Algebra 2 Systems of Linear and Quadratic Equations Test with Point Values (PDF)

Algebra 2 math test: Systems of Linear and Quadratic Equations – Maths PDF

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This nonlinear systems test for Algebra 2 covers systems of linear and quadratic equations (Common Core A-REI.C.7), with a free PDF to print.

This 45-minute test on systems of linear and quadratic equations has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Systems of Linear and Quadratic Equations
Standards: A-REI.C.7
Time: 45 minutes
Total: 20 points

Nonlinear systems test: questions

Question 1 – Check a solution [2 pts]

Determine whether \((3, 2)\) is a solution of \(y = x^{2} – 4x + 5\) and \(y = x – 1\).

Question 2 – Substitution [3 pts]

Solve the system \(y = x^{2} + x – 4\) and \(y = x + 1\). That is a quadratic and a linear equation.

Question 3 – Graph and algebra [3 pts]

Parabola and line.

The parabola \(y = x^{2} – 2x – 3\) and the line \(y = x – 3\) are graphed. Find both intersection points algebraically.

Question 4 – Circle and line [2 pts]

Circle and line.

Solve \(x^{2} + y^{2} = 10\) and \(y = x – 2\).

Question 5 – Number of intersections [2 pts]

For which values of \(k\) does the line \(y = k\) meet the parabola \(y = x^{2} – 4\) in two points?

Question 6 – Break-even [2 pts]

Revenue and cost.

A fundraiser has revenue \(R = -x^{2} + 16x\) and cost \(C = 4x + 20\) (in tens of dollars). Find the break-even values of \(x\).

Question 7 – Two numbers [2 pts]

Two numbers have a difference of 4 and a product of 45. Find all pairs of numbers.

Question 8 – Tangent line [2 pts]

Show that the line \(y = 4x – 4\) is tangent to \(y = x^{2}\).

Question 9 – Find the error [2 pts]

Maya solved \(y = x^{2} – 1\) and \(y = 3\) and wrote only \(x = 2\). Find the complete solution set.

Key facts behind this nonlinear systems test

Key facts

Substitute the line into the quadratic to get one equation in x.
Solve the resulting quadratic; then find y for each x.
D > 0: two intersection points; D = 0: one (tangent); D < 0: none.
A solution is an ordered pair (x, y).
The method also works for a line and a circle.

How to use this nonlinear systems test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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