| Circles & Area (51M) |
| H |
Pedagogical Insight: This curriculum integrates core high school science topics with ACT English and Math standards to demonstrate how reading and logic cross subject boundaries. By discussing the science context alongside the standard grammar rules and algebra steps, students build reading confidence and reduce test anxiety.
ACT SCIENCE SPARKS • Teacher Reference Guide Page 1 of 2
ACT Science Sparks
Curriculum Manual Master Answer Key & Alignment
Quick Reference Key
| Day | Scientific Topic | English Skill & Code | Eng Key | Math Skill & Code | Math Key |
|---|---|---|---|---|---|
| Day 11 | Lichen Bioindicators | Possessive Apostrophes (73F) | G | Exponential Growth (46M) | B |
| Day 12 | Instant Endothermic Cold Packs | Sentence Combining (71B) | A | Multi-Step Algebra (34M) | G |
| Day 13 | Coriolis Effect Meteorology | Relative Pronouns (73G) | G | Cylinder Volume (53M) | C |
| Day 14 | Newton white light splitting | Active vs. Passive Voice (72B) | B | Trig / Sine Function (62M) | G |
| Day 15 | Paleontological Tiktaalik Fossil | Relevance Add/Delete (72E) | C | Scatterplots & Fit (43M) | G |
| Day 16 | Sørensen logarithmic pH scale | Illogical Comparisons (71E) | C | Logarithmic Scales (58M) | H |
| Day 17 | Metamorphic stone formation | Idiomatic Prepositions (72C) | A | Coordinate Slope (52B) | G |
| Day 18 | Tectonic Mantle Convection | Transitions Choice (71D) | B | Inverse Relations (44M) | F |
| Day 19 | Edward Jenner Smallpox Vaccine | Dashes & Parentheses (73D) | B | Venn Diagram Sets (42B) | B |
| Day 20 | Edwin Hubble Cosmic Expansion | Sentence Organization (72B) | G | Direct Variation (31C) | H |
Grading & Scoring Rubric
Award full completion points based on booklet effort rather than initial accuracy. This lowers anxiety and encourages risk-taking:
Quick-Review Strategy Checklist
Encourage students to master these general-purpose test-taking reflexes during review slides:
ACT SCIENCE SPARKS • Teacher Reference Guide Page 2 of 2
Do not let the biology jargon overwhelm you. Treat variables precisely as simple algebraic placeholders and plug-and-chug!
Day 1 Complete! Onward to Day 2 →
DAY 2 ENGLISH (Absolute Zero)
Skill: Subject-Verb Agreement (ACT 73B)
The behavior of gas molecules at extremely low temperatures reveal that, when the heat energy is completely removed, all translational molecular motion ceases entirely at a point known as absolute zero.
A NO CHANGE
B reveals that, when the heat energy is completely removed,
C revealed that, when the heat energy are completely removed,
D reveals that, when the heat energy were completely removed,
Watch out for prepositional phrase distractions!
DAY 2 • ENGLISH ANSWER KEY CORRECT OPTION: B
The grammatical subject is behavior (singular), not the nearby plural noun molecules or temperatures which exist inside prepositional phrases. A singular subject requires a singular verb: reveals.
ACT STRATEGY SPARK
Strip away intermediate descriptions (e.g. of gas molecules) to pair the bare subject directly with the verb.
Up Next: Day 2 Math Connection →
DAY 2 MATH (Charles's Gas Law)
Skill: Rates & Proportions (ACT 31M)
A meteorological balloon holds \(15.0\text{ liters}\) of helium gas at a temperature of \(300\text{ Kelvin}\). If the volume \(V\) of a gas is directly proportional to its absolute temperature \(T\):
\(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)
What will the volume (in liters) of the balloon be when temperature drops to \(220\text{ Kelvin}\)?
A9.5
B11.0
C12.5
D20.5
E22.0
Proportional ratios are a foundational pillar of ACT math!
DAY 2 • MATH ANSWER KEY CORRECT OPTION: B
1. Setup the proportion: \(V_2 = \frac{V_1 \cdot T_2}{T_1}\)
2. Substitute the values: \(V_2 = \frac{15.0 \cdot 220}{300}\)
3. Simplify: \(V_2 = \frac{3300}{300} = 11.0\text{ liters}\)
ACT STRATEGY SPARK
Ratio Estimation: Temperature dropped from 300 to 220 (roughly 2/3 of starting). Volume must also drop to slightly above 2/3 of 15, which points directly to 11.0!
Day 2 Complete! Onward to Day 3 →
DAY 3 ENGLISH (Hydrothermal Vents)
Skill: Sentence Fragments (ACT 71A)
Hydrothermal vents on the ocean floor emit toxic, mineral-rich fluids fluids. Feeding extraordinary communities of giant tube worms and extremophile bacteria that thrive completely without sunlight.
F NO CHANGE
G fluids, which feed extraordinary communities
H fluids, feeding extraordinary communities
J fluids; feeding extraordinary communities
Can the second part stand alone as a sentence?
DAY 3 • ENGLISH ANSWER KEY CORRECT OPTION: H
The group of words starting with "Feeding extraordinary communities..." lacks a conjugated main verb, making it a fragment. Option H correctly attaches this descriptive participial phrase to the main clause using a comma.
ACT STRATEGY SPARK
The "-ing" Trap: Words ending in -ing (participles) are NOT main verbs unless accompanied by a helping verb (like is, was).
Up Next: Day 3 Math Connection →
DAY 3 MATH (Plate Tectonics Rate)
Skill: Coordinate Geometry & Units (ACT 52M)
A tectonic plate boundary moves at a steady rate of \(4.0\text{ cm/year}\). A research station coordinates this movement along a straight horizontal line.
