Download Graph the solutions to

Virginia Mathematics Checkpoint Assessment
ALGEBRA II AII.4
ANSWER KEY
Topic: Equations and Inequalities
Standards of Learning Blueprint Summary
Reporting Category
Expressions and Operations
Equations and Inequalities
Functions and Statistics
Geometry SOL
AII.1(a-d), AII.3
AII.4(a-d), AII.5
AII.2, AII.6, AII.7(a-h), AII.8,
AII.9, AII.10, AII.11, AII.12
None
Excluded from Testing
Number of Operational Items
Number of Field-Test Items
Total Number of Items on Test
Number of Items
13
13
24
50
10
60
Virginia Mathematics SOL Test Cut Scores
Failing Scores
Test
Math 3
Math 4
Math 5
Math 6
Math 7
Math 8
Algebra I
Geometry
Algebra II
Basic
# correct
% correct
16 of 40
17 of 50
18 of 50
16 of 50
17 of 50
17 of 50
n/a
n/a
n/a
40%
34%
36%
32%
34%
34%
n/a
n/a
n/a
Passing Scores
Proficient
Minimum
Minimum
# correct
% correct
26 of 40
65%
31 of 50
62%
31 of 50
62%
28 of 50
56%
31 of 50
62%
31 of 50
62%
25 of 50
50%
25 of 50
50%
27 of 50
54%
Algebra II Checkpoint AII.4 ANSWER KEY
Advanced
Minimum
Minimum
# correct
% correct
36 of 40
90%
45 of 50
90%
45 of 50
90%
45 of 50
90%
45 of 50
90%
46 of 50
92%
45 of 50
90%
44 of 50
88%
43 of 50
86%
Page 1
Checkpoint Items
1.
Directions: After showing your thinking, plot points on the number line.
Graph the solutions to 𝟒|𝟐𝒙 + 𝟓| + 𝟖 = 𝟏𝟐.
AII.4aa Solve absolute value equations and inequalities algebraically and graphically
Algebra II Checkpoint AII.4 ANSWER KEY
Page 2
2.
Directions: After showing your thinking, graph the solution on the number line.
Graph the solutions to |𝟐𝒙 − 𝟏| + 𝟐 > 𝟏𝟏.
AII.4aa Solve absolute value equations and inequalities algebraically and graphically
Algebra II Checkpoint AII.4 ANSWER KEY
Page 3
3.
Directions: After showing your thinking, graph the solution on the number line.
Graph the solutions to 𝟐|𝒙 − 𝟒| − 𝟑 < 𝟓.
AII.4aa Solve absolute value equations and inequalities algebraically and graphically
Algebra II Checkpoint AII.4 ANSWER KEY
Page 4
4.
Directions: After showing your thinking, plot points on the graph.
Graph the solutions to the quadratic equation shown.
AII.4bb Solve a quadratic equation over the set of complex numbers using an appropriate strategy
Algebra II Checkpoint AII.4 ANSWER KEY
Page 5
5.
Directions: Circle the box you want to select.
Which statement is true about the quadratic function graphed?
The function has one real root at 3
The function does not have any roots
The function has imaginary roots
The function has imaginary and real roots
AII.4bb Solve a quadratic equation over the set of complex numbers using an appropriate strategy
Algebra II Checkpoint AII.4 ANSWER KEY
Page 6
6.
Directions: Circle the box you want to select. You must select all correct answers.
Which functions have the same solutions as the quadratic function graphed?
𝑓(𝑥) = 4(𝑥 − 3)(𝑥 + 2)
𝑔(𝑥) = −2𝑥 2 + 2𝑥 − 12
𝑗(𝑥) = (𝑥 − 6)2
ℎ(𝑥) = 2(𝑥 + 3)(𝑥 − 2)
AII.4bb Solve a quadratic equation over the set of complex numbers using an appropriate strategy
Algebra II Checkpoint AII.4 ANSWER KEY
Page 7
7.
