Name: ______Date: ______
Algebra Mid-Term Review: Open Ended Response Practice
The Grant Center for Outdoor Education gives student groups experience in studying nature and helping to restore the environment for fish, birds, and animals.
1.While graphing data at the Grant Center, the students found many linear relationships. They wanted to write equations for some of the lines. Find equations for lines that meet these conditions:
a.Pass through the points (0, 8) and (4, 13)
b.Have a slope of –3 and pass through point (1, 4)
c.Pass through points (1, 1) and (3, 9)
2.Find equations that relate these conditions.
a.A line with slope 3.5 and y-intercept (0, –4)
b.Earnings E of a disk jockey who charges $25 for travel to an event and $20 per hour h of time worked
c.A line through (2, 15) and (6, 7)
d.Base b and height h of rectangles with area 100 cm2
3.A group of Metro Middle School students volunteered to work all day helping to build a new city playground. A local pizzeria offered to supply eight large pizzas for their lunch. The volunteers share the pizza equally.
a.Complete the following table showing how the amount of pizza for each volunteer depends on the number of volunteers.
Number of Volunteers / 1 / 2 / 4 / 8 / 16 / 32Number of Pizzas per Volunteer / 8
b.Is the relationship between the amount of pizza per volunteer and the number of volunteers linear, inverse, or some other pattern? Give an explanation justifying your answer.
c.Write an equation relating amount of pizza per volunteer P to number of volunteers n.
d.Find the amount of pizzas per volunteer if there are 12 volunteers.
4.Which of the following graph patterns would you expect to see if you were told that variables x and y are related by inverse variation? Explain your reasoning.
5.What is an equation of the line shown on the graph below?
6.Solve the following system of linear equations. Name the strategy that you use and show all of your work.
7.Draw a graph illustrating solutions to the following system of linear inequalities. Use the graph to find one possible solution to the system.
Find the equation of a line that is (a) parallel to the line with the given equation and (b) perpendicular to the line with the given equation.
8.y = 4x – 3a) ______b)______
9.y = –2x + 10a) ______b)______
Solve the following inequalities. Then, create number line graphs for each solution.
10.14 < 8x – 2
11.3x + 20 32
12.–3x + 11 > 32
Solve each of the following systems of equations for questions # 13 & 14.
13.
14.
16.If 8y – 8 = 24, find the value of 2y.
17.Solve .
18. Solve: -3( 2 – x) ≥ 6 ( x + 1)
19. Solve: |x + 1| - 7.8 < 6.2
20. A volleyball team scored 14 more points in its first game than in its third game. In the second game, the team scored 28 points. The total number of points scored was less than 80. What is the greatest number of points the team could have scored in its first game?
Algebra Mid-Term Review Open Ended Response
Answer Section
SHORT ANSWER
1.ANS:
a.y = x + 8
b.y = –3x + 7
c.y = 4x – 3
2.ANS:
a.y = 3.5x – 4
b.E = 25 + 20h
c.
d.b = or 100 = bhor h =
3.ANS:
Students may choose different units for pizza (for example, pizzas or slices). The answers provided here are based on whole pizzas as the unit. It would be just as correct to solve the problem using slices, but students will need to specify how many slices they get in each pizza.
a.
Number of Volunteers / 1 / 2 / 4 / 8 / 16 / 32Number of Pizzas per Volunteer / 8 / 4 / 2 / 1 / /
b.Inverse variation; The number of volunteers times the amount of pizza is 8 pizzas; that is, the equation has the form Pn= 8.
c.P = or Pn= 8 or n =
d. of a pizza each
4.ANS:
Graph pattern b; because inverse variation yields a graph that is decreasing and nonlinear, or because inverse variation yields a graph that is decreasing at a decreasing rate
5.ANS:y = 1.5x – 4
6.ANS:
Students may choose their solution methods. Possible solutions by substitution and by linear combination are shown below. In either case, the solution is (2, 3).
Solution by substitution:
is equivalent to .
Substituting, we get x + 3(7 – 2x) = 11.
Solving for x, we get
x + 21 – 6x = 11
–5x = –10
x = 2
Then, we can find y = 3.
Solution by linear combination:
is equivalent to .
Subtracting the top equation from the bottom gives us
5y = 15
y = 3
Then, we can find x = 2.
7.ANS:
One possible solution is (0, 0); answers will vary.
8.ANS:
a.y = 4x + b, where b is any number except –3
b.y = x + b, where b is any number
9.ANS:
a.y = –2x + b, where b is any number except 10
b.y = x + b, where b is any number
10.ANS:
2 < x
14 < 8x – 2
14 + 2 < 8x – 2 + 2
16 < 8x
2 < x
11.ANS:
x 4
3x + 20 – 20 32 – 20
3x 12
x 4
12.ANS:
x < –7
–3x + 11 > 32
–3x + 11 – 11 > 32 – 11
–3x > 21
x < –7
13.ANS:
Solution: (–2, 6); Students may solve this system in a variety of ways. One way is to graph both equations and find the intersection point of both lines.
PTS:1DIF:L2REF:Shapes of Algebra | Question Bank
14.ANS:
Solution: (2, 8); Students may solve this system a variety of ways. One way is to graph both equations and find the intersection point of both lines. In order to do this, students need to solve both equations for y so the equations are in the y = mx + b form. The equations of the lines are y = –x + 10 and
y = –2x + 12. Using combination, the equation 2x + y = 12 can be subtracted from the equation
x + y = 10 to get –x = –2 or x = 2. To find y substitute into the first equation to get y = 8.
15.ANS:
16.ANS:8
17.ANS:19
18.
19.
20.