Grade 11 Midterm Examination

Comprehensive Assessment Covering First Semester Content

Total Questions 50 Questions
Time Allowed 2 Hours 30 Minutes
Total Points 100 Points
Format Multiple Choice + Free Response

Exam Instructions

  • Read each question carefully before answering.
  • For multiple choice questions, select the best answer.
  • For free response questions, show all work for full credit.
  • Calculator use is permitted for the Mathematics section only.
  • Manage your time wisely across all sections.

📐 Section 1: Mathematics (20 points)

10 questions, 2 points each. Calculator permitted.

Reference Formulas

Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a

Sum of Arithmetic Series: S = n(a₁ + aₙ)/2

Distance Formula: d = √((x₂-x₁)² + (y₂-y₁)²)

1.Simplify: (3 + 2i)(4 - 5i)

  • 22 - 7i
  • 12 - 7i
  • 22 + 7i
  • 2 - 7i

2.Find all solutions to x² + 6x + 13 = 0.

  • x = -3 ± 2i
  • x = 3 ± 2i
  • x = -3 ± 4i
  • x = -6 ± 2i

3.What is the degree of the polynomial f(x) = 2x⁴ - 3x³ + x² - 7x + 5?

  • 3
  • 4
  • 5
  • 2

4.If sin(θ) = 3/5 and θ is in Quadrant I, what is cos(θ)?

  • 4/5
  • 3/4
  • 5/4
  • -4/5

5.Evaluate: log₂(32)

  • 4
  • 5
  • 6
  • 16

6.Which expression is equivalent to e^(2ln(x))?

  • 2x
  • x²
  • 2eˣ
  • ln(x²)

7.A polynomial function has zeros at x = -2, x = 1, and x = 3. Which could be the function?

  • f(x) = (x + 2)(x - 1)(x - 3)
  • f(x) = (x - 2)(x + 1)(x + 3)
  • f(x) = (x + 2)(x + 1)(x + 3)
  • f(x) = (x - 2)(x - 1)(x - 3)

8.What is the exact value of sin(π/4)?

  • 1/2
  • √2/2
  • √3/2
  • 1

9.The population of a city is modeled by P(t) = 50,000(1.03)^t where t is years since 2020. What does 1.03 represent?

  • The initial population
  • A 3% annual growth rate
  • A 30% annual growth rate
  • The population after 1 year

10.Solve: 2^(x+1) = 16

  • x = 2
  • x = 3
  • x = 4
  • x = 5

📚 Section 2: English Language Arts (20 points)

10 questions, 2 points each.

Passage A (Questions 11-14)

The rise of artificial intelligence in education presents both remarkable opportunities and significant challenges. Proponents argue that AI-powered tutoring systems can provide personalized learning experiences tailored to each student's pace and style, potentially democratizing access to quality education. Critics, however, warn that over-reliance on technology may undermine the irreplaceable human elements of teaching—the mentorship, emotional support, and spontaneous intellectual exchanges that shape not just what students know, but who they become. Perhaps the most prudent approach lies in viewing AI not as a replacement for human educators, but as a tool that, when thoughtfully implemented, can amplify their effectiveness while preserving the essentially human core of education.

11.The author's attitude toward AI in education can best be described as:

  • Enthusiastically supportive
  • Cautiously balanced
  • Deeply skeptical
  • Completely neutral

12.According to the passage, critics of AI in education are primarily concerned about:

  • The cost of implementing new technology
  • Students becoming too dependent on computers
  • The loss of human aspects of teaching
  • AI systems making errors in grading

13.The phrase "democratizing access to quality education" most nearly means:

  • Making education more political
  • Making quality education available to all
  • Allowing students to vote on curriculum
  • Reducing the cost of private schools

14.The author suggests that the best use of AI in education would be to:

  • Replace teachers in overcrowded classrooms
  • Enhance human teaching rather than replace it
  • Focus only on STEM subjects
  • Eliminate traditional classroom instruction

15.Select the sentence that corrects the grammatical error:

"Neither the students nor the teacher were able to solve the complex equation."

  • Neither the students nor the teacher was able to solve the complex equation.
  • Neither the students nor the teachers were able to solve the complex equation.
  • The sentence is correct as written.
  • Neither the student nor the teacher were able to solve the complex equation.

16.Which revision best improves the clarity and concision of this sentence?

"Due to the fact that the experiment failed, the scientists decided to start over from the beginning again."

  • Because the experiment failed, the scientists decided to start over.
  • Due to the experiment's failure, they started over from the beginning.
  • The experiment having failed, the scientists chose to begin again from the start.
  • Since the experiment was a failure, they decided to start again from the beginning.