Directions: After showing your thinking, write your answer in the box.
Jessica is solving quadratic equations by completing the square. What should
Jessica add to both sides of 𝒙𝟐 + 𝟏𝟒𝒙 = 𝟏𝟓 to complete the square?
49
AII.4bb Solve a quadratic equation over the set of complex numbers using an appropriate strategy
Algebra II Checkpoint AII.4 ANSWER KEY
Page 8
8.
Directions: After showing your thinking, circle the box you want to select.
Determine the number of real and complex solutions for the quadratic
equation 𝟔𝒙𝟐 + 𝟓𝒙 = 𝟏𝟎.
One real solution
Two real irrational
solutions
One real and one imaginary
solution
Two imaginary solutions
Two real rational solutions
One imaginary solution
AII.4bc Calculate the discriminant of a quadratic equation to determine the number of real and complex solutions
Algebra II Checkpoint AII.4 ANSWER KEY
Page 9
9.
Directions: Write your answer in the box as a fraction in simplest form.
Solve
𝟑𝒙−𝟏
𝟒𝒙
−
𝟐𝒙+𝟓
𝒙
= 𝟏𝟎.
−
21
45
AII.4cd Solve equations containing rational algebraic expressions with monomial or binomial denominators algebraically and
graphically
Algebra II Checkpoint AII.4 ANSWER KEY
Page 10
10.
Directions: Plot a point on the grid.
Plot a point to represent a solution to 𝟐𝒙𝟐 =
𝟏𝟎
𝟓𝒙
in the first quadrant.
AII.4cd Solve equations containing rational algebraic expressions with monomial or binomial denominators algebraically and
graphically
Algebra II Checkpoint AII.4 ANSWER KEY
Page 11
11.
Directions: Plot a point on the grid.
Plot a point to represent a solution to √𝒙 + 𝟏 = √𝒙 + 𝟓 in the first quadrant.
AII.4de Solve an equation containing a radical expression algebraically and graphically
Algebra II Checkpoint AII.4 ANSWER KEY
Page 12
12.
Directions: Write your answer in the box as a fraction in simplest form.
Solve 𝟓 + √𝟑𝒙 − 𝟐 = 𝟏𝟐.
51
3
AII.4de Solve an equation containing a radical expression algebraically and graphically
Algebra II Checkpoint AII.4 ANSWER KEY
Page 13
13.
Directions: Circle the box you want to select.
Which solutions satisfy the equation
4
−4
𝟑𝒙−𝟐
𝟏
𝒙+𝟒
= 𝟎?
1
4
3
2
2
3
−
−
3
2
AII.4df Verify possible solutions to an equation containing rational or radical expressions
Algebra II Checkpoint AII.4 ANSWER KEY
Page 14
14.
Directions: Circle the box you want to select. You must select all correct answers.
Which solutions satisfy the equation √𝒙(𝟐𝒙 − 𝟓) = √𝟑?
3
−3
1
2
3
2
1
2
−
−
3
2
AII.4df Verify possible solutions to an equation containing rational or radical expressions
Algebra II Checkpoint AII.4 ANSWER KEY
Page 15
15.
Directions: Circle the box you want to select. You must select all correct answers.
Two cars are traveling at the same rate. The blue car drives 50 miles further
than the red car. The red car drives for 1.5 hours and the blue car drives for
.75 hours.
Which equations can be used to determine the distance that each car traveled?
Note: Distance = (rate)(time)
𝑑 + 50
𝑑
=
1.5
. 75
50(.75) = 1.5𝑑
50(1.5) = .75𝑑
1.5𝑑 = .75(𝑑 + 50)
𝑑 + 50
𝑑
=
. 75
1.5
. 75𝑑 = 1.5(𝑑 + 50)
AII.4cg Apply an appropriate equation to solve a real-world problem
Algebra II Checkpoint AII.4 ANSWER KEY
Page 16