Response to
Intervention
Equations by Completing the
Square
1. Which of these is a perfect square trinomial? Choose Yes or No for each.
A 𝑥2− 14𝑥 + 49 Yes No
B 𝑥2+3 4𝑥 +
9
64 Yes No
C 2 17 289 4
x x Yes No
D 16𝑥2− 56𝑥 + 49 Yes No
Find the value for c that completes the square.
2. 𝑥2− 10𝑥 + 𝑐
_______________________________________ 3. 𝑥2+ 9𝑥 + 𝑐
_______________________________________ 4. 𝑥2−7
3𝑥 + 𝑐
_______________________________________ Solve each equation by completing the square.
5. 𝑥2− 2𝑥 = 24
_______________________________________ 6. 2𝑥2− 18𝑥 = 9.5
_______________________________________ 7. 𝑥2+ 1 = 10𝑥 − 15
_______________________________________ 8. The width of a rectangle is 11 centimeters
less than the length. The area of the rectangle is 242 square centimeters. Find the length and the width.
_______________________________________
9. The equation h16t2 24t 5 models
the height h of a ball t seconds after it was tossed upward. To the nearest tenth of a second, how long will the ball be in the air?
________________________________________
Response to Intervention
Post-Test: Solving Quadratic Equations by Factoring
1. What are the solutions of the quadratic equation x22x 3 0?
2. Choose True or False for each statement.
A You can solve a quadratic equation by graphing the related quadratic function and finding its x-intercepts.
True False
B The y-intercepts of a quadratic function are the solutions of the related quadratic equation.
True False
C If a quadratic function intersects the
x-axis at (5, 0) and (1, 0), the solutions of the related quadratic equation are 5 and 1.
True False
D If the solutions of a quadratic equation are 3 and 4, then the related quadratic function has
x-intercepts at (3, 0) and (4, 0).
True False
3. What are the solutions of the equation
(𝑥 + 6)(𝑥 − 8) = 0 ?
A 6 and 8 C 6 and 8
B 6 and -8 D 6 and 8
4. What are the solutions of the quadratic equation 𝑥2− 𝑥 = 56 ?
________________________________________ 5. Explain how to use the Zero Product
Property to solve the quadratic equation
𝑥2− 21𝑥 = 100 You may need to look up the definition.
________________________________________ 6. What are the solutions of the quadratic
equation 2𝑥2= 9𝑥 + 35
A 2.5 and 7 C 7 and 5
B 2.5 and 7 D 7 and 5
7. A rectangular prism has a volume of 110 cubic inches. Its dimensions are 5 inches, (x 2) inches, and
(x 7) inches. What is the value of x?
________________________________________
8. What are the solutions of the quadratic equation 9𝑥2− 144 = 0 ?
________________________________________ SKILL
Response to Intervention
Post-Test: Solving Systems of Linear Inequalities
1. Which points are solutions of the following system of linear inequalities?
{𝑥 − 4𝑦 < 12𝑥 + 𝑦 > −3
A (1, −3) C (2, 5)
B (8, −2) D (2, 0)
2. Solve the system by graphing.
{ 𝑥 + 𝑦 > 2𝑥 − 32𝑥 − 𝑦 ≤ 1
With inequalities you must shade where
common solutions exist. Do you dash or make a solid line for the graph of the inequality?
3. Consider a system of linear inequalities in which the boundary lines are parallel. Choose True or False for each statement.
A The system may have no solution.
True False
B The solutions of the system may be the solutions of exactly one inequality in the system.
True False
C The solutions of the system may be the points in the region between the two boundary lines.
True False
4. Solve the system by graphing.
{ 𝑦 > −4𝑥 − 𝑦 > 3
With inequalities you must shade where
Response to Intervention
Post-Test: Systems of Two Linear Equations
1. What is the solution of the linear system graphed below?
{ 6𝑥 + 3𝑦 = 182𝑥 + 𝑦 = 1
_______________________________________ 2. Solve the linear system by graphing.
{ 3𝑥 + 𝑦 = 3𝑥 − 𝑦 = 5
_______________________________________
3. Choose True or False for each statement.
A When solving a linear system, if you get an identity, such as 3x+2 3x+2, then the system has infinitely many solutions.
