MEI Straight Line Arithmagons✦
• Underground Maths Straight Line Pairs✦
• Math = Love (Sarah Carter)
  • Forms of Linear Equations Foldable
  • Point-Slope Form Dice Activity
  • Forms of Linear Functions Foldable
  • Forms of Linear Equations Flyswatter
  • Point-Slope Form Foldable

AS Maths – Pure – Straight Line Graphs

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept. (From 5:40)

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5D Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Straight Line Graphs 3 • Intersection of Two Lines• P1 Ex5D • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 22-24✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 276k: Solve linear simultaneous equations/systems of equations to determine the point of intersection of two lines.
• 445h: Determine the point of intersection of a line with a given equation and its perpendicular with a given y-intercept.
• 275a: Solve linear simultaneous equations/systems of equations using an existing plot of each line.
• 276: Exam Practice: Solving linear simultaneous equations/systems of equations using elimination or substitution
• 445: Exam Practice: Equations of perpendicular lines
• 275: Exam Practice: Solving linear simultaneous equations/systems of equations using graphical methods

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

AS Maths – Pure – Parallel Lines

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5E Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video (Up to 3:44)

Bicen Maths Live Lesson

No Live Lesson by Bicen Maths for this Section

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 25-29✦ (5E & F)

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 274a: Determine if two straight lines are parallel from their equations in the form y=mx+c
• 274b: Determine if two straight lines are parallel from their equations, requiring rearrangement with addition and subtraction only.
• 274c: Determine if two straight lines are parallel from their equations, requiring rearrangement with multiplication and division.
• 274d: Find an equation of a line parallel to another in the form y=mx+c
• 274e: Find an equation of a line parallel to another given in the form ax+by=c
• 274f: Find an equation of a line in the form y=mx+c which is parallel to the line segment connecting two points.
• 274g: Find an equation of a line in the form ax+by=c which is parallel to the line segment connecting two points.
• 495b: Determine an equation of a straight line, in the form ax + by = c, parallel to another using y-y₁=m(x-x₁)
• 274: Exam Practice: Equations of parallel lines
• 495: Exam Practice: Determining the equation of a straight line in point-slope form (y-y₁ = m(x-x₁))

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF in Next Section

AS Maths – Pure – Perpendicular Lines

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5F Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video

Bicen Maths Live Lesson

Straight Line Graphs 4 • Parallel and Perpendicular Lines • P1 Ex5E/F • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 25-29✦ (5E & F)

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 445a: Determine the gradient of a line perpendicular to another with a given gradient.
• 445b: Determine whether two lines are perpendicular given their equations (no rearrangement).
• 445c: Determine whether two lines are perpendicular given their equations (rearrangement required).
• 445d: Determine whether two lines are perpendicular by calculating their gradients.
• 445e: Find an equation of a line perpendicular to another that passes through a given point.
• 445f: Find an equation of a line perpendicular to another that passes through a given point (rearrangement required).
• 445g: Determine the equation of a line perpendicular to another line that passes through two given points.
• 445i: Determine a missing coordinate on a line given another is perpendicular to it.
• 445j: Determine a point on a line which is closest to another point.
• 445k: Determine the equation of an altitude of a triangle.
• 495d: Find an equation of a straight line, in the form ax + by = c, perpendicular to another using y-y₁=m(x-x₁)
• 445: Exam Practice: Equations of perpendicular lines
• 495: Exam Practice: Determining the equation of a straight line in point-slope form (y-y₁ = m(x-x₁))

Practice Questions

• Practise Questions

Other Videos

Parallel and Perpendicular Lines

Perpendicular Lines

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Mathematics Assessment Project Finding Equations of Parallel and Perpendicular Lines✦ (p10 Onwards)
• Standards Unit Connecting Perpendicular Lines✦
• Underground Maths Lots of lines✦
• Goal Free Problems
  • A-Level Algebra & Coordinate Geometry set Q19, Q24

Worksheet

• Jo Morgan Perpendicular Lines Worksheet✦ (TES Account Required)

AS Maths – Pure – Length and Area in Coordinate Systems

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5G Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Straight Line Graphs 5 • Distance between points, Area problems • P1 Ex5G • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 30-35✦

Exam Practice

• Exam Practice (Equation of a Straight Line)

Extra Questions

• Dr Frost Questions 1 · 2

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 289a: Use Pythagoras’ theorem to find the distance between two points.
• 289b: Use Pythagoras’ theorem to determine the perimeter of a rectangle on a coordinate grid.
• 289c: Use Pythagoras’ theorem to determine the perimeter of a rectangle given the coordinates of its vertices.
• 338b: Use Pythagoras’ theorem to find the distance between two points in simplified surd form.
• 289: Exam Practice: Distance between two 2D points given their coordinates
• 338: Exam Practice: Pythagoras’ Theorem with surds

Practice Questions

• Practise Questions

Other Videos

Finding the length of a line segment

Courtesy of Maths Genie

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Worksheets

• kutasoftware Worksheets
  • Using the Distance Formula
• MadAsMaths (T. Madas)
  • Line Coordinate Geometry Exam Questions Basic Q9, 17, 19, 34, 41; Standard Q11, 17, 23; Hard Q2, 5 (difficulty 2–4 of 5)

Further Activities and worksheets covering all concepts in this chapter at the bottom of this page

AS Maths – Pure – Modelling Straight Line Graphs

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5H Slides (Courtesy of Owen134866)

Dr Frost Video

• Whole Topic Video (From 10:44)