17.Identify the rhetorical device used: "Ask not what your country can do for you—ask what you can do for your country."

  • Hyperbole
  • Antithesis
  • Alliteration
  • Metaphor

18.Which word best completes this sentence? "The diplomat's _____ response managed to satisfy both parties without committing to either position."

  • candid
  • equivocal
  • forthright
  • explicit

19.In synthesizing sources for a research paper on climate change, which approach demonstrates the strongest integration?

  • Summarizing each source in separate paragraphs
  • Using only the most recent source available
  • Weaving together evidence from multiple sources to support a unified argument
  • Quoting sources at length without commentary

20.Which transition word best connects these sentences? "The initial results were promising. _____, the long-term data revealed significant problems with the hypothesis."

  • Furthermore
  • Similarly
  • However
  • Therefore

🔬 Section 3: Science (20 points)

10 questions, 2 points each.

21.A car accelerates uniformly from rest to 20 m/s in 5 seconds. What is its acceleration?

  • 2 m/s²
  • 4 m/s²
  • 5 m/s²
  • 100 m/s²

22.According to Newton's Third Law, when you push against a wall:

  • The wall pushes back with greater force
  • The wall pushes back with equal and opposite force
  • The wall pushes back with less force
  • The wall does not push back at all

23.What is the kinetic energy of a 2 kg object moving at 3 m/s?

  • 3 J
  • 6 J
  • 9 J
  • 18 J

24.A wave has a frequency of 50 Hz and a wavelength of 2 meters. What is its speed?

  • 25 m/s
  • 52 m/s
  • 100 m/s
  • 0.04 m/s

25.Which type of electromagnetic radiation has the highest energy?

  • Radio waves
  • Visible light
  • Gamma rays
  • Microwaves

Data Table: Projectile Motion Experiment

Launch Angle (°) Initial Velocity (m/s) Horizontal Range (m) Maximum Height (m)
152020.42.7
302035.35.1
452040.810.2
602035.315.3
752020.419.0

26.Based on the data table, at what launch angle is the horizontal range maximized?

  • 15°
  • 30°
  • 45°
  • 75°

27.According to the data, which pair of angles produces the same horizontal range?

  • 15° and 45°
  • 30° and 60°
  • 45° and 60°
  • 30° and 75°

28.In an electric circuit, if the voltage is doubled while the resistance remains constant, the current will:

  • Be halved
  • Remain the same
  • Double
  • Quadruple

29.Which statement best describes the relationship between mass and gravitational potential energy?

  • They are inversely proportional
  • They are directly proportional
  • They are not related
  • GPE depends only on height

30.A student claims that heavier objects fall faster than lighter objects. Which response best addresses this claim using scientific reasoning?

  • This is correct because heavier objects have more gravitational force acting on them.
  • In a vacuum, all objects fall at the same rate regardless of mass; differences on Earth are due to air resistance.
  • This is correct because mass directly affects acceleration due to gravity.
  • Lighter objects always fall slower because they have less momentum.

🎯 Section 5: SAT/ACT Skills (20 points)

5 multiple choice questions (2 points each) + 2 free response questions (5 points each).

41.When approaching a reading passage on the SAT, which strategy is most effective?

  • Read the questions first, then skim the passage for answers
  • Read the passage carefully once, taking mental notes of main ideas and structure
  • Skip difficult passages and return to them later
  • Focus only on the first and last paragraphs

42.On the ACT, you have 60 minutes for 60 English questions. What is the recommended pace per question?

  • 30 seconds per question
  • 1 minute per question
  • 2 minutes per question
  • 45 seconds per question

43.You've narrowed a math question down to two answer choices. What is the best strategy?

  • Always choose the first option
  • Plug both answers back into the original problem to verify
  • Choose the answer that "looks right"
  • Skip the question entirely

44.A student consistently makes careless errors on easy questions. Which strategy would most help?

  • Spend more time on difficult questions
  • Build in time to double-check easy and medium questions
  • Skip easy questions to focus on hard ones
  • Practice only difficult problems

45.When you don't know the answer to a question on the SAT or ACT, you should:

  • Leave it blank to avoid losing points
  • Make an educated guess after eliminating clearly wrong answers
  • Always choose option C
  • Spend extra time until you figure it out

46.Free Response (5 points)

A student receives their SAT score report showing the following:

  • Reading & Writing: 620/800
  • Math: 580/800
  • Total: 1200/1600

Their goal is to reach 1350. Analyze this score report and create a specific, prioritized study plan. Include: (a) which section to prioritize and why, (b) at least three specific strategies to improve, and (c) a realistic timeline for improvement.