If the starting coordinate is \(x = 24.5\text{ meters}\), what will the reading be after exactly \(150\text{ years}\) of movement?
(Note: 1 meter = 100 centimeters)
F24.9
G30.5
H34.5
J84.5
K624.5
Unit conversion mismatch is a dangerous trap!
DAY 3 • MATH ANSWER KEY CORRECT OPTION: G
1. Total movement: \(150\text{ years} \times 4.0\text{ cm/year} = 600\text{ cm}\)
2. Convert to meters: \(600\text{ cm} / 100 = 6.0\text{ meters}\)
3. Add displacement: \(24.5\text{ m} + 6.0\text{ m} = 30.5\text{ meters}\)
ACT STRATEGY SPARK
The most common error is forgetting to convert units and adding \(24.5 + 600 = 624.5\) (Option K). Always write down unit labels!
Day 3 Complete! Onward to Day 4 →
DAY 4 ENGLISH (Galileo's Gravity)
Skill: Word Choice & Tone (ACT 72F)
Legend states that Galileo dropped two spheres of distinct masses from the Leaning Tower of Pisa to prove that gravitational acceleration has zero to do with the mass of the objects.
A NO CHANGE
B is completely separate and totally independent from
C is independent of
D does not care about
Which option is academic, neutral, and highly concise?
DAY 4 • ENGLISH ANSWER KEY CORRECT OPTION: C
The ACT requires formal, academic tone and strictly avoids wordiness. Options A and D are too slangy/informal. Option B is highly redundant. Option C is neutral, precise, and concise.
ACT STRATEGY SPARK
Ockham's Razor: If all choices are grammatically acceptable, select the shortest and most direct answer.
Up Next: Day 4 Math Connection →
DAY 4 MATH (Projectile Wind Vectors)
Skill: Vectors & Trigonometry (ACT 61M)
A weather projectile is launched straight upward with a force vector of \(100\text{ Newtons}\). Simultaneously, a crosswind exerts a horizontal force of \(40\text{ Newtons}\) to the east.
Which of the following represents the magnitude of the resultant net force vector acting on the projectile?
A\(100 + 40\)
B\(\sqrt{100^2 + 40^2}\)
C\(\sqrt{100^2 - 40^2}\)
D\(100 \times \sin(40^\circ)\)
Think of the physical forces as sides of a right triangle!
DAY 4 • MATH ANSWER KEY CORRECT OPTION: B
1. The vertical force (\(100\text{ N}\) upward) and horizontal force (\(40\text{ N}\) east) act perpendicular to each other.
2. Perpendicular vectors combine to form a right triangle, where the hypotenuse is the resultant sum.
3. Apply Pythagorean: \(c = \sqrt{a^2 + b^2} = \sqrt{100^2 + 40^2}\)
ACT STRATEGY SPARK
ACT Math tests formulaic setups of physics models. Perpendicular force vectors can always be connected tail-to-tip to create a right triangle!
Day 4 Complete! Onward to Day 5 →
DAY 5 ENGLISH (Trophic Cascades)
Skill: Transition Words (ACT 71D)
The reintroduction of gray wolves to Yellowstone altered elk populations, allowing sapling aspens to regenerate. In contrast, beaver colonies multiplied rapidly as the newly abundant trees provided essential dam materials.
A NO CHANGE
B For example,
C Consequently,
D Nevertheless,
Analyze the relationship between tree growth and beaver growth!
DAY 5 • ENGLISH ANSWER KEY CORRECT OPTION: C
The sentence demonstrates a clear cause-and-effect relationship. The regeneration of aspen trees (cause) provided beavers with wood for shelters, leading directly to the expansion of colonies (effect). Therefore, we need a cause/effect transition like Consequently.
ACT STRATEGY SPARK
Transition Filter: Group choices into categories: (1) Contrast (However, Nevertheless), (2) Addition (Furthermore), (3) Cause/Effect (Therefore, Consequently).
Up Next: Day 5 Math Connection →
DAY 5 MATH (Food Web Probability)
Skill: Probability & Graphs (ACT 42M)
An ecologist models energy transfer efficiency in a lake ecosystem containing exactly \(60\text{ local species}\). A study matrix shows:
Primary Producers
24 species
Primary Consumers
20 species
Secondary Consumers
16 species
If the ecologist randomly selects one species, and then randomly selects a second distinct species, what is the probability that both are primary producers?
F\(\frac{24}{60} \times \frac{24}{60}\)
G\(\frac{24}{60} \times \frac{23}{59}\)
H\(\frac{24}{60} \times \frac{23}{60}\)
J\(\frac{24}{60} + \frac{23}{59}\)
K\(\frac{24}{60} + \frac{24}{60}\)
Does selecting the first species affect the pool for the second?
DAY 5 • MATH ANSWER KEY CORRECT OPTION: G
1. Probability of picking the first primary producer: \(P(\text{First}) = \frac{24}{60}\)
2. Because the species must be distinct (without replacement), 59 total remain with 23 producers left: \(P(\text{Second}) = \frac{23}{59}\)
3. Multiply: \(P(\text{Both}) = \frac{24}{60} \times \frac{23}{59}\)
ACT STRATEGY SPARK
The Replacement factor: If a scenario specifies "distinct items" or "without replacement," make sure both numerator and denominator decrease for the second fraction!
Week 1 Complete! Onward to Week 2 →
SECTION 2
Focus: Haber-Bosch Stoichiometry, Cellular ATP Functions, Keplerian Roots, Ocean Acidification, and Faraday Induction.
Let's continue to Day 6.
