Grade 11 Final Examination
Comprehensive Year-End Assessment with SAT/ACT Emphasis
Exam Instructions
- This exam is designed to mirror SAT/ACT format and difficulty.
- Read each question carefully and select the best answer.
- For free response and essay questions, show your work and reasoning.
- Calculator use is permitted for the Mathematics section only.
- Budget your time: approximately 3 minutes per question, plus 30 minutes for the essay.
📐 Section 1: Mathematics (24 points)
12 questions, 2 points each. Calculator permitted. SAT Math Domains: Algebra, Advanced Math, Problem-Solving & Data Analysis, Geometry & Trigonometry
Reference Formulas
Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
Pythagorean Identity: sin²θ + cos²θ = 1
Exponential Growth: A = P(1 + r)^t
Standard Deviation: σ = √[Σ(xᵢ - μ)² / n]
1.[SAT: Advanced Math] If f(x) = x³ - 4x² + x + 6 and f(2) = 0, which of the following is a factor of f(x)?
2.[SAT: Algebra] The system of equations below has infinitely many solutions. What is the value of k?
3x - 6y = 12
kx - 2y = 4
3.[SAT: Advanced Math] Simplify: (2 - 3i)/(1 + 2i)
4.[SAT: Geometry & Trig] In the unit circle, if an angle θ is in standard position with its terminal side passing through the point (-√3/2, 1/2), what is θ in radians?
5.[SAT: Problem-Solving & Data] A data set has mean 50 and standard deviation 8. According to the empirical rule, approximately what percentage of data falls between 34 and 66?
6.[SAT: Advanced Math] If log₃(x) + log₃(x - 2) = 1, what is the value of x?
7.[SAT: Advanced Math] The function g(x) = 2f(x - 3) + 1 is a transformation of f(x). Compared to f(x), the graph of g(x) is:
8.[SAT: Geometry & Trig] What is the exact value of tan(π/3)?
9.[SAT: Problem-Solving & Data] A car's value depreciates by 15% each year. If the car was purchased for $25,000, which expression represents its value after t years?
10.[SAT: Advanced Math] For what values of x is the inequality x² - 5x + 6 < 0 true?
11.[SAT: Algebra] A line passes through points (2, 5) and (6, 13). What is the equation of this line in slope-intercept form?
12.[SAT: Geometry & Trig] If sin(A) = cos(B) and both A and B are acute angles, what is A + B?
📚 Section 2: Reading & Writing (24 points)
12 questions, 2 points each. SAT R&W Domains: Craft & Structure, Information & Ideas, Standard English Conventions, Expression of Ideas
Passage A (Questions 13-17)
The concept of "attention economy" has fundamentally transformed how we understand value in the digital age. Unlike traditional economies based on material scarcity, the attention economy operates on the premise that human attention is the scarce resource. Every notification, headline, and video thumbnail competes for a slice of our finite cognitive bandwidth.
This shift has profound implications for democracy, mental health, and human agency. When attention becomes the primary currency, content creators and platforms are incentivized not to inform or enlighten, but to engage—often through outrage, fear, or superficial entertainment. The most successful algorithms don't optimize for truth or user well-being; they optimize for time spent scrolling.
Critics argue that we've essentially outsourced our attentional priorities to machines designed to exploit our psychological vulnerabilities. Yet others contend that such concerns are overblown, noting that every new communication technology, from the printing press to television, has generated similar moral panics. Perhaps the attention economy is not a fundamental rupture but merely the latest evolution in humanity's ongoing negotiation with its own inventions.
13.[SAT: Information & Ideas] The central claim of the passage is that:
14.[SAT: Craft & Structure] The phrase "finite cognitive bandwidth" (paragraph 1) most nearly means:
15.[SAT: Craft & Structure] The author introduces the perspectives in paragraph 3 primarily to:
16.[SAT: Information & Ideas] According to the passage, algorithms are designed to optimize for:
17.[SAT: Craft & Structure] The author's tone toward the attention economy can best be described as:
18.[SAT: Standard English Conventions] Select the option that corrects the error in the underlined portion.
"The committee have decided that their going to postpone the vote until next month."
19.[SAT: Standard English Conventions] Which version of the sentence uses correct parallel structure?
20.[SAT: Expression of Ideas] A student is writing an essay arguing that renewable energy should replace fossil fuels. Which sentence would best serve as a topic sentence for a paragraph about economic benefits?
21.[SAT: Expression of Ideas] Which transition best connects these two sentences?
"The initial trial results were promising, showing a 40% improvement in patient outcomes. _____, the follow-up study revealed that the benefits diminished significantly after six months."
22.[SAT: Standard English Conventions] Identify the sentence with correct punctuation.
23.[SAT: Craft & Structure] An author writes: "The senator's 'commitment' to education reform was about as genuine as a three-dollar bill." This statement primarily relies on which rhetorical technique?
24.[SAT: Expression of Ideas] A writer wants to emphasize the urgency of climate action. Which revision most effectively achieves this goal?
Original: "Scientists say we should probably do something about climate change soon."
