ACT Test Form Z14 Comprehensive Study Guide and Note Set

ACT Form Z14: General Administration and Testing Instructions

• Test Identification: Form Z14, released February $2025$ for the $2024$ | $2025$ cycle. This material is the confidential copyrighted property of ACT Education Corp.
• Testing Materials Provided:
  • Test booklet containing questions for English, Mathematics, Reading, and Science.
  • Scoring keys and conversion tables for determining ACT scores.
  • A report listing student answers, correctness, and correct answers for mistakes.
• General Rules and Directions:
  • Subject Correlation: Tests measure skills and abilities related to high school course work and college success.
  • Calculators: Permitted only on the Mathematics test.
  • Marking the Answer Document: Use a soft lead pencil (No. $2$). Marks must be heavy and black. Mechanical pencils and ink are strictly prohibited.
  • Scoring Logic: Scores are based only on the number of correct answers. There is no penalty for guessing.
  • Timing Protocols: Work is only permitted on the specific test during the allowed time. Looking back at completed tests or moving ahead to the next test results in disqualification.
  • Post-Test Conduct: Pencils must be laid down immediately when time is called. No alterations to ovals are allowed after time is called.

English Test Overview and Passage Concepts

• Test Structure: $45$ minutes for $75$ questions.
• Passage I: Fosbury’s Victorious Flop:
  • Dick Fosbury: A high school track athlete in $1963$ who revolutionized the high jump.
  • Historical Techniques:
    • Straddle Technique: Athlete runs at a sharp angle, launches off the inside foot, stretches the outside leg over the bar, and tumbles facedown/headfirst.
    • Scissor Kick Technique: Less common; requires launching off the outside foot and lifting legs over the bar to land feetfirst.
  • Innovation: The "Fosbury Flop" involved lifting the hips after launch, causing the head and shoulders to tilt back, sailing over the bar headfirst and chest-up, parallel to the ground.
  • Achievements: Improved personal record by $6$ inches in one day. Won the gold medal at the $1968$ Olympics in Mexico City, breaking the Olympic record with a height of $7'4"$ ($7\,\text{feet}\,4\,\text{inches}$).
  • Legacy: Since $1972$, every Olympic high jump gold medalist has used the Fosbury Flop.
• Passage II: Flamenco Flair:
  • Artist: Mercedes Ruiz, a flamenco dancer who performed at Spain’s Festival de Jerez in $2011$.
  • Historical Origins: First blossomed among Spain’s Andalusian population in the $18\text{th}$ century with influences from Arab, Indian, and Jewish cultures.
  • Styles:
    • Chico: Light and humorous.
    • Jondo: Serious.
  • Three Basic Elements: Music (guitarist), Dance (footwork and arm maneuvers), and Clapping (performed by palmistas in a form called palmas).
  • Duende: The collaborative ambiance or intensity created among participants.
• Passage III: Charles Cushman’s Kodachrome America:
  • Technological Shift: Charles Cushman loaded his first roll of Kodachrome color film on September $3$, $1938$, in a $35\text{-millimeter}$ camera.
  • Subject Matter: Historically significant documentary-style shots of Depression-era America transitioning to industrial development (e.g., the Golden Gate Bridge, Chicago street scenes, Indiana farm locomotives).
  • Archives: Cushman produced $14,500$ color images and a dozen annotated notebooks, now archived at Indiana University.
• Passage IV: Keys for Community:
  • Movement: The "Play Me, I’m Yours" project founded by British artist Luke Jerram.
  • Mechanism: Secondhand pianos are placed in high-traffic pedestrian sites in cities like London, Sydney, Los Angeles, and Cincinnati to promote social interaction.
• Passage V: More Than Meets the Eye:
  • Celestial Objects: Brown dwarfs, a class of objects between stars and planets.
  • Discovery Timeline: Theorized by Shiv Kumar in $1963$; named by Jill Tarter; confirmed via spectrum analysis in $1995$.
  • Characteristics: More massive than Jupiter but lacking the mass to fuel fusion reactions like stars. They are detected using infrared telescopes to find heat signatures.
  • Composition: Often retain their lithium supply because they cannot sustain fusion reactions to burn it.