[Write your response here - aim for 150-250 words]

47.Free Response (5 points)

Explain the concept of "error analysis" and why it is essential for SAT/ACT preparation. In your response:

  • Define what error analysis involves
  • Describe at least three categories of errors students commonly make
  • Explain how understanding your error patterns leads to score improvement
[Write your response here - aim for 150-250 words]

Scoring Guide

Section Points Possible Your Score
Mathematics 20 ____
English Language Arts 20 ____
Science 20 ____
Social Studies 20 ____
SAT/ACT Skills 20 ____
TOTAL 100 ____

Grade Scale: A: 90-100 | B: 80-89 | C: 70-79 | D: 60-69 | F: Below 60

Click to reveal Answer Key

Multiple Choice Answers

Section 1: Mathematics

  1. A - (3+2i)(4-5i) = 12 - 15i + 8i - 10i² = 12 - 7i + 10 = 22 - 7i
  2. A - Using quadratic formula: x = (-6 ± √(36-52))/2 = (-6 ± √(-16))/2 = -3 ± 2i
  3. B - The highest power of x is 4
  4. A - Using Pythagorean identity: cos²θ = 1 - sin²θ = 1 - 9/25 = 16/25, so cos θ = 4/5
  5. B - 2⁵ = 32, so log₂(32) = 5
  6. B - e^(2ln(x)) = e^(ln(x²)) = x²
  7. A - Zeros at x = -2, 1, 3 give factors (x+2)(x-1)(x-3)
  8. B - sin(π/4) = √2/2
  9. B - The 1.03 represents a 3% annual growth rate (100% + 3% = 103% = 1.03)
  10. B - 2^(x+1) = 16 = 2⁴, so x + 1 = 4, x = 3

Section 2: English Language Arts

  1. B - The author presents both sides and suggests a middle ground
  2. C - Critics worry about "irreplaceable human elements" being lost
  3. B - Making quality education available to everyone
  4. B - "amplify their effectiveness while preserving the essentially human core"
  5. A - With "neither...nor," the verb agrees with the noun closest to it (teacher = singular)
  6. A - Removes redundancy ("start over" and "again") and wordiness
  7. B - Antithesis: contrasting ideas in parallel structure
  8. B - Equivocal means deliberately ambiguous
  9. C - Synthesis involves integrating multiple sources into a unified argument
  10. C - "However" signals a contrast between promising initial results and later problems

Section 3: Science

  1. B - a = Δv/Δt = (20-0)/5 = 4 m/s²
  2. B - Newton's Third Law: forces are equal and opposite
  3. C - KE = ½mv² = ½(2)(3)² = ½(2)(9) = 9 J
  4. C - v = fλ = 50 × 2 = 100 m/s
  5. C - Gamma rays have the highest frequency and therefore highest energy
  6. C - Maximum range (40.8 m) occurs at 45°
  7. B - 30° and 60° both have range of 35.3 m (complementary angles)
  8. C - Ohm's Law: I = V/R, so doubling V doubles I
  9. B - GPE = mgh, so mass and GPE are directly proportional
  10. B - All objects fall at the same rate in a vacuum; air resistance causes differences

Section 4: Social Studies

  1. B - Checks and balances prevent concentration of power
  2. A - 13th Amendment (1865) abolished slavery
  3. B - Judicial review allows the Court to strike down unconstitutional laws
  4. B - John Locke's ideas about natural rights influenced this passage
  5. C - German submarine warfare and Zimmermann Telegram led to US entry in WWI
  6. B - Opportunity cost is the value of the next best alternative foregone
  7. B - Lower interest rates encourage borrowing and spending
  8. B - The Civil Rights Act of 1964 prohibits discrimination based on these categories
  9. B - Federalism divides power between national and state governments
  10. B - Law of supply: higher prices lead to greater quantity supplied

Section 5: SAT/ACT Skills

  1. B - Active reading with attention to structure is most effective
  2. B - 60 questions in 60 minutes = 1 minute per question
  3. B - Plugging in answers verifies which one works
  4. B - Allocating time to check easier questions reduces careless errors
  5. B - No penalty for guessing, so eliminate and guess strategically

Free Response Rubric (Questions 46-47)

5 points: Complete, well-organized response addressing all parts with specific details and clear reasoning.

4 points: Addresses all parts with good detail but may have minor gaps in reasoning or specificity.

3 points: Addresses most parts but lacks depth or contains some inaccuracies.

2 points: Partially addresses the prompt with limited detail or significant gaps.

1 point: Minimal response that shows some understanding but misses key elements.

0 points: No response or completely off-topic.