🔬 Section 3: Science (24 points)
12 questions, 2 points each. Physics, Advanced Science, and ACT Science Reasoning
25.[Physics: Mechanics] A 5 kg object is pushed across a frictionless surface with a force of 20 N. What is its acceleration?
26.[Physics: Energy] A roller coaster car has 50,000 J of potential energy at the top of a hill. Assuming no friction, what is its kinetic energy at the bottom?
27.[Physics: Waves] Two waves with frequencies of 256 Hz and 260 Hz are played simultaneously. What beat frequency will be heard?
28.[Physics: Electricity] Three 6Ω resistors are connected in parallel. What is the equivalent resistance?
ACT Science Passage: Ocean Acidification Study
Scientists measured the pH of seawater and the shell thickness of marine organisms at various locations over a 20-year period. Table 1 shows their findings.
| Year | Avg. Ocean pH | Atmospheric CO₂ (ppm) | Avg. Shell Thickness (mm) |
|---|---|---|---|
| 2000 | 8.12 | 369 | 2.8 |
| 2005 | 8.10 | 379 | 2.6 |
| 2010 | 8.08 | 389 | 2.4 |
| 2015 | 8.06 | 400 | 2.2 |
| 2020 | 8.04 | 414 | 2.0 |
29.[ACT Science] Based on Table 1, which statement best describes the relationship between atmospheric CO₂ and ocean pH?
30.[ACT Science] If current trends continue, what would be the predicted average shell thickness in 2025?
31.[ACT Science] A scientist hypothesizes that shell thickness decreases because lower pH inhibits calcium carbonate formation. Which finding would best support this hypothesis?
32.[Physics: Momentum] A 1000 kg car traveling at 20 m/s collides with and sticks to a 2000 kg truck at rest. What is the velocity of the combined vehicles immediately after collision?
33.[Physics: Optics] Light travels from air (n = 1.00) into glass (n = 1.50) at an angle of incidence of 45°. Which statement is true?
34.[Physics: Thermal] Heat is transferred from a hot object to a cold object until they reach thermal equilibrium. This process demonstrates:
35.[Scientific Reasoning] A researcher claims that a new fertilizer increases crop yield by 30%. What additional information would be most important for evaluating this claim?
36.[ACT Science] Which statement represents an inference rather than an observation from the ocean acidification data?
🎯 Section 5: SAT/ACT Skills & Essay (24 points)
4 multiple choice (2 points each) + 1 free response (6 points) + 1 essay (10 points)
49.A student scores 28 on the ACT. If the national average is 21 with a standard deviation of 5, the student's score is approximately how many standard deviations above the mean?
50.When reviewing a practice test, which error analysis approach is most effective for long-term improvement?
51.A student consistently runs out of time on the ACT Reading section (40 minutes for 4 passages). Which adjustment would most likely improve their performance?
52.Superscoring on the SAT means:
53.Free Response (6 points)
A student has 8 weeks before their SAT test date. Their diagnostic scores are:
- Reading & Writing: 560 (38th percentile)
- Math: 640 (78th percentile)
- Total: 1200
Create a detailed 8-week study plan that includes:
- Weekly focus areas and time allocations
- Specific strategies for improving the weaker section
- When and how to take practice tests
- A plan for the final week before the test
54.Essay (10 points)
Read the following prompt and write a well-organized essay.
Prompt:
Some educators argue that standardized tests like the SAT and ACT are essential tools for college admissions because they provide an objective, comparable measure of student readiness across different schools and backgrounds. Others contend that these tests are fundamentally flawed, measuring test-taking skills rather than true academic potential, and perpetuating inequities based on socioeconomic status.
Assignment: Write an essay in which you take a position on the value of standardized tests in college admissions. Support your position with evidence and reasoning. Consider both perspectives and explain why your position is more persuasive.
