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Students factorise and expand algebraic expressions including monic quadratic expressions; simplify algebraic products and quotients using index laws and apply the four operations to simple algebraic fractions with numerical denominators. They solve linear simultaneous equations, using algebraic and graphical techniques, explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials.
Year 10: Number and Algebra Classroom ActivitiesDownload
Linear and non-linear relationships
Year 10: Amazing Locus image

Standard ACMNA238

Solve problems involving parallel and perpendicular lines

Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

Activity: Amazing Locus

Students are presented with a challenging problem and provided with the tools to help break it down to see the relatively simple, yet amazing, solution. The problem requires students to calculate gradients, gradients of perpendicular lines, the equation of a line given point and gradient and finally solve a set of equations simultaneously. 
  • ACMNA238
  • ACMNA237
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Year 10: String Graphs Part3 image

Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

Activity: String Graphs Part3

This is part three of a four part series. In this activity students find the points of intersection between consecutive straight lines. (Simultaneous Equations). Students use a range of techniques: by-hand, graphically and using CAS. Students then formulate equations to summaries the consecutive points of intersection. 
  • ACMNA237
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/media library/Images/Activities/AUS-NZ/Missing Image Default

Standard ACMNA214

Find the distance between two points located on a Cartesian plane using a range of strategies, including graphing software

Standard ACMNA238

Solve problems involving parallel and perpendicular lines

Standard ACMNA296

Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations

Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

Activity: Circumcentre

Updated on

Watch Activity Tutorial

Coordinate Geometry - Students calculate gradients, perpendicular gradients, equations to lines (given point and gradient), solve simultaneous equations and calculate the distance between two points, and much more! This activity is part of a series on coordinate geometry and includes companion video tutorials and lots of extension opportunities.

  • ACMNA214
  • ACMNA238
  • ACMNA296
  • ACMNA237
Download
/media library/Images/Activities/AUS-NZ/Missing Image Default

Standard ACMNA234

Substitute values into formulas to determine an unknown

Standard ACMMG243

Formulate proofs involving congruent triangles and angle properties

Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

Activity: Centroid

Updated on

This activity is aligned with the Circumcentre and Orthocentre activities forming a natural progression for the Euler line activity. Students calculate gradients, equations to lines, solve equations simultaneously and use the calculator's tools to check their answers. 
  • ACMNA234
  • ACMMG243
  • ACMNA237
Download
/media library/Images/Activities/AUS-NZ/Missing Image Default

Standard ACMNA238

Solve problems involving parallel and perpendicular lines

Standard ACMNA296

Graph simple non-linear relations with and without the use of digital technologies and solve simple related equations

Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

Activity: Orthocentre

Updated on

Watch Activity Tutorial

Coordinate Geometry - Students calculate midpoints, gradients, perpendicular lines and use simultaneous equations to help determine the location of the orthocentre. A really cool property of the orthocentre is revealed in the extension component of the activity.

  • ACMNA238
  • ACMNA296
  • ACMNA237
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Year 10: Simultaneous Equatons Elimination image

Standard ACMNA237

Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology

Activity: Simultaneous Equatons Elimination

Students are provided with 10 pairs of equations to solve by elimination with the assistance of sliders and a pre-made template to make the process easier to understand. Reducing the number of steps makes the concept easier to understand so that focus can be cast upon the coefficients in the equations.

An extension option includes solving equations with three variables including the 3D representation of the successive results as the intersection of planes, lines and points.

  • ACMNA237
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