Bicen Maths Live Lesson

Straight Line Graphs 6 • Linear Modelling • P1 Ex5H • 🤖

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 36-40✦

Extra Questions

• Dr Frost Questions

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 269d: Find the area enclosed by a straight line and its intercepts with the axes.
• 332a: Determine the output of a linear model.
• 332d: Interpret the gradient of a straight line which is drawn in context.
• 332e: Interpret the y-intercept of a straight line which is drawn in context.
• 332f: Determine the equation of a straight line which is drawn in context.
• 445m: Solve problems involving the intersection of perpendicular lines with the coordinate axes.
• 445n: Determine the equation of the diagonal of a kite given the coordinates of the vertices on the other diagonal.
• 445o: Determine the coordinates of a point on a kite given one diagonal and another point.
• 445p: Determine the area of a rectangle whose diagonal is a coordinate axis.
• 445q: Show that points make geometric shapes when connected using gradients of parallel and perpendicular lines and their lengths.
• 445r: Determine the area of a triangle with horizontal or vertical base by finding the point of intersection of two perpendicular lines.
• 495f: Determine the area of a triangle enclosed by an axis and two intersecting lines.
• 495g: Determine the area of a quadrilateral enclosed by both axes and two intersecting lines.
• 495h: Determine the equation of a line for a given context using y-y₁=m(x-x₁)
• 495i: Determine the area of a triangle given by 3 coordinates, given the equation of a line between two of them.
• 269: Exam Practice: x and y intercepts of a line
• 332: Exam Practice: Real-life linear graphs
• 445: Exam Practice: Equations of perpendicular lines
• 495: Exam Practice: Determining the equation of a straight line in point-slope form (y-y₁ = m(x-x₁))

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platforms (with Videos & Exercises)

• Khan Academy
  • Applying Intercepts and Slope

Activities

• The Chalk Face Mobile Phone Contracts

Worksheets

• Jethwa Maths Starter Activities (p7-8)
• Physics & Maths Tutor
  • Linear Models: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers

Activities

• The Chalk Face Straight Line Graphs Checklist✦
• MEI Tilted Square✦
• Mr Slack Specify a Line (TES Account Required)
• Mr Southern Maths Co-ordinate Geometry Mixed Exercise  and with Graphs (Preview in tweet below)
• NRICH (student problems)
  • Coordinate Geometry & Graphs
  • Parabella✦
• Transum
  • Coordinate Geometry Table
• Interactive Maths
  • Coordinate Geometry: QQI | 10QQI
• Jo Morgan
  • Find the coordinates (A level taster)✦ (by Jo Morgan)
• Andy Lutwyche
  • Erica's Errors On Straight Line Graphs

External Whole Topic Past Paper Style Questions

• Jethwa Maths Worksheet (p1-3), Topic Test (p1-4) & Starter Activities
• Dr Frost Topic Test✦ (Teacher Log in Required)
• Mathsaurus Mixed Exam Board PPQs
• Naiker Maths Exam Qs (2005-2011)✦ & MS✦
• Numerous Further Solomon Worksheets in Next Chapter at Bottom of Perpendicular Bisectors Section
• PMT
  • Summary Straight Lines PPQs
  • Edexcel Set 1 Co-Ordinate Geometry – Straight Lines PPQs (Old Spec) *Some Differentiation
  • Edexcel Set 2 Co-Ordinate Geometry – Straight Lines PPQs (Old Spec) *Some Differentiation
  • OCR Set 1 C1 Co-Ordinate Geometry PPQs & MS (Old Spec)
  • OCR MEI C1 Co-Ordinate Geometry 1 PPQs & MS (Old Spec)
  • OCR MEI C1 Co-Ordinate Geometry 2 PPQs & MS (Old Spec)
  • OCR MEI C1 Co-Ordinate Geometry 3 PPQs & MS (Old Spec)
  • OCR MEI C1 Co-Ordinate Geometry 4 PPQs & MS (Old Spec)
  • OCR MEI C1 Co-Ordinate Geometry 5 PPQs & MS (Old Spec)
  • Summary Cheat Sheet
• Pret Homework (@Flipmath)
  • Coordinate Geometry (@Flipmath, pdf)
• Susan Wall (Active A-level Maths)
  • Linear Functions: The properties of linear functions · Parallel and perpendicular · Perpendicular bisectors (Susan Wall;

Worksheets

• Mathshelper (Jon Stone)
  • Coordinate Geometry Hard
  • Lines Summary
• Maths Genie
  • Straight Line Graphs: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 1 Coordinate Geometry: Worksheets · Unit Test
• Physics & Maths Tutor
  • Straight Lines: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MME
  • C1 Straight Line Coordinate Geometry: Questions | Answers
• SRWhitehouse
  • Straight Line worksheets✦
• Dr Oliver Mathematics
  • Coordinate Geometry – Linear Graphs: Exam questions✦
  • Coordinate Geometry – Linear Graphs: Dr Oliver✦
• MadAsMaths (T. Madas)
  • Line Coordinate Geometry Exam Questions Basic Q23, 29, 32, 36–37; Standard Q22, 32, 37, 40; Hard Q1, 7, 11, 16, 18; Enrichment Q2–5, 9–13 (difficulty 3–5 of 5)
  • Line Coordinate Geometry Practice Using Standard Formulae Q1–12
• Stuart Price (sxpmaths)
  • Unit 1: Points and Lines (A level booklet)✦
• Susan Whitehouse
  • Straight lines summary✦