DAY 6 ENGLISH (Haber-Bosch Process)
Skill: Modifier Placement (ACT 72D)
Synthesizing ammonia from atmospheric nitrogen, the crop yields of the entire world were revolutionized by Fritz Haber and Carl Bosch in the early twentieth century.
A NO CHANGE
B Synthesizing ammonia from atmospheric nitrogen, the entire world's crop yields
C Synthesizing ammonia from atmospheric nitrogen, Fritz Haber and Carl Bosch
D Synthesizing ammonia from atmospheric nitrogen, Fritz Haber's and Carl Bosch's yields
Ask yourself: WHO was doing the synthesizing?
DAY 6 • ENGLISH ANSWER KEY CORRECT OPTION: C
The sentence begins with an action: "Synthesizing ammonia...". The noun directly following the comma must be the entity that actually performs that action. Crop yields cannot synthesize; only the scientists, Fritz Haber and Carl Bosch, can.
ACT STRATEGY SPARK
Draw an arrow from the starting modifier to the first noun after the comma. If it is an illogical match, the modifier is dangling!
Up Next: Day 6 Math Connection →
DAY 6 MATH (Stoichiometric Ratios)
Skill: Ratios & Multi-Step (ACT 32M)
In the Haber-Bosch chemical reaction, nitrogen gas and hydrogen gas react in a fixed molar ratio of \(1:3\) to produce ammonia gas, according to the balanced equation:
\(\text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3\)
If a chemical reactor is supplied with exactly \(12.0\text{ moles}\) of \(\text{N}_2\) and excess \(\text{H}_2\), and the reaction runs at an \(80\%\) efficiency rate, how many moles of ammonia (\(\text{NH}_3\)) will be synthesized?
F9.6
G15.0
H19.2
J24.0
K28.8
Keep track of the coefficients before applying percentages!
DAY 6 • MATH ANSWER KEY CORRECT OPTION: H
1. 1 mole of \(\text{N}_2\) theoretically yields 2 moles of \(\text{NH}_3\).
2. Yield from \(12.0\text{ moles}\) of \(\text{N}_2\): \(12.0 \times 2 = 24.0\text{ moles NH}_3\).
3. Apply the \(80\%\) reaction efficiency rate: \(24.0 \times 0.80 = 19.2\text{ moles}\).
ACT STRATEGY SPARK
Always perform chemical ratio conversions first, then apply any efficiency percentages or final scale factors!
Day 6 Complete! Onward to Day 7 →
DAY 7 ENGLISH (ATP Synthase)
Skill: Verb Tense Consistency (ACT 73E)
In 1997, Paul Boyer and John Walker won the Nobel Prize for chemistry. They demonstrated how the enzyme ATP synthase acts as a biological turbine, which captured chemical energy to produce adenosine triphosphate.
A NO CHANGE
B captures
C had captured
D will capture
Is the enzyme still capturing energy today?
DAY 7 • ENGLISH ANSWER KEY CORRECT OPTION: B
The prize discovery is in the past, but the biological facts are described in the present tense. ATP synthase is a living enzyme that still captures chemical energy. Matching the parallel verb acts confirms Option B.
ACT STRATEGY SPARK
Universal Present Tense: Always describe scientific facts or mechanisms in the present tense, even inside historical contexts.
Up Next: Day 7 Math Connection →
DAY 7 MATH (ATP Yield Functions)
Skill: Function Modeling (ACT 45M)
In cellular respiration, the metabolic breakdown of 1 molecule of glucose yields a maximum of \(32\text{ molecules of ATP}\). However, the cell consumes an initial investment of \(2\text{ ATP}\) to start the glycolysis pathway.
Which of the following functions represents the net yield of ATP molecules, \(y\), as a function of the number of glucose molecules fully oxidized, \(x\)?
F\(y = 2x - 32\)
G\(y = 32x + 2\)
H\(y = 30x\)
J\(y = 32x - 2x\)
Read the wording carefully: Is the 2-ATP penalty per glucose molecule?
DAY 7 • MATH ANSWER KEY CORRECT OPTION: H
1. For 1 glucose oxidized, maximum yield is \(32\text{ ATP}\).
2. Since the cell must invest 2 ATP for each glucose molecule's process, net yield is constant: \(32 - 2 = 30\text{ ATP}\) per glucose.
3. Therefore, \(x\) glucose molecules yield: \(y = 30x\).
ACT STRATEGY SPARK
Isolate Constants vs. Coefficients: Since the 2 ATP investment is required for each glucose, it modifies the slope coefficient itself, not as a standalone intercept!
Day 7 Complete! Onward to Day 8 →
DAY 8 ENGLISH (Kepler Telescope)
Skill: Parallel Structure (ACT 71C)
The Kepler Space Telescope revolutionized astrophysics by monitoring star brightness, detecting periodic dips in light, and to discover thousands of diverse exoplanets orbiting distant suns.
A NO CHANGE
B discovered thousands
C discovering thousands
D it discovered thousands
Look at the structure of the preceding list items!
DAY 8 • ENGLISH ANSWER KEY CORRECT OPTION: C
The sentence lists parallel telescope actions. The first two items use the gerund (-ing) form: (1) monitoring, and (2) detecting. To maintain parallel structure, the third must be: (3) discovering.
ACT STRATEGY SPARK
Whenever you see a list of items joined by and or or, they must match in tense, voice, and part of speech!
Up Next: Day 8 Math Connection →
DAY 8 MATH (Kepler's Exponents)
Skill: Fractional Exponents (ACT 56M)
According to Kepler's Third Law, the square of orbital period \(P\) (in Earth years) equals the cube of its semi-major axis \(a\) (average distance in AU):
\(P^2 = a^3\)
If an exoplanet has a semi-major orbital axis of \(a = 4\text{ AU}\), what is its orbital period \(P\) in Earth years?
