Algebra 2 Solving Quadratic Equations Test with Point Values (PDF)

Algebra 2 math test: Solving Quadratic Equations – Maths PDF

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This algebra 2 quadratic equations test for Algebra 2 covers solving quadratic equations (Common Core A-REI.B.4a, A-REI.B.4b), with a free PDF to print.

This 45-minute test on solving 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: Solving Quadratic Equations
Standards: A-REI.B.4a, A-REI.B.4b
Time: 45 minutes
Total: 20 points

Algebra 2 quadratic equations test: questions

Question 1 – Square roots [2 pts]

Solve \(3(x + 2)^{2} = 48\).

Question 2 – Factoring [2 pts]

Solve \(3x^{2} – 11x – 4 = 0\) by factoring.

Question 3 – Complete the square [3 pts]

Solve \(x^{2} – 10x + 4 = 0\) by completing the square. Leave irrational answers in radical form.

Question 4 – Quadratic formula [3 pts]

Solve \(2x^{2} – 3x – 4 = 0\) with the quadratic formula. Give exact answers.

Question 5 – Number of solutions [2 pts]

The sign of the discriminant tells how many times the parabola meets the x-axis.

The graphs of \(y = x^{2} – 4\), \(y = x^{2}\), and \(y = x^{2} + 2\) are shown in some order. Without solving, state the discriminant sign and the number of real solutions when each function equals 0.

Question 6 – Complex solutions [2 pts]

Solve \(x^{2} + 4x + 8 = 0\).

Question 7 – Rectangle [2 pts]

Rectangle with area 84 square meters.

A rectangular patio is 5 meters longer than it is wide, and its area is 84 square meters. Find its dimensions.

Question 8 – Falling object [2 pts]

h(t) = -16t² + 32t + 20.

An object’s height is \(h(t) = -16t^{2} + 32t + 20\) feet. When does it reach the ground? Give the exact value.

Question 9 – Find the parameter [2 pts]

For what values of \(k\) does \(x^{2} – 6x + k = 0\) have two real solutions?

Key facts behind this algebra 2 quadratic equations test

Key facts

Square roots: isolate the square, then take ± the root.
Factoring: use the zero product property.
Quadratic formula: x = (-b ± √(b² – 4ac)) / (2a).
Discriminant > 0: two real; = 0: one real; < 0: two complex.
Check solutions, and reject those that do not fit the context.

How to use this algebra 2 quadratic equations 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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