This was the unit test for Thread 1, linear systems. It was an assessment of learning: it counts toward your grade.
You had 60 minutes. The test was 48 marks, with 12 marks in each of the four evaluation categories, and there was space to answer on the test itself. Grid paper was provided where you needed it.
How the test was organized
Each page of the test was one category. The times were my guide for how long each page should take.
| Page | Category | Marks | About | What the questions asked |
|---|---|---|---|---|
| 1 | Knowledge | 12 | 15 min | Solve three linear systems: one by graphing, one by substitution, one by elimination. |
| 2 | Thinking | 12 | 13 min | Check a claimed solution, decide how many solutions a system has without solving it, and work backwards from a known solution. |
| 3 | Communication | 12 | 11 min | Choose and justify a method for several systems, and explain two key ideas about linear systems in words. |
| 4 | Application | 12 | 11 min | Set up, but do not solve, three word problems: define the variables in sentences and write the two equations. |
What each category rewarded
- Knowledge was accurate algebraic work: a correct solution found by the method asked for.
- Thinking was analysis: connecting two ideas to solve a problem, and justifying a conclusion.
- Communication was explanation: using the vocabulary of this unit (intersect, parallel, coincident, equivalent equations) precisely.
- Application was mathematics tied to a context: “let” statements with units where they apply, and equations that each model one fact from the situation.
Where it came from
Everything on the test was practised in Reviewing Linear Systems. If a question gave you trouble, that review is the place to go back to.
Curriculum connection
B1.1
solve systems of two linear equations involving two variables, using the algebraic method of substitution or elimination (Sample problem: Solve , for and algebraically, and verify algebraically and graphically);
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B1.2
solve problems that arise from realistic situations described in words or represented by linear systems of two equations involving two variables, by choosing an appropriate algebraic or graphical method (Sample problem: The Robotics Club raised $5000 to build a robot for a future competition. The club invested part of the money in an account that paid 4% annual interest, and the rest in a government bond that paid 3.5% simple interest per year. After one year, the club earned a total of $190 in interest. How much was invested at each rate? Verify your result.).
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B1.3
identify the relationship between the slopes of parallel and perpendicular lines, and use this relationship to solve related problems;
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B1.5
represent the equations of lines in different forms (e.g., , , ) and translate between these forms, as appropriate for the context.
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