F2
G4
H8
J16
K64
Remember how to convert powers to roots!
DAY 8 • MATH ANSWER KEY CORRECT OPTION: H
1. Plug in \(a = 4\): \(P^2 = 4^3 = 64\).
2. Take the square root of both sides: \(P = \sqrt{64} = 8\text{ years}\).
3. In exponent form: \(P = a^{3/2} = 4^{3/2} = (\sqrt{4})^3 = 2^3 = 8\).
ACT STRATEGY SPARK
Fractional Exponent Rule: \(\sqrt[n]{x^m} = x^{m/n}\). The denominator is the root index, and the numerator is the interior power!
Day 8 Complete! Onward to Day 9 →
DAY 9 ENGLISH (Ocean Acidification)
Skill: Pronoun-Antecedent Agreement (ACT 73A)
As marine ecosystems absorb excess carbon dioxide, the pH of the ocean drops. This change makes it difficult for a calcifying organism, such as a coral polyp, to build their protective calcium carbonate skeleton.
A NO CHANGE
B its protective calcium carbonate skeleton.
C our protective calcium carbonate skeleton.
D its' protective calcium carbonate skeleton.
Is "a coral polyp" singular or plural?
DAY 9 • ENGLISH ANSWER KEY CORRECT OPTION: B
The pronoun must agree in number with its antecedent noun. The antecedent is "a calcifying organism, such as a coral polyp", which is singular. Thus we require its. Option D ("its'") is not a real word.
ACT STRATEGY SPARK
Never choose its' on the ACT English section—there is no such word in the English language!
Up Next: Day 9 Math Connection →
DAY 9 MATH (Ocean pH Statistics)
Skill: Descriptive Stats & Mean (ACT 41M)
An oceanographic sensor collects water pH values at five zones in a marine estuary. The logged dataset contains these five values:
\(7.8,\; 8.1,\; 7.9,\; 8.0,\; 8.2\)
If the sensor collects a sixth pH value, and the new mean of all six values is exactly \(8.05\), what is the value of that sixth pH measurement?
A8.0
B8.1
C8.2
D8.3
E8.4
Use the sum method to find missing dataset entries!
DAY 9 • MATH ANSWER KEY CORRECT OPTION: D
1. Sum of initial 5 data points: \(7.8 + 8.1 + 7.9 + 8.0 + 8.2 = 40.0\)
2. Required sum of all 6 points to yield a mean of 8.05: \(6 \times 8.05 = 48.3\)
3. Subtract: \(48.3 - 40.0 = 8.3\).
ACT STRATEGY SPARK
The Average-Sum Shortcut: Always translate average questions into sum questions. Sum = Mean × N.
Day 9 Complete! Onward to Day 10 →
DAY 10 ENGLISH (Michael Faraday)
Skill: Redundancy & Concision (ACT 72A)
In 1831, Michael Faraday discovered electromagnetic induction, proving that moving a magnet through a wire coil could generate an electric current that was electrical in nature.
F NO CHANGE
G a flow of current that is electrical.
H an electric current.
J an electric flow of current.
Is "electric" repetitive when combined with "current"?
DAY 10 • ENGLISH ANSWER KEY CORRECT OPTION: H
The sentence contains redundancy. An electric current is inherently electrical in nature. Options F, G, and J repeat this concept. Option H is clean, correct, and concise.
ACT STRATEGY SPARK
The Redundancy Rule: The ACT absolute hates stating the same concept twice using different words. If you can remove descriptive words without losing details, delete!
Up Next: Day 10 Math Connection →
DAY 10 MATH (Circular Magnetic Induction)
Skill: Circles & Area Change (ACT 51M)
An electrical technician measures the magnetic induction flux through a flat, circular loop of flexible wire. The starting radius of the circular wire loop is \(R = 10\text{ cm}\).
If the technician mechanically stretches the wire so that its radius increases to a new value of \(R_{new} = 15\text{ cm}\), what is the ratio of the new circular area to the original starting area?
F\(2:3\)
G\(3:2\)
H\(9:4\)
J\(4:9\)
K\(225:10\)
How does scaling a 1D length affect a 2D area?
DAY 10 • MATH ANSWER KEY CORRECT OPTION: H
1. Find the linear radius scaling ratio: \(\text{Ratio}_R = \frac{15}{10} = \frac{3}{2}\).
2. Since circle area is proportional to the square of the radius (\(A = \pi r^2\)), square the linear ratio:
\(\text{Ratio}_A = \left(\frac{3}{2}\right)^2 = \frac{9}{4}\).
ACT STRATEGY SPARK
The Scale-Area Rule: If you scale any 2D shape by linear factor \(k\), its area scales by \(k^2\)! Skip slow manual area calculations.
Week 2 Complete! Onward to Week 3 →
SECTION 3
Focus: Lichen Punctuation, Exponential Cultures, Endothermic Thermodynamics, Coriolis Winds, and Tiktaalik Fossils.
Let's continue to Day 11.
DAY 11 ENGLISH (Lichen Bioindicators)
Skill: Possessives & Apostrophes (ACT 73F)
Lichens possess no roots and absorb water directly from the air. Therefore, a lichens' sensitivity to sulfur dioxide provides scientists with an excellent, cost-effective bioindicator of air quality.
F NO CHANGE
G lichen's sensitivity to sulfur dioxide provides scientists
H lichens sensitivity to sulfur dioxide provides scientists
J lichen's sensitivity to sulfur dioxide provide scientists
Look closely at the singular article "a" at the start of the clause!
