Unit 2 Test Student Copy Project: Algebra I // Phase 02
Unit 2 Assessment
Coordinate Geometry & Functions
Student_ID:
Date_Stamp:
Sector:
Operational Instructions:
Verify all data points before plotting. For calculations, provide step-by-step verification. Graphs must be rendered with precision using a straight edge where applicable.
01
Which ordered pair represents the origin on the coordinate plane?
(1, 0)
(0, 1)
(0, 0)
(1, 1)
02
Plot and label the following coordinate points on the grid below:
P1 = (3, -2) P2 = (-1, 4) P3 = (0, 0) P4 = (-2, -3)
x
y
03
Which of the following geometric representations defines a function?
A vertical line
A horizontal line
A parabola opening left
A circle centered at (0,0)
04
Graph the function \( y = 2x - 1 \) on the coordinate plane. Ensure the y-intercept and one other point are clear.
05
Evaluate the relation below using the Vertical Line Test. Is this a function?
Yes, it is a function.
No, it is not a function.
06
Determine the slope of the line passing through (2, 5) and (6, 13). Show all algebraic verification steps.
07
What is the defined slope of any horizontal line?
Undefined
1
0
-1
08
Analyze the distance-time graph. Describe the car's state between hours 2 and 4 .
2h
4h
Distance
09
A linear function passes through (1, 3) with a slope of -2. Write the equation in \( y = mx + b \) form.
10
Identify the quadrant containing points with a negative x-coordinate and a positive y-coordinate .
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
Review Guide Worksheet Protocol: Review // Unit 02
Unit 2 Review Guide
Coordinate Geometry & Functions Mastery
Student_ID:
Date_Stamp:
PART_01
The Coordinate Plane
1. Describe the protocol for plotting the coordinate point (-4, 2). Define what each integer represents in the system.
2. In which quadrant would (5, -3) be localized? Justify your classification using coordinate signs.
3. Define the precise coordinates of the Origin.
PART_02
Functions & The Vertical Line Test
4. Define a mathematical function. Focus on the relationship between inputs and outputs.
5. Explain the operational steps of the Vertical Line Test. How does it confirm function status?
6. Construct a visual representation for each category:
Category A: Valid Function
Category B: Non-Function
PART_03
Slope Analysis
7. Calculate the slope for a line passing through (1, 7) and (3, 11). Use the slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
8. Interpret a positive slope. What does it indicate about the vector's direction?
9. Identify slope values for special linear cases:
Case: Vertical Line
Case: Horizontal Line
PART_04
Graph Interpretation
10. Analyze the thermal cooling graph of a liquid. Detail the behavior for each time interval.
0m
5m
10m
15m
Temp (°C)
0-5 MIN:
5-10 MIN:
10-15 MIN:
11. For the linear equation \( y = -x + 4 \), determine the primary characteristics:
Y-Intercept (b):
Slope (m):
Unit 2 Assessment Slide Deck Grid and Graph Mastery
Unit 2 Assessment: Coordinate Geometry & Functions
Review • Assess • Reflect
Welcome students and introduce the plan for the day: a quick review, the unit assessment, and a short reflection. Emphasize demonstrating their learning.
Quick Review: Coordinate Plane
The Essentials
• What is the coordinate plane ?
• How do we plot points ? $(x, y)$
• Where are the axes and origin ?
x y
Four Quadrants
Prompt students to think about what they remember about the coordinate plane. Ask for examples of where it's used in real life.
Functions & Vertical Line Test
Checking the Relation
What is a function ? (One input, one output)
How can we tell if a graph represents a function?
The Vertical Line Test
Pass or Fail?
Function
Not Function
Review the concept of functions and how to determine if a relation is a function. Introduce or re-emphasize the vertical line test.
Quick Review: Slope
Steepness & Direction
What is slope ?
How do we calculate it? (Rise over Run)
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Positive
-
Negative
0
Zero (Horiz.)
Undefined (Vert.)
Discuss slope as a measure of steepness and direction. Remind them of the slope formula and how to interpret different types of slope.
Interpreting Graphs
Graphs tell a story. What information can we find?
0
Intercepts
Specific Points
Trends
Review how to extract information from a graph, such as intercepts, intervals of increase/decrease, and specific function values.
Practice Time
Review Guide
Work through the worksheet to refresh your memory on these key concepts!
10 Minutes
Solo or Pairs
Distribute the Review Guide Worksheet. Give students about 10 minutes to work on a few problems before going over them.
Review Solutions
Let's review the solutions together.
