1. Context clues are surrounding words that help define a term. The phrase "regulates the passage of substances" immediately follows and defines the membrane's permeability.
2. The passage also mentions that molecules "cross the membrane", which proves the membrane is not completely solid or resistant, ruling out Option A.
3. "Permeable" derives from the Latin permeare, meaning "to pass through". In science, materials that permit substances to cross them are called permeable.
Key Skill: Utilizing Textual Context Clues Slide 4 of 20
DAY 02 TSIA2 Math Prep
Biology & Life Sciences
An environmental scientist measures the growth of a bacterial colony in nutrient-rich agar. The population \( P \) of the colony \( t \) hours after the observation begins is modeled by the linear function:
\( P(t) = 175t + 450 \)
Based on this model, how many bacteria will be in the colony after exactly 8 hours?
A 1,400
B 1,850
C 2,125
D 3,600
TSIA2 Diagnostic Standard: Algebraic Reasoning Slide 5 of 20
DAY 02 Answer & Explanation
B
1,850 bacteria
P(8) = 175(8) + 450
The problem asks for the population after 8 hours. The variable representing hours is \( t \). Plug in 8 and follow PEMDAS.
1. Write down the modeled linear function: \( P(t) = 175t + 450 \).
2. Identify that \( t = 8 \) represents the time of observation.
3. Substitute \( t = 8 \) into the equation:
\( P(8) = 175(8) + 450 \).
4. Multiply first (order of operations):
\( 175 \times 8 = 1,400 \).
5. Add the constant starting value:
\( 1,400 + 450 = 1,850 \) bacteria.
Key Skill: Evaluating Linear Function Equations Slide 6 of 20
DAY 02 TSIA2 ELAR Prep
Biology & Life Sciences
Identify the Grammatical Error
"A complex cascade of biochemical reactions, which includes light absorption and carbon fixation, occur inside the chloroplasts of photosynthetic organisms."
A Change "includes" to "include"
B Change "occur" to "occurs"
C Change "chloroplasts" to "chloroplast"
D Change "reactions" to "reaction"
TSIA2 Writing Strand: Subject-Verb Agreement Slide 7 of 20
DAY 02 Answer & Explanation
B
Change "occur" to "occurs"
Eliminate intervening prepositional modifiers and relative clauses: "A complex cascade occur..." represents a mismatch of singular subject and plural verb.
1. The true subject of the sentence is "A complex cascade", which is a singular noun phrase.
2. The plural noun "reactions" is inside a prepositional phrase ("of biochemical reactions") and cannot act as the subject of the sentence.
3. The verb "occur" is plural, which creates an agreement error with the singular "cascade". It must be written as the singular "occurs" to be correct.
Key Skill: Stripping Sentence Clutter to Match Subject & Verb Slide 8 of 20
DAY 03 TSIA2 Math Prep
Biology & Life Sciences
In pea plants, yellow seed color (\(Y\)) is dominant over green seed color (\(y\)). A botanist crosses a heterozygous yellow pea plant (\(Yy\)) with a homozygous recessive green pea plant (\(yy\)).
If this cross produces exactly 160 offspring, what is the expected number of yellow-seeded offspring?
A 40
B 80
C 120
D 160
TSIA2 Diagnostic Standard: Probabilistic & Statistical Reasoning Slide 9 of 20
DAY 03 Answer & Explanation
B
80 offspring
Expected = Probability × Total
Construct a Punnett Square with sides labeled \( Y, y \) and \( y, y \). What percentage carries at least one dominant \( Y \)?
1. Determine gametes of both parent plants: Parent 1 is heterozygous (\( Yy \)) and Parent 2 is homozygous recessive (\( yy \)).
2. Match alleles in a cross table:
- Offspring 1: \( Yy \) (Yellow) | Offspring 2: \( Yy \) (Yellow)
- Offspring 3: \( yy \) (Green) | Offspring 4: \( yy \) (Green)
3. The probability of obtaining yellow seeds (\( Yy \)) is \( \frac{2}{4} = 0.5 \) (or 50%).
4. Calculate expected frequency: \( 160 \times 0.5 = 80 \) offspring.
Key Skill: Expected Value and Genetics Probability Slide 10 of 20
DAY 03 TSIA2 ELAR Prep
Biology & Life Sciences
Reading Passage
"Leafcutter ants harvest leaves not to eat them directly, but to feed a specialized fungus that they cultivate in underground gardens. This fungus breaks down toxic plant cellulose into edible proteins for the ants. In return, the ants protect the fungus from pests and supply it with leaves, forming an obligate mutualistic bond where neither species can survive without the other."
