This algebra 1 solving quadratics test checks solving quadratic equations in 45 minutes, with 9 questions for a total of 20 points.
This test covers solving quadratic equations and modeling with them, Common Core A-REI.B.4 and A-CED.A.1. It has nine questions worth 20 points. A calculator is allowed. Show all work for full credit.
- Grade: Algebra 1
- Chapter: Solving Quadratic Equations
- Common Core: A-REI.B.4a, A-REI.B.4b, A-APR.B.3, A-CED.A.1
- Time: 45 minutes
- Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 3 pts; Question 4: 3 pts; Question 5: 2 pts; Question 6: 3 pts; Question 7: 2 pts; Question 8: 2 pts; Question 9: 1 pt)
Algebra 1 Solving Quadratics Test: questions 1–5
Question 1: Square roots (2 points)
Solve each equation.
- \(3x^{2}=48\) (1 point)
- \((x+1)^{2}=25\) (1 point)
Question 2: Factoring (2 points)
Solve each equation.
- \(x^{2}+3x-40=0\) (1 point)
- \(3x^{2}-x-2=0\) (1 point)
Question 3: Complete the square (3 points)
Solve \(x^{2}+6x-2=0\) by completing the square. Give exact solutions, then round to the nearest hundredth.
Question 4: Quadratic formula (3 points)
Solve \(2x^{2}-3x-4=0\) using the quadratic formula. Give exact solutions, then round to the nearest hundredth.
Question 5: Discriminant (2 points)
Answer each part.
- Find the discriminant of \(3x^{2}-6x+4=0\) and state how many real solutions it has. (1 point)
- Find the value of \(k\) for which \(x^{2}-8x+k=0\) has exactly one real solution. (1 point)
Algebra 1 Solving Quadratics Test: questions 6–9
Question 6: Use a graph (3 points)
The graph of \(y=x^{2}-4x-5\) is shown.
- Use the graph to solve \(x^{2}-4x-5=0\). (1 point)
- Name the vertex and the axis of symmetry. (1 point)
- For which values of \(x\) is \(y < 0\)? (1 point)
Question 7: Rectangle (2 points)
A rectangular banner is 5 feet longer than it is wide, and its area is 84 square feet. Find its width and length.
Question 8: Ball flight (2 points)
A ball is hit upward and its height in feet after \(t\) seconds is \(h(t)=-16t^{2}+40t+24\). The graph is shown.
- After how many seconds does the ball hit the ground? (1 point)
- Explain why one solution of the equation is not used. (1 point)
Question 9: No real solution (1 point)
A student says that \(x^{2}=-9\) has the solutions \(x=3\) and \(x=-3\). Explain the error.
How to use this algebra 1 solving quadratics test
Take this algebra 1 solving quadratics test without notes, then grade it with the test answer key out of 20 points.
See every chapter on the Algebra 1 math page.