DAY 11 • ENGLISH ANSWER KEY CORRECT OPTION: G
The clause starts with the singular indefinite article "a", demanding a singular noun: "a lichen." To show singular possession, add an apostrophe and an "s": lichen's.
ACT STRATEGY SPARK
The Possessive Blueprint: Singular possessive is Noun + 's (lichen's). Plural possessive ending in s is Noun + ' (lichens').
Up Next: Day 11 Math Connection →
DAY 11 MATH (Exponential Growth)
Skill: Exponential Modeling (ACT 46M)
A population of bacteria in a petri dish culture starts with exactly \(200\text{ organisms}\). The population doubles in size every \(4\text{ hours}\).
Which of the following mathematical functions represents the total number of bacteria cells, \(N(t)\), in the petri dish after exactly \(t\) hours of continuous incubation?
A\(N(t) = 200 \times 2^{4t}\)
B\(N(t) = 200 \times 2^{t/4}\)
C\(N(t) = 200 \times 4^t\)
D\(N(t) = 200 + 2^{t/4}\)
Test a real number of hours: Where does the population stand at t = 4?
DAY 11 • MATH ANSWER KEY CORRECT OPTION: B
1. Exponential growth model: \(N(t) = \text{Initial} \times (\text{Rate})^{\text{cycles}}\).
2. Initial count is \(200\) and compounding rate is \(2\) (doubling).
3. Since doubling takes 4 hours, the cycles completed equals \(t / 4\): \(N(t) = 200 \times 2^{t/4}\).
ACT STRATEGY SPARK
The Plug-and-Test Strategy: Pick a simple number. At \(t = 4\text{ hours}\), bacteria must double once to \(400\). Option B gives \(200 \times 2^1 = 400\) instantly!
Day 11 Complete! Onward to Day 12 →
DAY 12 ENGLISH (Cold Packs)
Skill: Sentence Combining (ACT 71B)
Instant cold packs rely on an endothermic reaction. This occurs when solid ammonium nitrate dissolves in water. This chemical dissolution absorbs thermal heat energy from the immediate surroundings.
Which is the most concise way to combine these three sentences?
A Instant cold packs rely on an endothermic reaction, which absorbs heat as ammonium nitrate dissolves.
B An endothermic reaction is what cold packs rely on; this occurs when dissolving ammonium nitrate to absorb heat.
C Instant cold packs rely on an endothermic reaction, and it occurs when ammonium nitrate dissolves to absorb heat.
D In cold packs, endothermic reactions occur, and this is because ammonium nitrate dissolves, absorbing surrounding heat.
Look for the sentence that eliminates passive words and unnecessary pronouns!
DAY 12 • ENGLISH ANSWER KEY CORRECT OPTION: A
Sentence combining is a concision challenge. Option A combines all three facts (cold pack, endothermic reaction, dissolution heat absorption) using a single relative clause, avoiding redundant pronouns like "and it occurs".
ACT STRATEGY SPARK
Concision Priority: Shorter is better. Look for active relative pronouns (like which) over long compound coordinating conjunction chains.
Up Next: Day 12 Math Connection →
DAY 12 MATH (Thermal Specific Heat)
Skill: Multi-Step Algebra (ACT 34M)
The heat energy \(q\) absorbed by a substance is modeled by the equation:
\(q = m \cdot c \cdot \Delta T\)
where \(m\) is mass in grams, \(c\) is the specific heat capacity (\(4.2\text{ J/g}^\circ\text{C}\) for water), and \(\Delta T\) is the change in temperature. If exactly \(840\text{ Joules}\) heats a \(20.0\text{ g}\) sample of water, what is the temperature change (\(\Delta T\))?
F\(2.0^\circ\text{C}\)
G\(10.0^\circ\text{C}\)
H\(20.0^\circ\text{C}\)
J\(42.0^\circ\text{C}\)
K\(100.0^\circ\text{C}\)
Rearrange the variables to solve for temperature change!
DAY 12 • MATH ANSWER KEY CORRECT OPTION: G
1. Isolate the target variable, temperature change (\(\Delta T\)): \(\Delta T = \frac{q}{m \cdot c}\).
2. Substitute values: \(\Delta T = \frac{840}{20.0 \times 4.2}\).
3. Simplify denominator and divide: \(\Delta T = \frac{840}{84} = 10.0^\circ\text{C}\).
ACT STRATEGY SPARK
Literal Equations: Always rearrange variables algebraically *before* plugging in numbers. This organizes scratch work and cuts computation errors!
Day 12 Complete! Onward to Day 13 →
DAY 13 ENGLISH (Coriolis Effect)
Skill: Relative Pronouns (ACT 73G)
Cyclonic storm rotations are caused by the Coriolis effect, a phenomenon of Earth's rotation whom deflects winds to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
F NO CHANGE
G that deflects winds to the right
H who deflects winds to the right
J whom deflecting winds to the right
Is the Coriolis effect a human being?
DAY 13 • ENGLISH ANSWER KEY CORRECT OPTION: G
The relative pronouns "who" and "whom" refer only to humans. The antecedent is "a phenomenon," which is an abstract scientific process. For non-human concepts, use that or which (Option G).
ACT STRATEGY SPARK
Relative Pronoun Filter: who/whom = people. which/that = things. where = places. when = times. Memorize this filter!
Up Next: Day 13 Math Connection →
DAY 13 MATH (Cylinder Precipitation Volume)
Skill: Cylinder Volume (ACT 53M)
An agricultural test plot of circular shape has a radius of \(R = 10\text{ meters}\). During a storm, the rainfall forms a uniform cylinder of water of depth \(h = 0.05\text{ meters}\) over the plot.