A Leafcutter ants have developed defenses against toxic forest plants.
B Cultivating agricultural crops is a behavior unique to social insects.
C Leafcutter ants and fungi share an essential, interdependent relationship.
D Fungal enzymes are highly effective at breaking down plant cellulose.
TSIA2 Reading Strand: Main Idea & Informational Synthesis Slide 11 of 20
DAY 03 Answer & Explanation
C
Leafcutter ants and fungi share an essential, interdependent relationship.
The passage details mutual services (the ants feed/protect, the fungus digests) and ends with a strong summary: "obligate mutualistic bond where neither species can survive without the other."
1. Options A and D present accurate factual sentences from the text, but they represent supporting details rather than the central idea of the complete passage.
2. Option B introduces an overgeneralization ("Agricultural crops are unique to social insects") that is not supported by the passage.
3. Option C captures the mutual benefit, summarizing the concept of "obligate mutualistic bond" in a clear, comprehensive main idea statement.
Key Skill: Distinguishing Main Idea from Supporting Details Slide 12 of 20
DAY 04 TSIA2 Math Prep
Biology & Life Sciences
A spherical eukaryotic cell has a radius of exactly 4 micrometers. A larger cell in the same tissue has a radius of 8 micrometers.
By what factor is the volume of the larger cell greater than the volume of the smaller cell?
A 2
B 4
C 8
D 16
TSIA2 Diagnostic Standard: Geometric & Spatial Reasoning Slide 13 of 20
DAY 04 Answer & Explanation
C
8 times
Volume scaling ratio = k³
The volume of a sphere is \( V = \frac{4}{3}\pi r^3 \). When the radius doubles (\( 2r \)), how many times does the cubed portion increase?
1. Find the scale factor of the radius:
\( k = \frac{\text{Radius}_{\text{large}}}{\text{Radius}_{\text{small}}} = \frac{8}{4} = 2 \).
2. The formula for the volume of a sphere is \( V = \frac{4}{3}\pi r^3 \). This means volume has a cubic relationship with the radius: \( V \propto r^3 \).
3. Apply the scale factor rule for volume:
\( \text{Volume Ratio} = k^3 = (2)^3 \).
4. Solve the cubic calculation: \( 2 \times 2 \times 2 = 8 \).
Key Skill: Scaling Rules for Area & Volume (Dimensionality) Slide 14 of 20
DAY 04 TSIA2 ELAR Prep
Biology & Life Sciences
Sentence Logic & Transition Words
"Polar bears possess thick layers of blubber and translucent fur to withstand freezing arctic temperatures. [ ________ ], their black skin underneath absorbs maximum solar radiation, providing an additional layer of heat retention."
A Consequently
B Furthermore
C Nevertheless
D Conversely
TSIA2 Writing Strand: Transition Words & Sentence Logic Slide 15 of 20
DAY 04 Answer & Explanation
B
Furthermore
The sentence is listing additional structural and physiological elements that serve the same heating goal. It does not display a cause-effect or contrast relationship.
1. Consequently (Option A) indicates a cause-and-effect relationship, but black skin absorbing heat is not a biological result of having blubber.
2. Nevertheless (Option C) and Conversely (Option D) represent contrasting transitions. However, these two physiological properties support and reinforce each other.
3. Furthermore (Option B) represents an additive relationship, perfectly introducing a separate biological adaptation that works in tandem with the first.
Key Skill: Categorizing Transition Meanings (Addition vs. Contrast) Slide 16 of 20
DAY 05 TSIA2 Math Prep
Biology & Life Sciences
An ecologist monitors a white-tailed deer population in a protected state forest. The data table displays the winter deer count over 5 consecutive years:
| Year Observed | Deer Census Count |
|---|---|
| Year 1 | 148 |
| Year 2 | 155 |
| Year 3 | 162 |
| Year 4 | 145 |
| Year 5 | 150 |
What is the mean winter deer count over this 5-year observation period?
A 148
B 150
C 151
D 152
TSIA2 Diagnostic Standard: Probabilistic & Statistical Reasoning Slide 17 of 20
DAY 05 Answer & Explanation
D
152 deer
Mean = Sum ÷ Count (N=5)
"Mean" indicates the standard arithmetic average. Add the numbers up and divide by the number of observations (5 years).
1. Sum all five years of recorded deer data:
\( \text{Sum} = 148 + 155 + 162 + 145 + 150 \).
