Inequalities Unit Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

____	1.	Use the graph to write the solution of this quadratic inequality: 

A.	, 	C.	, 	
B.	, 	D.	, 	

____	2.	Represent the solution of this quadratic inequality on a number line: 
A.		
B.		
C.		
D.		

____	3.	Solve the quadratic inequality: 
A.	x <  or x > , 	C.	x <  or x > , 	
B.	 < x < , 	D.	 < x < , 	

____	4.	Which coordinates are a solution of the inequality ?
A.	(2, 8)	B.	(0, 1)	C.	(3, 7)	D.	(5, 8)	

____	5.	Match the inequality  to its graph.
A.		C.		
B.		D.		

____	6.	Write an inequality to describe this graph.

A.	–3x + 3y < –9	C.	3x – 3y < –9	
B.	3x – 3y > –9	D.	–3x + 3y > –9	

____	7.	Which statement describes an error in the graph of ?

A.	The incorrect region is shaded.	
B.	The parabola opens in the wrong direction.	
C.	The vertex is incorrect.	
D.	The parabola should be a broken line.	

____	8.	Which graph represents the inequality y £ ?
A.		C.		
B.		D.		

____	9.	Solve this linear-quadratic system algebraically.

A.	(1, –2) and (–1, 6)	C.	(6, 1) and (–2, –1)	
B.	(1, 6) and (–1, –2)	D.	(–2, 1) and (6, –1)	

Short Answer

	1.	Graph the inequality: 

	2.	Solve this quadratic-quadratic system algebraically.

Problem

	1.	The length of a rectangular garden is 5 m greater than its width. The area of the garden is at least 
45 m2. What are possible dimensions of the garden, to the nearest tenth of a metre? Show your work. Verify the solution.

	2.	Two numbers are related in this way:
Twice the square of the first number minus the second number is -3. 
The square of the sum of the first number and 5 is equal to the second number minus 2.
a)	Create a system of equations to represent this relationship. 
b)	Solve the system to determine the numbers. Explain the strategy you used.
Inequalities Unit Test
Answer Section

MULTIPLE CHOICE

	1.	ANS:	B	PTS:	0	DIF:	Easy	
REF:	5.1 Solving Quadratic Inequalities in One Variable	LOC:	11.RF8
TOP:	Relations and Functions	KEY:	Procedural Knowledge

	2.	ANS:	B	PTS:	0	DIF:	Easy	
REF:	5.1 Solving Quadratic Inequalities in One Variable	LOC:	11.RF8
TOP:	Relations and Functions	KEY:	Procedural Knowledge

	3.	ANS:	C	PTS:	0	DIF:	Moderate	
REF:	5.1 Solving Quadratic Inequalities in One Variable	LOC:	11.RF8
TOP:	Relations and Functions	KEY:	Procedural Knowledge

	4.	ANS:	A	PTS:	0	DIF:	Easy	
REF:	5.2 Graphing Linear Inequalities in Two Variables	LOC:	11.RF7
TOP:	Relations and Functions	KEY:	Procedural Knowledge

	5.	ANS:	D	PTS:	0	DIF:	Easy	
REF:	5.2 Graphing Linear Inequalities in Two Variables	LOC:	11.RF7
TOP:	Relations and Functions	KEY:	Conceptual Understanding | Procedural Knowledge

	6.	ANS:	B	PTS:	0	DIF:	Moderate	
REF:	5.2 Graphing Linear Inequalities in Two Variables	LOC:	11.RF7
TOP:	Relations and Functions	KEY:	Conceptual Understanding | Procedural Knowledge

	7.	ANS:	D	PTS:	0	DIF:	Easy	
REF:	5.3 Graphing Quadratic Inequalities in Two Variables	LOC:	11.RF7
TOP:	Relations and Functions	KEY:	Conceptual Understanding

	8.	ANS:	A	PTS:	0	DIF:	Moderate	
REF:	5.3 Graphing Quadratic Inequalities in Two Variables	LOC:	11.RF7
TOP:	Relations and Functions	KEY:	Conceptual Understanding | Procedural Knowledge

	9.	ANS:	A	PTS:	0	DIF:	Easy	
REF:	5.5 Solving Systems of Equations Algebraically	LOC:	11.RF6
TOP:	Relations and Functions	KEY:	Procedural Knowledge

SHORT ANSWER

	1.	ANS:	

PTS:	0	DIF:	Moderate	REF:	5.2 Graphing Linear Inequalities in Two Variables
LOC:	11.RF7	TOP:	Relations and Functions	
KEY:	Conceptual Understanding | Procedural Knowledge

	2.	ANS:	
There are no real solutions.

PTS:	0	DIF:	Moderate	REF:	5.5 Solving Systems of Equations Algebraically
LOC:	11.RF6	TOP:	Relations and Functions	
KEY:	Conceptual Understanding | Procedural Knowledge

PROBLEM

	1.	ANS:	
Write an inequality to represent the problem.
Let x m represent the width of the garden.
Then its length is  m.
And its area, in square metres, is .

The area is at least 45 m2.
So, an inequality is:

Use a graphing calculator to graph the corresponding quadratic function: 
Determine the x-intercepts:  and 
From the graph, the inequality is greater than or equal to 0 for 
Since the width of the garden is positive, the solution of the problem is: 
The width of the garden is greater than or equal to approximately 4.7 m and its length is greater than or equal to approximately , or 9.7 m.

Verify the solution.
The area of the garden with dimensions 4.7 m and 9.7 m is:

This is greater than 45 m2, so the possible dimensions are correct.

PTS:	0	DIF:	Difficult	REF:	5.1 Solving Quadratic Inequalities in One Variable
LOC:	11.RF8	TOP:	Relations and Functions	
KEY:	Communication | Problem-Solving Skills	

	2.	ANS:	
a)	Let x represent the first number and let y represent the second number.
	The statement that twice the square of the first number minus the second number is -3 can be modelled with the equation: 
	The statement that the square of the sum of the first number and 5 is equal to the second number minus 2 can be modelled with the equation: 

	So, the system of equations that represents this relationship is: 
		j
		k
b)	From equation j, substitute  in equation k.
	
	So,  or 	

	Substitute each value of x in equation j.
	When :
		When :
	
	The numbers are: -2 and 11; 12 and 291

	Verify the solutions using the statement of the problem.
	For  and :
	Two times (-2)2 minus 11 is -3.
	The square of  is equal to 
	These numbers satisfy the problem statement.

	For  and :
	Two times (12)2 minus 291 is -3.
	 is equal to 291 minus 2.
	These numbers satisfy the problem statement.

	So, the numbers are: -2 and 11; 12 and 291

PTS:	0	DIF:	Difficult	REF:	5.5 Solving Systems of Equations Algebraically
LOC:	11.RF6	TOP:	Relations and Functions	
KEY:	Communication | Problem-Solving Skills