Grade 8 Unit Exam_Simultaneous Linear Equations

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

____	1.	Which ordered pair is the solution of the system graphed?

a.		c.		
b.		d.		

____	2.	Which ordered pair is a solution of the system of equations?

a.		c.		
b.		d.		

____	3.	In astronomy, the immense distances between celestial bodies are measured in light-years, the distance that light can travel in one year. One light-year is approximately 5,880,000,000,000 miles. If a star is 8.5 light-years from Earth, approximately how many miles is it from Earth?
a.	mi	c.	mi	
b.	mi	d.	mi	

____	4.	A system of equations is graphed below.

What conclusion can you draw from the graph and why?

a.	The system has infinitely many solutions because the graph shows two lines.	
b.	The system has no solutions because neither line goes through the origin.	
c.	The solution of the system is (3, –2) because that is the point where the two lines intersect.	
d.	The solution of the system does not appear on the graph because the axes are shown only from –5 to 5.	

____	5.	Solve the system of equations.

a.		c.		
b.		d.		

____	6.	Archie makes and sells small posters and large posters at craft fairs. Suppose Archie charges s dollars for a small poster and l dollars for a large poster. The system of equations  and  represents the total amounts Archie earned selling posters at two different fairs. How much does he charge for a large poster?  
a.	$50	c.	$20	
b.	$25	d.	$15	

____	7.	Which of the following is equivalent to ?
a.		c.		
b.		d.		

____	8.	How many solutions does the system graphed have?

a.	none	c.	2	
b.	1	d.	infinitely many	

____	9.	Simplify .
a.	0	c.	5	
b.	1	d.	25	

____	10.	There are  atoms in 1 gram of oxygen. How many atoms are there in 600 grams of oxygen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.
a.		c.		
b.		d.		

____	11.	In 2010, the population of the Dominican Republic was about . The population of Haiti was about . About how much more was the population of Haiti than the Dominican Republic?
a.		c.		
b.		d.		

____	12.	Which is the quotient of  in scientific notation?
a.		c.		
b.		d.		

____	13.	Which is the product of  in scientific notation?
a.		c.		
b.		d.		

EXTENDED RESPONSE:

	1.	Part A: The average adult human has about 25,000,000,000 red blood cells and about 34,000,000 white blood cells. What is each of these numbers in scientific notation?
Part B: How many more red blood cells does the average adult human have than white blood cells? Express your answer in scientific notation rounded to two decimal places and explain your answer.

Short Answer

	1.	Solve   by graphing.

	2.	A1-Rental charges $35 plus $6 per hour to rent a mini-loader, while BilJax charges $15 plus $8 per hour. 

Part A: Write a system of equations to represent the mini-loader rental costs. 
Part B: What is the solution to a system of equations? What does the solution represent for this situation? 
Part C: Find the solution to the system. 
Part D: If you want to rent a mini-loader for less than 10 hours, which company should you use? Why? 
Part E: If you want to rent a mini-loader for more than 10 hours, which company should you use? Why?

	3.	BONUS QUESTION: The following pyramid has a square base. Find the height of the pyramid. (+ 3 points)

Grade 8 Unit Exam_Simultaneous Linear Equations
Answer Section

MULTIPLE CHOICE

	1.	ANS:	D	PTS:	1	
NAT:	NT.CCSS.MTH.10.8.8.EE.8 | NT.CCSS.MTH.10.8.8.EE.8.a | NT.CCSS.MTH.10.8.8.EE.8.b
DOK:	DOK 1

	2.	ANS:	D	PTS:	1	
NAT:	NT.CCSS.MTH.10.8.8.EE.8 | NT.CCSS.MTH.10.8.8.EE.8.a	
DOK:	DOK 1

	3.	ANS:	B	PTS:	1	REF:	MCT80472	
NAT:	NT.CCSS.MTH.10.7.7.EE.3 | NT.CCSS.MTH.10.8.8.EE.3 | NT.CCSS.MTH.10.8.8.EE.4
STA:	NY.NYLES.MTH.05.7.7.N.5 | NY.NYLES.MTH.05.7.7.N.12	
LOC:	NCTM 6-8.NOP.2.a | NCTM 6-8.NOP.2.b | NCTM 6-8.NOP.1.e	
TOP:	Scientific Notation		KEY:	word | scientific notation | multiply
DOK:	DOK 2

	4.	ANS:	C	PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.8.a
DOK:	DOK 3

	5.	ANS:	B	PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.8
DOK:	DOK 2

	6.	ANS:	C	PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.8.b
KEY:	system of linear equations	DOK:	DOK 2

	7.	ANS:	C	PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.1
DOK:	DOK 1

	8.	ANS:	A	PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.8.a
DOK:	DOK 1

	9.	ANS:	B	PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.1
DOK:	DOK 1

	10.	ANS:	C	PTS:	1	REF:	117d5862-4683-11df-9c7d-001185f0d2ea
OBJ:	Application	NAT:	NT.CCSS.MTH.10.8.8.EE.1	
STA:	NY.NYLES.MTH.05.ALG.A.N.4 | NY.NYLES.MTH.05.ALG.A.A.12
LOC:	MTH.C.10.05.03.02.005 | MTH.C.10.05.03.03.002	
TOP:	Multiplication Properties of Exponents		DOK:	DOK 2

	11.	ANS:	A	PTS:	1	
NAT:	NT.CCSS.MTH.10.8.8.EE.3 | NT.CCSS.MTH.10.8.8.EE.4		
DOK:	DOK 1

	12.	ANS:	B	PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.4
DOK:	DOK 1

	13.	ANS:	C	PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.4
DOK:	DOK 1

ESSAY

	1.	ANS:	
Part A: 
Part B: The difference of the two numbers in standard notation is  When this number is rounded to two decimal places, the answer is 

PTS:	1	REF:	MCT80097	
NAT:	NT.CCSS.MTH.10.7.7.EE.3 | NT.CCSS.MTH.10.8.8.EE.3 | NT.CCSS.MTH.10.8.8.EE.4
STA:	NY.NYLES.MTH.05.7.7.N.5	LOC:	NCTM 6-8.NOP.1.e	
TOP:	Scientific Notation		KEY:	word | scientific notation
DOK:	DOK 2

SHORT ANSWER

	1.	ANS:	

PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.8 | NT.CCSS.MTH.10.8.8.EE.8.a
DOK:	DOK 2

	2.	ANS:	
Part A: 

Part B: The solution is the set of values that satisfy both equations, and is written as an ordered pair such as . The solution represents when the cost and rental time is the same for both companies.
Part C:  or 10 hours at a cost of $95.
Part D: At less than 10 hours, BilJax will coast less than A1-Rental.
Part E: At more than 10 hours, A1-Rental will cost less than BilJax.

PTS:	1	NAT:	NT.CCSS.MTH.10.8.8.EE.8 | NT.CCSS.MTH.10.8.8.EE.8.c
DOK:	DOK 3

	3.	ANS:	
69 m

184 ¸ 2 = 92	(This finds the length of the base leg of the right triangle.)

a2 = 1152 – 922
a2 = 13225 – 8464
a2 = 4761

a = 69

PTS:	1	REF:	9954afe7-9631-11dd-8a40-001185f11039	
NAT:	NT.CCSS.MTH.10.8.8.G.7	STA:	NY.NYLES.MTH.05.7.7.G.8
LOC:	MTH.C.11.03.02.05.02.002	TOP:	The Pythagorean Theorem
KEY:	Pythagorean Theorem | right triangle			DOK:	DOK 2