Welcome to AS91256 Co-ordinate Geometry
NoteCourse Information
This is a three-week intensive course preparing you for the NCEA Level 2 AS91256 assessment.
TipStudent Workbook (Printable)
About This Course
This website contains resources and content for teaching co-ordinate geometry at Year 11 level. The course is designed as a six-week programme of study leading to assessment under the NCEA Level 2 standard AS91256, worth two credits.
Course Expectations
What You’ll Need
- Calculator: Scientific or graphics calculator
- Notebook: For taking notes and practice problems
- Ruler: For drawing accurate graphs and diagrams
- Graph paper: Recommended for homework and practice
- Commitment: Attend all classes and complete homework regularly
Learning Expectations
Students are expected to:
- Attend regularly: All lessons build on previous concepts
- Participate actively: Ask questions and engage in problem-solving
- Complete homework: Practice is essential for mastery
- Seek help early: Don’t wait until assessment time if you’re struggling
- Practice independently: Work through worksheets and examples
- Show all working: Demonstrate your problem-solving process
Assessment Timeline
- Weeks 1-4: Learn and apply core concepts through lessons and guided practice
- Week 5: Targeted application and mixed-problem practice
- Week 6 (Lessons 1-3): Dedicated practice sessions
- Week 6 (Lessons 4-5): Assessment sessions
- Assessment Duration: 1-1.5 hours
- Credits: 2 NCEA Level 2 credits (Internal Assessment)
Lesson Schedule
| Week | Monday | Tuesday | Wednesday | Thursday | Friday |
|---|---|---|---|---|---|
| Week 1 | Lesson 1: Cartesian Coordinates | Lesson 2: Map It | Lesson 3: Distance Formula | Application: distance in context | Practice: coordinates + distance |
| Week 2 | Lesson 4: Midpoint | Lesson 5: Gradient Basics | Lesson 6: Gradient Formula | Practice: gradient skills | Application: gradient in context |
| Week 3 | Lesson 7: Linear Equations + Intersections | Lesson 8: Parallel Lines | Lesson 9: Perpendicular Lines | Practice: lines and gradients | Application: multi-step line problems |
| Week 4 | Lesson 10: Gradient + Point | Practice: equations and intersections | Application: parallel/perpendicular | Mixed practice (all prior) | Catch-up / extension |
| Week 5 | Lesson 11: Practice and Revision | Practice: targeted weaknesses | Practice: NZQA-style questions | Practice: timed skills | Review: key formulas |
| Week 6 | Practice Session 1 (Lesson 11) | Practice Session 2 (Lesson 11) | Practice Session 3 (Lesson 11) | Assessment Session 1 (Assessment) | Assessment Session 2 (Assessment) |
Course Overview
Co-ordinate geometry (also known as analytic geometry) combines algebra and geometry using a coordinate system. Students will learn to:
- Plot and identify points in the Cartesian plane
- Calculate distances between points
- Find midpoints of line segments
- Determine gradients (slopes) of lines
- Work with equations of lines
- Solve problems involving parallel and perpendicular lines
Course Structure
Week 1: Foundations
Week 2: Midpoint and Gradients
Week 3: Lines and Relationships
Week 4: Consolidation of Line Equations
- Lesson 10: Equation from gradient and a point
- Practice with intersections, parallel and perpendicular lines
- Mixed-problem sessions to connect methods
Week 5: Practice Focus
- Lesson 11: Practice and revision
- Targeted practice blocks and NZQA-style questions
Week 6: Practice and Assessment
- Three practice lessons using Lesson 11
- Two assessment lessons (see Assessment)
Success Strategies
TipTips for Success
- Practice regularly: Mathematics improves with consistent practice
- Show all your working: Marks are awarded for process, not just answers
- Check your answers: Use multiple methods to verify solutions
- Draw diagrams: Visualize problems on graph paper
- Learn from mistakes: Review incorrect answers to understand where you went wrong
- Ask questions: If you’re unsure, ask your teacher or classmates
- Use online resources: Khan Academy, Desmos, and other tools available in References
Achievement Standards
AS91256: Apply co-ordinate geometry methods in solving problems
- Achievement: Use formulas correctly and solve straightforward problems
- Merit: Select appropriate methods and solve multi-step problems with reasoning
- Excellence: Solve complex problems with chains of logical reasoning and full justification
View full details on the Assessment page.
Getting Started
If you’re a teacher, start with the Lessons section to access structured lesson plans.
If you’re a student, explore the Resources section for worksheets and worked examples.