Using the formula for cylinder volume, \(V = \pi R^2 h\), what is the total volume of precipitation (in cubic meters) deposited on this test plot?
A\(0.5\pi\)
B\(1.0\pi\)
C\(5.0\pi\)
D\(10.0\pi\)
E\(50.0\pi\)
Don't forget to square the radius first!
DAY 13 • MATH ANSWER KEY CORRECT OPTION: C
1. Formula: \(V = \pi R^2 h\).
2. Substitute values: \(V = \pi \cdot (10)^2 \cdot 0.05\).
3. Multiply: \(V = \pi \cdot 100 \cdot 0.05 = 5.0\pi\text{ m}^3\).
ACT STRATEGY SPARK
Keep \(\pi\) in the Expression: Notice that all answers feature \(\pi\). Never waste time multiplying by 3.14 unless requested!
Day 13 Complete! Onward to Day 14 →
DAY 14 ENGLISH (Newton's Optics)
Skill: Active vs. Passive Voice (ACT 72B)
In 1666, the classic experiment of splitting white light into a rainbow spectrum using a glass prism was performed by Isaac Newton in his dark room.
A NO CHANGE
B Isaac Newton performed in his dark room.
C Newton did, performing in his dark room.
D was performed in his dark room by Isaac Newton.
Which option places the active subject BEFORE the action?
DAY 14 • ENGLISH ANSWER KEY CORRECT OPTION: B
Options A and D use the passive voice ("was performed by..."), which is wordy. Active voice is always preferred on the ACT. In Option B, the subject "Isaac Newton" directly performs the action: "Isaac Newton performed."
ACT STRATEGY SPARK
Active Voice Priority: When editing, active phrasing is always preferred over passive phrasing if both are grammatically sound!
Up Next: Day 14 Math Connection →
DAY 14 MATH (Snell's Law Optics)
Skill: Trigonometry / Sine (ACT 62M)
According to Snell's Law, when light travels from air into a glass prism, the relationship is modeled by:
\(n_1 \cdot \sin(\theta_1) = n_2 \cdot \sin(\theta_2)\)
If the refractive index of air is \(n_1 = 1.0\), the refractive index of glass is \(n_2 = 1.5\), and the angle of incidence is \(\theta_1 = 30^\circ\), what is the value of \(\sin(\theta_2)\)?
(Note: \(\sin(30^\circ) = 0.5\))
F\(\frac{1}{6}\)
G\(\frac{1}{3}\)
H\(\frac{1}{2}\)
J\(\frac{3}{4}\)
K\(\frac{2}{3}\)
Express your answer as a clean simplified fraction!
DAY 14 • MATH ANSWER KEY CORRECT OPTION: G
1. Isolate the target value: \(\sin(\theta_2) = \frac{n_1 \cdot \sin(\theta_1)}{n_2}\).
2. Substitute: \(\sin(\theta_2) = \frac{1.0 \cdot 0.5}{1.5} = \frac{0.5}{1.5}\).
3. Convert decimal fraction into clean integer ratio: \(\frac{0.5}{1.5} = \frac{1}{3}\).
ACT STRATEGY SPARK
Multiply numerator and denominator by 2 to instantly clear decimals from complex fractions: \(\frac{0.5 \times 2}{1.5 \times 2} = \frac{1}{3}\).
Day 14 Complete! Onward to Day 15 →
DAY 15 ENGLISH (Tiktaalik Fossil)
Skill: Add / Delete Sentences (ACT 72E)
In 2004, paleontologists in Northern Canada discovered a fossilized Tiktaalik. This creature represents a crucial evolutionary transitional form between shallow-water fish and land-dwelling tetrapods. Paleontology remains a highly competitive field for academic funding. The fossil features a flexible wrist joint alongside traditional fish scales.
The author is considering deleting the underlined sentence. Should it be kept or deleted?
A • Keep It Because it provides essential economic context about scientific research.
B • Keep It Because it transitions the paragraph into the physical attributes of fossils.
C • Delete It Because it diverges from the primary focus of the paragraph on the Tiktaalik discovery.
D • Delete It Because it contradicts the historical facts of the fossil's physical structure.
Does funding competition have anything to do with Tiktaalik's physical anatomy?
DAY 15 • ENGLISH ANSWER KEY CORRECT OPTION: C
The paragraph is strictly about the paleontological anatomy of the Tiktaalik as an evolutionary bridge. The underlined sentence introduces an entirely separate topic: funding competitiveness. It must be deleted because it diverges from the primary focus (Option C).
ACT STRATEGY SPARK
The Relevance Test: Read the paragraph without the sentence. If the passage reads smoother and maintains coherence, delete!
Up Next: Day 15 Math Connection →
DAY 15 MATH (Fossil Mass Scatterplot)
Skill: Scatterplots & Best Fit (ACT 43M)
A paleontologist maps fossil femur length \(x\) (in cm) versus estimated body mass \(y\) (in kg) on a scatterplot. The line of best fit is calculated as:
\(y = 1.2x - 15.0\)
Based on this linear regression model, what is the estimated body mass (in kg) of a fossil specimen with a femur length of \(50\text{ cm}\)?
F15
G45
H50
J60
K75
Simply evaluate the function at x = 50!
DAY 15 • MATH ANSWER KEY CORRECT OPTION: G
1. Equation: \(y = 1.2x - 15.0\).
2. Substitute \(x = 50\): \(y = 1.2(50) - 15.0\).
3. Evaluate: \(y = 60.0 - 15.0 = 45\text{ kilograms}\).
ACT STRATEGY SPARK
Line of Best Fit: If an algebraic model is provided, ignore scatterplot visualizations entirely and perform a direct algebraic function substitution!
