Algebra Concepts Exam Booklet
Integrated Assessment • Q4
QUARTER 4 ALGEBRA CONCEPTS EXAM
Time Limit: 90 Mins 40 Multiple Choice
Student Name
Date
Class Period
Basic Linear Formulas
Slope Formula
m =
y₂ - y₁
x₂ - x₁
Slope-Intercept y = mx + b
Point-Slope y - y₁ = m(x - x₁)
Standard Form Ax + By = C
Visual Slope Models
Positive Slope m > 0 (Rises Right)
Negative Slope m < 0 (Falls Right)
Zero Slope m = 0 (Horizontal)
Undefined Slope m = Vertical (No Run)
Algebra Quick Guide
Function Notation
The expression f(x) is simply a way to write output values, where x is the input and f(x) is the output.
Starting Value
In the equation y = mx + b, b is the y-intercept or the starting value, and m is the slope or rate of change.
Inequality Keywords
| Keyword | Symbol |
|---|
| "At most", "No more than" | ≤ |
| "At least", "Minimum" | ≥ |
| "Less than", "Under" | < |
| "Greater than", "More than" | > |
GENERAL INSTRUCTIONS: Read each question carefully. You may use the formula cards and guides above for help on any problem. For each multiple-choice question, show your math work in the workspace box provided beneath the question, then circle your choice clearly. Do not leave any workspace completely blank.
Quarter 4 Algebra Concepts IA Exam Page 2 of 13
Question 1
What is the slope-intercept form of a linear equation?
A) y = mx + b
B) Ax + By = C
C) y - y₁ = m(x - x₁)
D) m = y/x
Workspace / Reasoning Block
Question 2
In the equation y = 3x + 7, what is the slope?
A) 7
B) 3
C) x
D) 10
Workspace / Reasoning Block
Question 3
In the equation y = -2x + 5, what is the y-intercept?
A) -2
B) -5
C) 5
D) 2
Workspace / Reasoning Block
Question 4
What are the coordinates of the origin point on a coordinate grid?
A) (1, 1)
B) (0, 1)
C) (1, 0)
D) (0, 0)
Workspace / Reasoning Block
Quarter 4 Algebra Concepts IA Exam Page 3 of 13
Question 5
Solve the basic equation: x + 4 = 10
A) 6
B) 14
C) 10
D) 4
Workspace / Reasoning Block
Question 6
Solve the equation: 3x = 12
A) 9
B) 4
C) 15
D) 36
Workspace / Reasoning Block
Question 7
Solve the equation: 2x + 3 = 11
A) 8
B) 7
C) 4
D) 5
Workspace / Reasoning Block
Question 8
Solve the equation: 5x - 2 = 18
A) 3
B) 10
C) 20
D) 4
Workspace / Reasoning Block
Quarter 4 Algebra Concepts IA Exam Page 4 of 13
Question 9
What is the slope of the line that passes through (0, 0) and (2, 4)?
A) 2
B) 1/2
C) -2
D) 4
Workspace / Reasoning Block
Question 10
What is the slope of the line represented by the equation y = -4x + 6?
A) 6
B) -4
C) 4
D) -6
Workspace / Reasoning Block
Question 11
If a line has a slope of 0, what does the graph look like?
A) Vertical
B) Rises to the right
C) Horizontal
D) Falls to the right
Workspace / Reasoning Block
Question 12
Which point is the y-intercept of the line y = 2x - 3?
A) (0, 2)
B) (-3, 0)
C) (2, 0)
D) (0, -3)
Workspace / Reasoning Block
Quarter 4 Algebra Concepts IA Exam Page 5 of 13
Question 13
If x = 4, what is the value of y in the equation y = 2x + 1?
A) 9
B) 7
C) 8
D) 6
Workspace / Reasoning Block
Question 14
Which coordinate point is on the line y = x + 5?
A) (1, 5)
B) (1, 6)
C) (0, 0)
D) (2, 5)
Workspace / Reasoning Block
Question 15
A line has a slope of 3 and a y-intercept of -2. What is its equation in slope-intercept form?
A) y = -2x + 3
B) y = 3x + 2
C) y = 3x - 2
D) y = 2x - 3
Workspace / Reasoning Block
Question 16
Convert the equation 2x + y = 6 to slope-intercept form.
A) y = 2x - 6
B) y = -2x - 6
C) y = 2x + 6
D) y = -2x + 6
Workspace / Reasoning Block
Quarter 4 Algebra Concepts IA Exam Page 6 of 13
Question 17
Which equation represents a line with a negative slope?
A) y = -3x + 4
B) y = 3x - 4
C) y = 2x + 1
D) y = x
Workspace / Reasoning Block
Question 18
Which statement correctly describes the lines y = 2x + 1 and y = 2x - 5?
A) They are perpendicular.
B) They are parallel.
C) They are the same line.
D) They intersect at (0, 0).