2. Compute the exact summation result:
\( \text{Sum} = \mathbf{760} \).
3. Divide by the total number of years (which is 5):
\( \text{Mean} = \frac{760}{5} \).
4. Execute the division: \( 152 \).
Key Skill: Arithmetic Mean and Core Data Summary Slide 18 of 20
DAY 05 TSIA2 ELAR Prep
Biology & Life Sciences
Reading Passage
"CRISPR-Cas9 gene editing represents a breathtaking leap forward in medical biotechnology, offering the unprecedented potential to permanently eradicate devastating genetic disorders like sickle cell anemia. While regulatory safeguards must be meticulously designed to prevent ethical overreach, we must not let excessive caution paralyze clinical trials that could save millions of lives."
A deeply skeptical and alarmed
B enthusiastically supportive yet cautious
C strictly objective and detached
D dismissive of safety concerns
TSIA2 Reading Strand: Tone & Rhetorical Analysis Slide 19 of 20
DAY 05 Answer & Explanation
B
enthusiastically supportive yet cautious
Note the balanced language: "breathtaking leap... could save millions" shows excitement, while "safeguards must be meticulously designed" shows caution.
1. Tone is identified through the author's word choices (diction) and general argument structure.
2. High-energy vocabulary such as "breathtaking leap" and "unprecedented potential" eliminates the "strictly objective" (Option C) and "skeptical" (Option A) choices.
3. The explicitly stated need that "safeguards must be meticulously designed to prevent ethical overreach" directly disproves that the author is "dismissive of safety concerns" (Option D).
Key Skill: Dissecting Diction to Identify Balanced Authorial Tone Slide 20 of 20
The passage asserts that "ice floats". An object only floats on a liquid if its physical density is lower than that liquid.
1. An inference is a conclusion derived logically from facts stated in the text.
2. The text notes that as water solidifies, it exhibits "anomalous expansion" and the lattice "holds the molecules further apart". Increasing volume while mass is constant results in lower density.
3. The explicit evidence "ice floats" directly supports the inference that solid water (ice) is less dense than liquid water (Option B).
Key Skill: Linking Structural Text Details to Scientific Principles Slide 4 of 20
DAY 07 TSIA2 Math Prep
Chemistry & Matter
A chemist calculates the percent composition by mass of a Carbon Dioxide (\(\text{CO}_2\)) molecule. The atomic mass of Carbon is approximately 12 g/mol, and the atomic mass of Oxygen is 16 g/mol.
What is the approximate percent composition of Oxygen by mass in Carbon Dioxide? (Round to the nearest whole percent).
A 27%
B 36%
C 50%
D 73%
TSIA2 Diagnostic Standard: Quantitative Reasoning Slide 5 of 20
DAY 07 Answer & Explanation
D
73% Oxygen
By Total Compound Mass
The formula has two Oxygen atoms. Calculate the total molecular mass: \( 12 + 2(16) = 44 \). What fraction is Oxygen?
1. Total molar mass of \(\text{CO}_2\):
\( \text{Molar Mass} = 1(\text{C}) + 2(\text{O}) \)
\( \text{Molar Mass} = 12 + 2(16) = 44 \text{ g/mol} \).
2. Compute total mass contributed by Oxygen:
\( \text{Mass of O} = 2 \times 16 = 32 \text{ g/mol} \).
3. Set up the percentage fraction:
\( \text{Percent Composition} = \frac{\text{Mass of O}}{\text{Total Mass}} \times 100\% = \frac{32}{44} \times 100\% \).
4. Execute math: \( \frac{32}{44} \approx 0.7272 \) or 72.7%. Rounded up, we get 73%.
Key Skill: Calculations of Percentages and Chemical Ratios Slide 6 of 20
DAY 07 TSIA2 ELAR Prep
Chemistry & Matter
Pronoun-Antecedent Agreement
"When Dmitri Mendeleev organized the first periodic table, they arranged the elements by atomic mass and left blank spaces for undiscovered elements."
A Change "organized" to "organize"
B Change "they" to "he"
C Change "elements" to "element"
D Change "left" to "leaving"
TSIA2 Writing Strand: Pronoun-Antecedent Agreement Slide 7 of 20
DAY 07 Answer & Explanation
B
Change "they" to "he"
Locate the pronoun's antecedent. Dmitri Mendeleev is a singular, male historical noun. The pronoun must agree in number and gender.