Week 3 Complete! Onward to Week 4 →
SECTION 4
Focus: Sørensen pH Comparisons, Logarithmic Acids, Topographic Trail Slopes, Mantle Conductivities, Antigen Venn sets, and Expanding Cosmology.
Let's continue to Day 16.
DAY 16 ENGLISH (Sørensen's pH Scale)
Skill: Illogical Comparisons (ACT 71E)
In 1909, Søren Sørensen developed the logarithmic pH scale, showing that the hydronium ion concentration of highly acidic compounds is vastly greater than neutral water.
A NO CHANGE
B neutral water is.
C that of neutral water.
D those of neutral water.
Are we comparing a concentration directly to water itself?
DAY 16 • ENGLISH ANSWER KEY CORRECT OPTION: C
You cannot compare concentration (an abstract value) directly to "neutral water" (a physical substance). Option C uses the singular phrase "that of" (shorthand for "the concentration of") to balance the comparison.
ACT STRATEGY SPARK
The Apples-to-Oranges Rule: Use "that of" for singular comparisons and "those of" for plural comparisons to avoid illogical sentence structures!
Up Next: Day 16 Math Connection →
DAY 16 MATH (Logarithmic pH)
Skill: Advanced Logarithms (ACT 58M)
The pH of an aqueous solution is a logarithmic scale representing the concentration of hydronium ions, \([\text{H}_3\text{O}^+]\):
\(\text{pH} = -\log_{10} [\text{H}_3\text{O}^+]\)
If a sample of acidic rainwater has a measured concentration of exactly \([\text{H}_3\text{O}^+] = 10^{-5}\text{ moles per liter}\), what is its pH value?
F-5
G1.5
H5
J10
K15
Use the power rule of logarithms to simplify the negative exponent!
DAY 16 • MATH ANSWER KEY CORRECT OPTION: H
1. Substitute values: \(\text{pH} = -\log_{10} (10^{-5})\).
2. Move exponent to front (power rule): \(\text{pH} = -(-5) \cdot \log_{10}(10)\).
3. Since \(\log_{10}(10) = 1\), simplify: \(\text{pH} = 5 \cdot 1 = 5\).
ACT STRATEGY SPARK
Inverse Property: \(\log_b (b^x) = x\). If there is a negative in front of log, simply swap the sign of the exponent to find the answer instantly!
Day 16 Complete! Onward to Day 17 →
DAY 17 ENGLISH (Metamorphic Rocks)
Skill: Idiomatic Prepositions (ACT 72C)
Metamorphic rocks are formed when intense subterranean heat and pressure alter existing sedimentary or igneous rocks into a completely new, foliar stone.
A into a completely new, foliar stone.
B with a completely new, foliar stone.
C onto a completely new, foliar stone.
D at a completely new, foliar stone.
Which preposition idiomatically matches the verb "alter"?
DAY 17 • ENGLISH ANSWER KEY CORRECT OPTION: A
The verb "alter" is conventions-paired with the preposition "into" when describing a change of physical structure: "alter rocks into a new stone." Options B, C, and D are unidiomatic.
ACT STRATEGY SPARK
Idioms: Trust your ear! Read the sentence with each preposition option. The correct convention will feel natural and flow smoothly.
Up Next: Day 17 Math Connection →
DAY 17 MATH (Topographic Slope)
Skill: Coordinate Slope (ACT 52B)
A geologist measures slope steepness on a topographic map. Point A is located at coordinates \((x_1, y_1) = (200\text{ m}, 840\text{ m})\), where \(x\) is horizontal distance and \(y\) is altitude.
Point B is located at coordinates \((x_2, y_2) = (320\text{ m}, 990\text{ m})\). What is the gradient slope (rise over run) of the trail connecting Point A to Point B?
F\(0.80\)
G\(1.25\)
H\(1.50\)
J\(2.25\)
K\(4.00\)
Calculate change in altitude divided by change in distance!
DAY 17 • MATH ANSWER KEY CORRECT OPTION: G
1. Formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
2. Substitute coordinates: \(m = \frac{990 - 840}{320 - 200}\).
3. Evaluate: \(m = \frac{150}{120} = \frac{5}{4} = 1.25\).
ACT STRATEGY SPARK
Rise Over Run: Never swap numerator and denominator. Rise (y) is always on top. Swapping gives \(120/150 = 0.80\) (Option F), a common trap!
Day 17 Complete! Onward to Day 18 →
DAY 18 ENGLISH (Mantle Convection)
Skill: Transition Words (ACT 71D)
Convection currents in Earth's mantle transfer thermal energy from the hot core toward the cooler crust. Furthermore, this movement is extremely gradual, moving tectonic plates by only a few centimeters each year.
A NO CHANGE
B However,
C Therefore,
D Similarly,
Does the massive heat transfer contrast with the tiny movement rate?
DAY 18 • ENGLISH ANSWER KEY CORRECT OPTION: B
The passage contains a contrast. The first sentence describes massive energy transfer. The second highlights how slow the physical crustal movement is. To link massive energy to small physical movement, we use the contrast transition "However".
ACT STRATEGY SPARK
Analyze the relationship between clauses before selecting: (1) repetition/addition, (2) conflict/contrast, or (3) cause/effect.
Up Next: Day 18 Math Connection →
DAY 18 MATH (Inverse Resistance)
Skill: Inverse Relationships (ACT 44M)
The thermal resistance \(R\) of an insulating material is inversely proportional to its thermal conductivity constant \(k\). For a constant material thickness:
\(R = \frac{C}{k}\)
where \(C\) is a constant. If an insulator has a resistance of \(R = 12\text{ units}\) when its conductivity is \(k = 0.2\text{ units}\), what will its thermal resistance be when conductivity increases to \(k = 0.6\text{ units}\)?