Workspace / Reasoning Block
Question 19
Two lines are perpendicular. One has a slope of 4. What is the slope of the other?
A) -4
B) 1/4
C) -1/4
D) 1
Workspace / Reasoning Block
Question 20
Two lines are parallel if their slopes are:
A) Opposites of each other
B) Reciprocals of each other
C) Added together to equal zero
D) Equal to each other
Workspace / Reasoning Block
Quarter 4 Algebra Concepts IA Exam Page 7 of 13
Question 21
What is the slope of a line perpendicular to y = -2x + 1?
A) 1/2
B) -1/2
C) 2
D) -2
Workspace / Reasoning Block
Question 22
Write the equation of a line with a slope of 2 that passes through the point (0, 3).
A) y = 3x + 2
B) y = 2x + 3
C) y = 2x - 3
D) y = -2x + 3
Workspace / Reasoning Block
Question 23
What is the equation of the line that has a slope of 1 and passes through (0, 0)?
A) y = x + 1
B) y = -x
C) y = x
D) y = 1
Workspace / Reasoning Block
Question 24
Which equation represents a line that is parallel to y = 5x + 2?
A) y = -5x + 2
B) y = 1/5x + 2
C) y = -1/5x - 2
D) y = 5x - 4
Workspace / Reasoning Block
Quarter 4 Algebra Concepts IA Exam Page 8 of 13
Question 25
Translate the verbal phrase: "A number increased by 5 is 12."
A) n + 5 = 12
B) n - 5 = 12
C) 5n = 12
D) n/5 = 12
Workspace / Reasoning Block
Question 26
Translate the verbal statement: "A number is less than or equal to 10."
A) n ≥ 10
B) n ≤ 10
C) n < 10
D) n > 10
Workspace / Reasoning Block
Question 27
Connor has $15 and spends $2 on each carnival game. Which expression represents his remaining money after playing g games?
A) 15 + 2g
B) 2g - 15
C) 15 - 2g
D) 15 / 2g
Workspace / Reasoning Block
Question 28
Solve the one-step inequality: x + 5 < 12
A) x > 7
B) x < 17
C) x > 17
D) x < 7
Workspace / Reasoning Block
Quarter 4 Algebra Concepts IA Exam Page 9 of 13
Question 29
Solve the equation: y - 6 = 14
A) 20
B) 8
C) -8
D) 12
Workspace / Reasoning Block
Question 30
Solve the equation: -2x = -10
A) -5
B) 5
C) 12
D) -12
Workspace / Reasoning Block
Question 31
Solve the equation: x + 3 = 3
A) 3
B) 6
C) 0
D) -3
Workspace / Reasoning Block
Question 32
What is the solution to the system of equations: y = 5 and y = x + 2?
A) (5, 3)
B) (5, 7)
C) (7, 5)
D) (3, 5)
Workspace / Reasoning Block
Quarter 4 Algebra Concepts IA Exam Page 10 of 13
Question 33
Identify the correlation: "As the temperature outside gets hotter, sales of ice cream increase."
A) Positive Correlation
B) Negative Correlation
C) No Correlation
D) Constant Correlation
Workspace / Reasoning Block
Question 34
Identify the correlation: "As the number of miles driven increases, the amount of gas left in the tank decreases."
A) Positive Correlation
B) Negative Correlation
C) No Correlation
D) Constant Correlation
Workspace / Reasoning Block
Question 35
A scatter plot shows points scattered randomly with no visible pattern. This is:
A) Positive correlation
B) Negative correlation
C) No correlation
D) Constant correlation
Workspace / Reasoning Block
Question 36
If the line of best fit is y = 2x + 1, what is the predicted value of y when x = 3?
A) 5
B) 6
C) 8
D) 7
Workspace / Reasoning Block
Quarter 4 Algebra Concepts IA Exam Page 11 of 13
Question 37
In the linear equation y = 4x + 10, what is the starting value (y-intercept)?
A) 10
B) 4
C) x
D) y
Workspace / Reasoning Block
Question 38
A gym charges $20 to join and $10 per month. Which equation models the total cost y for x months?
A) y = 20x + 10
B) y = 10x + 20
C) y = 10x - 20
D) y = 30x
Workspace / Reasoning Block
Question 39
Which equation is mathematically equivalent to y = 3x?
A) x + y = 3
B) y + 3x = 0
C) 3x - y = 0
D) x = 3y
Workspace / Reasoning Block
Question 40
A farmer sells apples for $2 each and peaches for $3 each. If total sales were $30, which equation models this using apples a and peaches p?