Unit 2 Test Answer Key Instructor Protocol // Key 02
Assessment Answer Key
Unit 2: Coordinate Geometry & Functions
Teacher Resource Only
Total Points 20 PTS
Pass Threshold 70% (14/20)
Target Proficiency 90% (18/20)
ID_01
Origin Coordinates:
(0, 0)
[1 POINT]
ID_02
Coordinate Mapping Verification:
P1: (3, -2) → Quad IV
P2: (-1, 4) → Quad II
P3: (0, 0) → Origin
P4: (-2, -3) → Quad III
Scoring: 1 point per correct location/label. (4 Total)
ID_03
Function Identification:
A horizontal line
Note: Horizontal lines pass the VLT (one unique y for every x). Vertical lines and circles fail.
ID_04
Linear Function Graphing \( y = 2x - 1 \):
• Y-INT: (0, -1)
• SLOPE: 2/1 (Rise 2, Run 1)
• COORD: (1, 1), (2, 3), (-1, -3)
ID_05
VLT Verification:
No, it is not a function.
The vertical line intersects the relation at two distinct points, violating the function definition.
ID_06
Slope Calculation Verification:
m = (y₂ - y₁) / (x₂ - x₁)
Final Slope (m) = 2
ID_07
Horizontal Line Slope:
m = 0
ID_08
Interval Analysis (2h - 4h):
Car is stationary / Stopped.
The slope is zero, indicating distance does not change relative to time. Velocity = 0 km/h.
ID_09
Equation Derivation (m=-2, P=(1,3)):
y = mx + b
Equation: \( y = -2x + 5 \)
ID_10
Quadrant Identification (-x, +y):
Quadrant II
Grid and Graph Lesson Plan Instructor_Manual // Lesson 02
Grid and Graph Mastery
Unit 2 Assessment: Coordinate Geometry & Functions
65 Minutes Total
Target_Audience
9th Grade Algebra
Session_Focus
Assess & Reflect
Subject_Code
COORDINATE_GEO
Core_Logic: Why This Matters
This summative phase allows the instructor to verify student proficiency in translating spatial concepts to algebraic expressions. Before advancing to systems of equations, mastery of the coordinate plane and function definition is mission-critical.
Learning_Objectives
OBJ_01
Render points accurately across all four quadrants of a Cartesian system.
OBJ_02
Verify function status using the Vertical Line Test protocol.
OBJ_03
Derive slope coefficients from sets of discrete data points.
OBJ_04
Translate linear equations into visual coordinate representations.
Pre_Deployment_Checklist
Replicate Unit 2 Test student copies for the entire sector.
Synchronize Assessment Slide Deck with projector hardware.
Provide high-contrast writing implements and straight-edge tools.
Validate Review Guide against the master answer key.
Operational_Timeline
01
Calibration & Review
15:00 MIN
Initialize the session using the Assessment Slide Deck . Focus specifically on the Vertical Line Test and Slope formula derivation, as these are historically high-error areas.
Teacher Prompt:
"Before we test, look at Slide 4. Why does a vertical line fail to represent a function relationship?"
02
Assessment Execution
45:00 MIN
Deploy the Unit 2 Test . Ensure absolute silence for the duration of the testing cycle. Maintain active surveillance for procedural errors (e.g., misreading axes).
Standard_Mod
Provide grid paper for scratch work.
Extended_Time
Allow 15 additional minutes in Zone B.
03
Post-Action Reflection
05:00 MIN
Data collection: Collect all test materials. Facilitate a 30-second "Gut Check" reflection. Students should mark one topic on their Review Guide that they still find "non-functional" in their understanding for next-session review.
Unit 2 Test Student Copy Project: Algebra I // Phase 02
Unit 2 Assessment
Coordinate Geometry & Functions
Student_ID:
Date:
Operational Instructions:
Verify all data points before plotting. For calculations, provide step-by-step verification. Graphs must be rendered with precision.
01
Which ordered pair represents the origin on the coordinate plane?
(1, 0)
(0, 1)
(0, 0)
(1, 1)
02
Plot and label the following coordinate points on the grid:
P1=(3,-2) P2=(-1,4) P3=(0,0) P4=(-2,-3)
x
y
03
Which of the following geometric representations defines a function?
A vertical line
A horizontal line
A parabola (left)
A circle (0,0)
04
Graph the function \( y = 2x - 1 \). Label the y-intercept.
05
Is the relation below a function? Use the Vertical Line Test.
Yes, function
No, not function
06
Determine the slope of the line passing through (2, 5) and (6, 13). Show all steps.
07
What is the defined slope of any horizontal line?
Undefined
1
0
-1
08
Analyze the car's state between hours 2 and 4 .
09
Write the equation for a line through (1, 3) with slope -2.