F4
G6
H12
J24
K36
If conductivity triples, what must happen to the resistance?
DAY 18 • MATH ANSWER KEY CORRECT OPTION: F
1. Solve for constant of proportionality \(C\): \(C = R \cdot k = 12 \cdot 0.2 = 2.4\).
2. Substitute \(C = 2.4\) back and solve for new resistance with \(k_{new} = 0.6\):
\(R_{new} = \frac{2.4}{0.6} = 4\text{ units}\).
ACT STRATEGY SPARK
The Inverse Shortcut: Since conductivity \(k\) tripled (\(0.2 \rightarrow 0.6\)), resistance \(R\) must be divided by 3: \(12 / 3 = 4\). Solve in seconds!
Day 18 Complete! Onward to Day 19 →
DAY 19 ENGLISH (Edward Jenner)
Skill: Dashes & Parentheses (ACT 73D)
In 1796, Edward Jenner inoculated a young boy with cowpox virus—a mild disease contracted from cattle, and later exposed him to smallpox, establishing the world's first successful vaccine.
A NO CHANGE
B a mild disease contracted from cattle—and later
C a mild disease contracted from cattle; and later
D a mild disease contracted from cattle, later
If you open a parenthetical dash, what must you use to close it?
DAY 19 • ENGLISH ANSWER KEY CORRECT OPTION: B
The phrase "a mild disease contracted from cattle" is non-essential parenthetical information. The author opened this description with an em-dash (—). Symmetrical punctuation demands a matching closing em-dash after cattle (Option B).
ACT STRATEGY SPARK
The Dash-Pair Rule: Em-dashes exist as pairs when setting off clauses. Never mix-and-match a dash opening with a comma closing!
Up Next: Day 19 Math Connection →
DAY 19 MATH (Venn Diagram Sets)
Skill: Sets & Venn Diagrams (ACT 42B)
In an immunological study of \(100\text; cell samples\), researchers track the presence of surface Antigen A and Antigen B. The data shows:
Has Antigen A
65 cells
Has Antigen B
45 cells
Has NEITHER
15 cells
How many cell samples in this study contain BOTH Antigen A and Antigen B?
A10
B25
C35
D45
E85
Remember that some cells are counted twice in the raw list!
DAY 19 • MATH ANSWER KEY CORRECT OPTION: B
1. Total cells containing at least one Antigen (A or B): \(100 - 15\text{ (neither)} = 85\) cells.
2. Sum of separate single antigen counts: \(65\text{ (A)} + 45\text{ (B)} = 110\).
3. Overlap containing BOTH is the excess over actual active count: \(110 - 85 = 25\text{ cells}\).
ACT STRATEGY SPARK
The Venn Equation: \(A \cup B = A + B - (A \cap B)\). Add separate categories and subtract the total union to find "both" overlap immediately!
Day 19 Complete! Onward to the final Day 20! →
DAY 20 ENGLISH (Edwin Hubble)
Skill: Sentence Order (ACT 72B)
[1] His measurements showed that distant galaxies are moving away from Earth at speeds proportional to their distance. [2] In 1929, Edwin Hubble published a landmark cosmological study. [3] This key observation provided the first empirical evidence that the universe is continuously expanding.
To make this paragraph most logical, Sentence 1 should be placed:
F • Where it is now Keep the paragraph in its current chronological order.
G • After Sentence 2 Place Sentence 1 immediately after Sentence 2 to clarify "His".
H • After Sentence 3 Place Sentence 1 at the very end of the paragraph.
J • Deleted entirely Remove Sentence 1 as it breaks paragraph flow.
Look at the pronoun "His" at the beginning of Sentence 1!
DAY 20 • ENGLISH ANSWER KEY CORRECT OPTION: G
Sentence 1 starts with the pronoun "His". Placed first, there is no antecedent noun. Sentence 2 introduces proper noun "Edwin Hubble." Therefore, Sentence 2 must precede Sentence 1. Once Hubble is introduced, Sentence 1 can follow logically.
ACT STRATEGY SPARK
Pronoun Clues: On organization questions, track pronouns and demonstratives (this, these). The noun must always be introduced first!
Up Next: Day 20 Math Connection →
DAY 20 MATH (Hubble's Constant Variation)
Skill: Direct Variation (ACT 31C)
According to Hubble's Law, the recessional velocity \(v\) of a galaxy (in km/s) is directly proportional to its distance \(d\) from Earth (in Megaparsecs, Mpc):
\(v = H_0 \cdot d\)
If a galaxy at distance \(d = 2\text{ Mpc}\) has velocity \(v = 140\text{ km/s}\), what is the recessional velocity of a second galaxy located at distance \(d = 5\text{ Mpc}\)?
F70
G280
H350
J700
K1400
Direct proportion means that as distance scales, velocity scales by the same factor!
DAY 20 • MATH ANSWER KEY CORRECT OPTION: H
1. Solve for Hubble's constant coefficient \(H_0\): \(H_0 = \frac{v}{d} = \frac{140}{2} = 70\text{ km/s per Mpc}\).
2. Substitute \(H_0 = 70\) and new distance \(d = 5\text{ Mpc}\) back: \(v = 70 \cdot 5 = 350\text{ km/s}\).
ACT STRATEGY SPARK
The Factor Shortcut: Distance scaled from 2 to 5 (a factor of 2.5). Velocity must scale by 2.5: \(140 \times 2.5 = 350\)!
Congratulations! You have completed all 20 Days of Daily Sparks!
