Algebra 1 Solving Quadratic Equations Test with Point Values (PDF)

Algebra 1 math test: Solving Quadratic Equations – Maths PDF

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This algebra 1 quadratic equations test for Algebra 1 covers solving quadratic equations (Common Core A-REI.B.4a, A-REI.B.4b, A-SSE.B.3a, A-CED.A.1), with a free PDF to print.

This 45-minute test on quadratic equations covers Common Core A-REI.B.4a, A-REI.B.4b, A-SSE.B.3a, and A-CED.A.1 and is worth 20 points. Work alone, show all steps, and use a calculator only if your teacher allows it. Partial credit is given for correct work, so write down your reasoning even when you are unsure of the final answer.

Time and points

About this test

Grade: Algebra 1
Chapter: Solving Quadratic Equations
Standards: A-REI.B.4a, A-REI.B.4b, A-SSE.B.3a, A-CED.A.1
Time: 45 minutes
Total: 20 points

Algebra 1 quadratic equations test: questions

Question 1 – Square roots [2 pts]

Solve \(x^{2} – 64 = 0\). (1 point)
Solve \(3x^{2} = 75\). (1 point)

Question 2 – Factoring [2 pts]

Solve \(x^{2} + 2x – 24 = 0\) by factoring.

Question 3 – Factoring with a leading coefficient [2 pts]

Solve \(3x^{2} – 10x + 3 = 0\).

Question 4 – Completing the square [2 pts]

Solve \(x^{2} + 8x + 5 = 0\) by completing the square.

Question 5 – Quadratic formula [2 pts]

Solve \(3x^{2} – 2x – 4 = 0\) with the quadratic formula. Leave the answer in simplest radical form.

Question 6 – Discriminant [2 pts]

Equations for question 6.

Find the discriminant of each equation and state the number of real solutions.

Question 7 – Rectangle area [3 pts]

Area 84 square meters.

The length of a rectangle is 5 meters more than its width \(w\), and its area is 84 square meters.

Write an equation for the area. (1 point)
Solve the equation. (1 point)
State the dimensions. (1 point)

Question 8 – Ball thrown from a platform [3 pts]

Height of a ball thrown from a platform.

A ball’s height in feet is \(h(t) = -16t^{2} + 40t + 24\). The ball hits the ground when \(h(t) = 0\).

Write the equation in simpler form by dividing by the common factor \(-8\). (1 point)
Solve it. (1 point)
Explain which solution is reasonable. (1 point)

Question 9 – Find the error [2 pts]

A student solved \((x – 2)^{2} = 25\) by writing \(x – 2 = 5\), so \(x = 7\). Explain the error and give all solutions.

Key facts behind this algebra 1 quadratic equations test

Key facts

Standard form: ax² + bx + c = 0 with a ≠ 0.
Zero product property: if A·B = 0, then A = 0 or B = 0.
Square roots: x² = k gives x = ±√k.
Quadratic formula: x = (-b ± √(b² – 4ac)) / 2a.
The discriminant b² – 4ac: positive for two real solutions, zero for one, negative for none.

How to use this algebra 1 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 1 chapters: Algebra 1 math.

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