Mathematics Test Quantitative Details and Formulas

• Test Structure: $60$ minutes for $60$ questions.
• Coordinate Geometry:
  • Translation: A point at $(-4, 10)$ translated right $10$ units and down $4$ units results in $(6, 6)$.
  • Slope: If a line only passes through $(3, 4)$, its slope cannot be determined without a second point.
• Algebra and Functions:
  • Evaluation: For $f(x, y) = 3x^2 - 2y$, $f(2, 3) = 3(2)^2 - 2(3) = 12 - 6 = 6$.
  • Linear Equations: $9 - 11x = 13 - 9x$; simplified to $-2x = 4$, so $x = -2$.
  • Simplification: $7[3 - 2(x - 4)] = 7[3 - 2x + 8] = 7[11 - 2x] = 77 - 14x$.
• Word Problems and Modeling:
  • Reimbursement: $\$10.00$ per day + $\$0.445$ per mile. For $2$ days and $220$ total miles: $2 \times 10 + 220 \times 0.445 = 20 + 97.9 = \$117.90$.
  • Profit: Haley’s lemonade profit for $x$ cups: $0.50x - (2.30 + 1.50) = 0.5x - 3.8$.
• Geometry:
  • Triangles: In $\Delta ABC$, if $\angle B = 90^{\circ}$ and $\angle A = 4 \times \angle C$, then $4C + C = 90$, meaning $5C = 90$ and $\angle C = 18^{\circ}$.
  • Area of Trapezoid: $A = \frac{1}{2}(b_1 + b_2)h$. Given $A = 20$, $h = 5$, $b_1 = 2$, then $20 = 0.5(2 + b)5 \rightarrow 40 = 10 + 5b \rightarrow 30 = 5b \rightarrow b = 6\,\text{feet}$.
  • Circles/Sectors: A track area with diameter $240\,\text{meters}$ ($r = 120\,\text{m}$). Area of a $60^{\circ}$ sector = $\frac{1}{6} \times \pi(120)^2 = \frac{14400\pi}{6} = 2400\pi\,\text{m}^2$.
• Probability and Statistics:
  • Expected Value: If a player has a $0.8$ probability of making a free throw, to make $20$, they expect to attempt $\frac{20}{0.8} = 25$ throws.
  • Ratios: Based on a frequency table, the ratio of proficient students ($\text{score} \geq 70$) is calculated by summing frequencies for the $70-100$ range relative to the $50-69$ range.
• Trigonometry and Vectors:
  • Right Triangle: An awning $5\,\text{feet}$ long extending $2\,\text{feet}$ horizontally. The angle $\theta$ between the building and the awning is solved via $\sin(\theta) = \frac{2}{5}$, thus $\theta = \sin^{-1}(\frac{2}{5})$.
  • Sine Rule Area: Area of a triangle with sides $a, b$ and angle $C$: $\\text{Area} = \frac{1}{2}ab\sin(C)$. For sides $6\,\text{m}$, $4\,\text{m}$ and $\angle 30^{\circ}$: $0.5 \times 6 \times 4 \times 0.5 = 6\,\text{m}^2$.
• Complex Numbers:
  • Identity: $i^2 = -1$. Operations involving the expression $\frac{2 + 3i}{i}$ involve multiplying by $\frac{-i}{-i}$ to rationalize the denominator.