Your essay will be scored based on:
- Clear thesis and position (2 points)
- Organization and paragraph structure (2 points)
- Evidence and reasoning (3 points)
- Language and conventions (2 points)
- Consideration of counterarguments (1 point)
Scoring Guide
| Section | Points Possible | Your Score |
|---|---|---|
| Mathematics (12 MC × 2 pts) | 24 | ____ |
| Reading & Writing (12 MC × 2 pts) | 24 | ____ |
| Science (12 MC × 2 pts) | 24 | ____ |
| Social Studies (12 MC × 2 pts) | 24 | ____ |
| SAT/ACT Skills (4 MC + Free Response + Essay) | 24 | ____ |
| TOTAL | 120 | ____ |
Grade Scale: A: 108-120 (90%+) | B: 96-107 (80-89%) | C: 84-95 (70-79%) | D: 72-83 (60-69%) | F: Below 72
Click to reveal Answer Key
Multiple Choice Answers
Section 1: Mathematics
- B - If f(2) = 0, then (x - 2) is a factor by the Factor Theorem
- A - For infinitely many solutions, equations must be proportional: 3/k = -6/-2 = 12/4, so k = 1
- A - (2-3i)/(1+2i) × (1-2i)/(1-2i) = (2-4i-3i+6i²)/(1+4) = (2-7i-6)/5 = (-4-7i)/5
- B - Point (-√3/2, 1/2) is in Q2; cos θ = -√3/2, sin θ = 1/2 → θ = 5π/6
- B - 34 = 50-16 = μ-2σ; 66 = 50+16 = μ+2σ; this covers about 95% of data
- B - log₃(x(x-2)) = 1 → x² - 2x = 3 → x² - 2x - 3 = 0 → (x-3)(x+1) = 0; x = 3 (x = -1 invalid)
- B - (x-3) shifts right 3; 2f stretches vertically by 2; +1 shifts up 1
- B - tan(π/3) = sin(π/3)/cos(π/3) = (√3/2)/(1/2) = √3
- C - 15% depreciation means 85% remains each year: 25000(0.85)^t
- B - x² - 5x + 6 = (x-2)(x-3) < 0 when 2 < x < 3
- A - Slope = (13-5)/(6-2) = 8/4 = 2; y - 5 = 2(x-2) → y = 2x + 1
- B - If sin(A) = cos(B), then A and B are complementary, so A + B = 90°
Section 2: Reading & Writing
- B - The passage discusses the attention economy as a significant shift in value creation
- C - "Cognitive bandwidth" refers to mental processing capacity
- B - The author presents both critical and dismissive perspectives to show balance
- C - "They optimize for time spent scrolling"
- C - The author presents multiple views without strong advocacy, showing measured analysis
- A - "they're" (they are) is the correct contraction
- D - Both B (to + infinitive) and C (gerunds) demonstrate correct parallel structure
- B - This directly addresses economic benefits and transitions from the previous topic
- C - "Nevertheless" signals contrast between promising initial results and later problems
- B - Nonrestrictive clause requires commas on both sides
- B - Uses irony (quotation marks around "commitment") and analogy (three-dollar bill)
- C - This version uses strong, urgent language ("warn," "immediate," "essential," "catastrophic")
Section 3: Science
- A - F = ma → a = F/m = 20/5 = 4 m/s²
- C - Conservation of energy: PE at top = KE at bottom = 50,000 J
- A - Beat frequency = |f₁ - f₂| = |256 - 260| = 4 Hz
- C - 1/R_eq = 1/6 + 1/6 + 1/6 = 3/6 = 1/2, so R_eq = 2Ω
- B - As CO₂ increases from 369 to 414 ppm, pH decreases from 8.12 to 8.04
- C - Shell thickness decreases by 0.2 mm every 5 years; 2020: 2.0 → 2025: 1.8 mm
- B - Lower calcium carbonate would directly support the proposed mechanism
- A - Conservation of momentum: (1000)(20) + (2000)(0) = (3000)v → v = 20000/3000 = 6.67 m/s
- B - Light going from lower to higher refractive index bends toward the normal
- C - Heat flowing from hot to cold until equilibrium demonstrates the second law of thermodynamics
- B - A control group is essential for establishing whether the fertilizer caused the improvement
- C - Predicting future ecosystem effects is an inference; other options state observations
Section 4: Social Studies
- B - Progressives sought government reform to address social problems
- B - The elastic clause allows Congress to make laws necessary to execute its powers
- C - Market economies rely on supply and demand to determine prices
- B - FDR delivered this speech in March 1933 during the Great Depression
- B - The speech aimed to restore confidence during economic crisis
- C - 26th Amendment (1971) lowered voting age to 18
- B - Fiscal policy involves taxation and government spending decisions
- B - Incorporation applies Bill of Rights to states through 14th Amendment
- B - Containment aimed to prevent communism from spreading to new countries
- B - More money supply → lower interest rates
- B - Due process requires fair procedures before deprivation of rights
- A - Pollution harming others is a negative externality (cost imposed on third parties)
Section 5: SAT/ACT Skills
- B - (28 - 21) / 5 = 7/5 = 1.4 standard deviations
- B - Categorizing errors and tracking patterns allows targeted improvement
- C - Setting time limits and practicing active reading addresses timing issues
- B - Superscoring combines highest section scores from different test dates
Free Response and Essay Rubrics
Question 53 (6 points) - Study Plan Rubric:
- 1-2 points: Weekly structure with clear time allocations
- 1-2 points: Specific R&W improvement strategies (vocabulary, grammar rules, passage strategies)
- 1 point: Appropriate practice test schedule (every 2-3 weeks, full simulation)
- 1 point: Final week plan (review, rest, logistics)
Question 54 (10 points) - Essay Rubric:
- Thesis (2 pts): Clear position stated; 1 pt for vague position, 2 pts for clear, specific thesis
- Organization (2 pts): Logical paragraph structure, transitions; 1 pt for some organization, 2 pts for clear structure
- Evidence/Reasoning (3 pts): 1 pt for general claims, 2 pts for some evidence, 3 pts for specific, relevant evidence with clear reasoning
- Language (2 pts): 1 pt for adequate, 2 pts for sophisticated word choice and few errors
- Counterarguments (1 pt): 1 pt for acknowledging and addressing opposing view