Tasks | Early Adolescence | Simultaneous Equations

Tasks - Year 8,9

Simultaneous Equations   by Thelma Perso, Senior Curriculum Officer Mathematics

Phase of Development:   Early Adolescence

Learning Area/s:	Mathematics
Strand/s	Substrand/s
Algebra	Understand Graphs Represent Variation Understand Symbols Solve equations and inequalities
Working Mathematically	Apply and Verify
Expected Outcomes:	Students use graphic calculator to enhance understanding of intersection of lines and curves.
Context:	I have used this activity with year 9 and 10 students.
Learning Activities/ Experience:	Students use graphics calculator to graph curves and lines and find points of intersection. Students start with the point of intersection and find equations of the curves intersecting there.
Resources:	Learning Technologies - Graphics Calculator Worksheet

Worksheet

Simultaneous Equations - Points of Intersection

1. Use your calculator to draw the graphs of y = x² - 3 and y = x - 1.

2. Sketch the graph. 3. Estimate the points of intersection. x = _____ y = _____ x = _____ y = _____

4. Use the CALC menu and select intersect; hence find the points of intersection using TRACE.

Left Point = ______(__,__)______

Right Point = ______(__,__)______

5. These points are only graphical approximations.

Check their accuracy using substitution.

1. Use your calculator to draw the graph of y = x² - 3x - 2.

2. Sketch the graph. 3. Find the equations of 3 lines which intersect this curve at the point ( 4 , 2) and some other point (at the same time). (i)   y = _____ (ii)   y = _____ (iii)   y = _____

4. How many lines are there which intersect the curve y = x2 - 3x - 2 in only one place?

5. Can you find the equation(s) of this line(s) ?