A) 3a + 2p = 30
B) a + p = 30
C) 2a - 3p = 30
D) 2a + 3p = 30
Workspace / Reasoning Block
Teacher Reference Manual • Solutions
QUARTER 4 ALGEBRA EXAM ANSWER KEY
Assessment Code: IA-Q4-ALGEBRA-SPED Page 12 of 13
Quick-Reference Grading Grid (40 Questions • 2.5 Points Each)
| Q# | Key |
|---|
| Q1 | A |
| Q2 | B |
| Q3 | C |
| Q4 | D |
| Q5 | A |
| Q6 | B |
| Q7 | C |
| Q8 | D |
| Q9 | A |
| Q10 | B |
| Q# | Key |
|---|
| Q11 | C |
| Q12 | D |
| Q13 | A |
| Q14 | B |
| Q15 | C |
| Q16 | D |
| Q17 | A |
| Q18 | B |
| Q19 | C |
| Q20 | D |
| Q# | Key |
|---|
| Q21 | A |
| Q22 | B |
| Q23 | C |
| Q24 | D |
| Q25 | A |
| Q26 | B |
| Q27 | C |
| Q28 | D |
| Q29 | A |
| Q30 | B |
| Q# | Key |
|---|
| Q31 | C |
| Q32 | D |
| Q33 | A |
| Q34 | B |
| Q35 | C |
| Q36 | D |
| Q37 | A |
| Q38 | B |
| Q39 | C |
| Q40 | D |
Performance Category Analysis
Foundational Concepts (10 Questions) Questions: 1, 2, 3, 4, 11, 12, 13, 14, 17, 37
Points: 25.0 pts Weight: 25.0%
Solving Equations (10 Questions) Questions: 5, 6, 7, 8, 28, 29, 30, 31, 32, 39
Points: 25.0 pts Weight: 25.0%
Linear Analysis & Equations (12 Questions) Questions: 9, 10, 15, 16, 18, 19, 20, 21, 22, 23, 24, 38
Points: 30.0 pts Weight: 30.0%
Modeling, Translation & Statistics (8 Questions) Questions: 25, 26, 27, 33, 34, 35, 36, 40
Points: 20.0 pts Weight: 20.0%
Grading Policy Suggestions
Each question is worth 2.5 points for a total of 100 points. To evaluate student progress effectively, award 1.5 points for correct mathematical process shown in the workspace block, and 1.0 point for the correct option selection.
Quarter 4 Algebra Concepts Answer Key Page 13 of 13
Detailed Explanations & Standard Alignments
1. Foundational Concept Solutions
Q2 (Key: B): Direct identification of slope from y = mx + b. The coefficient of x is 3, which represents the slope (Option B).
Q3 (Key: C): Direct identification of y-intercept from y = mx + b. The constant term is 5, representing the y-intercept (Option C).
Q4 (Key: D): The origin of any standard coordinate plane is at the point (0, 0) (Option D).
Q12 (Key: D): The y-intercept of the line is when x = 0, which corresponds to the coordinate point (0, -3) (Option D).
Q13 (Key: A): Evaluate by substitution: y = 2(4) + 1 = 8 + 1 = 9 (Option A).
2. Solving Equations Solutions
Q5 (Key: A): One-step subtraction: x + 4 = 10 leads to x = 10 - 4 = 6 (Option A).
Q6 (Key: B): One-step division: 3x = 12 leads to x = 12 / 3 = 4 (Option B).
Q7 (Key: C): Two-step solution: 2x + 3 = 11 leads to 2x = 8, which simplifies to x = 4 (Option C).
Q8 (Key: D): Two-step solution: 5x - 2 = 18 leads to 5x = 20, which simplifies to x = 4 (Option D).
Q28 (Key: D): One-step inequality: x + 5 < 12 leads to x < 7 (Option D).
3. Linear Analysis & Equations Solutions
Q9 (Key: A): Slope formula: m = (4 - 0) / (2 - 0) = 4 / 2 = 2 (Option A).
Q15 (Key: C): Simply plug the values into slope-intercept form (y = mx + b), giving y = 3x - 2 (Option C).
Q16 (Key: D): Standard form conversion: 2x + y = 6 is converted by subtracting 2x from both sides, giving y = -2x + 6 (Option D).
Q18 (Key: B): Both lines have identical slopes of m = 2 but different y-intercepts (1 and -5). They are parallel (Option B).
Q19 (Key: C): Perpendicular lines have opposite reciprocal slopes. The opposite reciprocal of 4 is -1/4 (Option C).
4. Modeling, Translation & Statistics Solutions
Q25 (Key: A): "Increased by" translates to addition, and "is" translates to equality, yielding n + 5 = 12 (Option A).
Q26 (Key: B): "Less than or equal to" is represented by the symbol ≤, giving n ≤ 10 (Option B).
Q27 (Key: C): Starting with $15 and spending $2 per game yields the subtraction expression 15 - 2g (Option C).
Q34 (Key: B): Since one variable increases (miles driven) and the other decreases (gas in tank), this represents a negative correlation (Option B).
Q40 (Key: D): Standard form modeling: (Cost of apples • a) + (Cost of peaches • p) = Total Sales, yielding 2a + 3p = 30 (Option D).
Confidential Teacher Reference Document. Do not distribute to students. Quarter 4 Cumulative Evaluation System.