True False
B When solving a linear system, if you get a false statement, such as 4 -3, then the system has infinitely many solutions.
True False
C When graphing a linear system, if the two lines intersect at only one point, then the system has no solution.
True False
D When graphing a linear system, if the two lines are parallel, then the
system has exactly one solution.
True False
4. Solve the system by substitution.
{ 2𝑥 + 3𝑦 = 9𝑥 + 𝑦 = −1
________________________________________ 5. Solve the system by elimination.
{ 2𝑥 + 3𝑦 = 11𝑥 + 4𝑦 = −2
________________________________________ SKILL
Response to Intervention
Post-Test: The Quadratic Formula
Identify a, b, and c for each quadratic equation. Then set up an equation for the solution using the quadratic formula. Do not solve.
1. 2𝑥2− 10𝑥 + 3 = 7
_______________________________________ 2. −3𝑥2= −10
_______________________________________ Solve each equation using the quadratic formula.
3. 2𝑥2+ 1𝑥 = −3
_______________________________________ 4. 𝑥2− 4𝑥 + 9 = 9
_______________________________________
5. Look at each equation. Does the equation have two real solutions? Select Yes or No for each.
A 4𝑥2− 8𝑥 + 4 = 0 Yes No
B 2𝑥2− 4𝑥 = 30 Yes No
C 3𝑥2− 2𝑥 + 1 = −3 Yes No
Find the discriminant. Then state the number of real solutions of each quadratic equation.
6. 5𝑥2− 1𝑥 + 2 = 0
________________________________________ 7. −𝑥2= −36
________________________________________ 8. 𝑥2= 10𝑥 − 25
________________________________________ 9. A baseball is hit by a bat 2 feet above the
ground and has an initial velocity of 40 feet per second. The height of the baseball t seconds after being hit can be modeled by the equation:
ℎ(𝑡) = −16𝑡2+ 40𝑡 + 2
a. How long does the ball stay in the air? Round your answer to the nearest tenth.
____________________________________ b. Calculate the discriminant for a
height of 28 feet. Will the baseball ever reach that height? Explain how you know.
____________________________________ ____________________________________ ____________________________________ SKILL
Response to Intervention
Post-Test: Transforming Quadratic Functions
1. Consider the graph of the quadratic function 𝑔(𝑥) = −12𝑥2. Which of the
following statements is true?
A It is wider than the graph of f x( )x2. B It is narrower than the graph of
2 ( )
f x x .
C It is a reflection across the x-axis of 2
( ) .
f x x
2. How are the graphs of f x( )x2, ℎ(𝑥) =
2𝑥2, and 𝑔(𝑥) = −2𝑥2 related? Graph all
three functions in the coordinate plane.
_______________________________________ _______________________________________ _______________________________________
3. Which function’s graphs appear wider than the graph of f x( )x2?
A 𝑔(𝑥) = 2𝑥2 C 𝑔(𝑥) = 0.3𝑥2
B 𝑔(𝑥) =29𝑥2 D 𝑔(𝑥) = −35 𝑥2
4. Choose True or False for each statement.
A The vertex of the graph of
𝑔(𝑥) + 4 = 2(𝑥 + 9)2 is ( 9 ,4).
True False
B The vertex of the graph of
𝑔(𝑥) = 3(𝑥 + 1)2− 6 is the highest point of the graph.
True False
5. Graph 𝑔(𝑥) − 5 = −(𝑥 − 2)2. SKILL
Solve the systems using the substitution method.
1) 2)
Solve the systems using the elimination method.
3) 4)
Solve the systems using the matrices.
5)
6)