Reading Test Detailed Analysis

• Passage I: Literary Narrative ("Song for My Father" by Eric Liu):
  • Summary: The narrator reflects on a memorial book for his father, Chao-hua Liu, who immigrated to the US in $1955$ and died in $1991$.
  • Key Conflict: The narrator faces frustration and shame due to his lack of Chinese literacy (knowing the "ideographic roots" and "brush strokes"), which prevents him from reading his father's own writings.
  • Metaphor: Identity is described as an "opaque inheritance."
• Passage II: Social Science (Library Quiet vs. Social Spaces):
  • Passage A (Jennifer Howard): Discusses the "learning-commons model" where libraries install coffee shops and group-work spaces but notes that students often crave the "quaint hush" for research.
  • Passage B (Alan Jacobs): Contrasts the historical challenge of finding quiet for reading with modern proposals by Andy Burnham to make libraries social places, a move criticized by Victoria Coren as turning libraries into "internet cafes."
• Passage III: Humanities (The Mona Lisa):
  • Innovative Techniques: Leonardo da Vinci utilized the contrapposto position (face looking a different direction than the body) to represent three-dimensional movement.
  • Gaze: Unlike traditional demure poses with downcast eyes, the Mona Lisa looks directly at the viewer, which was considered defiant.
  • Media: Leonardo shifted from quick-drying tempera (using egg yolk) to oil paint, which allowed for more detail and luminosity due to its slow drying time.
• Passage IV: Natural Science (Feathered Dinosaurs):
  • Key Find: Li Yingfang discovered the Sinosauropteryx ("Chinese lizard wing") in $1996$.
  • Evolutionary Theory: Feathers may have first evolved for color display (attracting mates) rather than flight. Sinosauropteryx had filaments resulting in an orange-and-white-striped appearance.
  • Biological Evidence: Tiny sacs called melanosomes contain melanin varieties (eumelanin for gray/black and pheomelanin for chestnut/reddish-brown).

Science Test Experimental Data and Results

• Passage I: Europa Impact Models:
  • Variables: Comet diameters ($0.5\,\text{km}$ and $1.0\,\text{km}$); Model A (Frozen water layer only); Model B (Frozen water over liquid water).
  • Observations: Larger comets ($1.0\,\text{km}$) created greater radius effects and deeper melting/vaporization than $0.5\,\text{km}$ comets.
• Passage II: Mutant Fungi (N. crassa):
  • Biochemical Pathway: Precursor $\rightarrow$ Ornithine $\rightarrow$ Citrulline $\rightarrow$ Argininosuccinate $\rightarrow$ Arginine.
  • Enzymes: T, U, V, and W facilitate specific steps. Strains with defects in specific enzymes cannot produce arginine unless the subsequent compound in the pathway is provided in the growth medium.
• Passage III: Lizard Reproduction (U. stansburiana):
  • Experiment: Four groups (Q-T) incubated at different nighttime temperatures ($8^{\circ}\text{C}$, $18^{\circ}\text{C}$, $22^{\circ}\text{C}$, $29^{\circ}\text{C}$).
  • Conclusion: Increasing nighttime temperature generally decreased clutch time but did not follow a simple linear relationship with average egg mass ($330\,\text{mg}$ at $29^{\circ}\text{C}$ vs $300\,\text{mg}$ at $8^{\circ}\text{C}$).
• Passage IV: Pendulum Frequency (f):
  • Student 1 Thesis: Frequency $\text{f}$ is affected by mass $\text{M}$ (heavier spheres increase gravitational acceleration and speed).
  • Student 2 Thesis: Frequency $\text{f}$ is independent of mass $\text{M}$ but decreases as length $\text{L}$ increases because the distance per cycle increases.
• Passage V: Coffee Bean Carbon Dioxide ($CO_2$) Release:
  • Experiment 1: Longer roasting time and higher roasting temperatures result in increased $CO_2$ release (mg/g).
  • Experiment 2: Smaller particle size in ground beans results in a significantly higher release of $CO_2$ (up to $8.0+ \,\text{mg/g}$) compared to larger particles.
• Passage VI: Carotenoids (CTs) and UV/Visible Light:
  • Spectrophotometry: Measures absorbance (A) at wavelengths ($\lambda$) from $200\,\text{nm}$ to $700\,\text{nm}$.
  • $\lambda_{max}$ Values: Phytoene ($286\,\text{nm}$), Auroxanthin ($399\,\text{nm}$), Beta-carotene ($451\,\text{nm}$), Spirilloxanthin ($492\,\text{nm}$).

Scoring and Conversion Methodology

• Weighting:
  • English: $75$ questions.
  • Mathematics: $60$ questions.
  • Reading: $40$ questions.
  • Science: $40$ questions.
• Composite Calculation: Average of the four scaled scores ($1-36$), rounded to the nearest whole number ($.5$ rounds up).
• Scale Conversion Example (Form Z14):
  • 36 Scale Score: English $73-75$; Math $58-60$; Reading $39-40$; Science $39-40$.
  • 20 Scale Score: English $43-44$; Math $28-29$; Reading $21-22$; Science $19-20$.