1. Pronouns must match their antecedent in number (singular/plural) and gender.
2. The original pronoun "they" is plural, creating an agreement error with the singular antecedent "Dmitri Mendeleev".
3. Replacing "they" with "he" corrects the error seamlessly (Option B), matching Mendeleev as a singular male figure.
Key Skill: Linking Singular Pronouns to Singular Proper Nouns Slide 8 of 20
DAY 08 TSIA2 Math Prep
Chemistry & Matter
The Ideal Gas Law represents the mathematical relationship between pressure (\(P\)), volume (\(V\)), amount of gas in moles (\(n\)), the gas constant (\(R\)), and temperature (\(T\)):
\( PV = nRT \)
Which of the following correctly expresses the temperature (\(T\)) in terms of the other variables?
A T = \frac{nR}{PV}
B T = PV - nR
C T = \frac{PV}{nR}
D T = nR(PV)
TSIA2 Diagnostic Standard: Algebraic Reasoning Slide 9 of 20
DAY 08 Answer & Explanation
C
T = \frac{PV}{nR}
Isolated variable: T
The target variable \(T\) is currently multiplied by the group term \( nR \). Perform the inverse operation to isolate \(T\).
1. Write down the starting equation: \( PV = nRT \).
2. The variable group \( nR \) is being multiplied by \( T \) on the right side.
3. To undo multiplication, apply division (the inverse operation) to both sides of the equation:
\( \frac{PV}{nR} = \frac{nRT}{nR} \).
4. Simplify the right side: the \( nR \) terms cancel out, leaving \( T \) isolated.
\( T = \frac{PV}{nR} \).
Key Skill: Rearranging Variables in Multi-Variable Formulas Slide 10 of 20
DAY 08 TSIA2 ELAR Prep
Chemistry & Matter
Reading Passage
"Nuclear fission splits heavy atomic nuclei into smaller fragments, releasing massive quantities of energy. Conversely, nuclear fusion joins light isotopes, like hydrogen, together to form helium under extreme pressures. Nuclear fusion represents a far more elegant and mathematically perfect energy source than fission, as it produces zero long-lived radioactive waste."
A Fission splits heavy atomic nuclei into smaller fragments.
B Fusion joins light isotopes to form helium under pressure.
C Fusion represents a far more elegant and perfect energy source.
D Nuclear fusion produces zero long-lived radioactive waste.
TSIA2 Reading Strand: Distinguishing Fact vs. Opinion Slide 11 of 20
DAY 08 Answer & Explanation
C
Fusion represents a far more elegant and perfect energy source.
Facts can be objectively proven or disproven by measurements. Opinions use value-laden subjective adjectives like "elegant" and "perfect".
1. Options A, B, and D describe measurable, physical, and chemical realities that can be verified in a physics lab. Thus, they are facts.
2. The assertion that fusion is "elegant" and "mathematically perfect" represents a subjective value judgment, which cannot be measured.
3. Recognizing opinion words helps TSIA2 test-takers isolate subjective commentary from objective evidence.
Key Skill: Spotting Subjective Value Words in Scientific Text Slide 12 of 20
DAY 09 TSIA2 Math Prep
Chemistry & Matter
An archaeologist measures the decay of the radioactive isotope Carbon-14 in an ancient wooden artifact. Carbon-14 has a known half-life of exactly 5,730 years.
If testing reveals that the wood currently contains exactly 12.5% of its original Carbon-14 content, what is the approximate age of the artifact?
A 5,730 years
B 11,460 years
C 17,190 years
D 22,920 years
TSIA2 Diagnostic Standard: Probabilistic & Statistical Reasoning Slide 13 of 20
DAY 09 Answer & Explanation
C
17,190 years
Exactly 3 Half-Lives Completed
Trace the halving pattern starting from 100%: 100% → 50% → 25% → 12.5%. How many decay cycles does this represent?
1. A radioactive half-life is the duration required for a substance to reduce to half its previous mass.
2. Map the decay steps:
- 0 half-lives: 100%
- 1 half-life: 50%
- 2 half-lives: 25%
- 3 half-lives: 12.5%
3. Multiply the number of cycles by the half-life duration:
\( 3 \times 5,730 \text{ years} = 17,190 \text{ years} \).
Key Skill: Calculating Logarithmic Half-Life Fractions Slide 14 of 20
DAY 09 TSIA2 ELAR Prep
Chemistry & Matter
Synthesize & Combine Sentences
1. "Exothermic reactions release energy into the surrounding environment."
2. "Endothermic reactions absorb thermal energy from their surroundings."
A Exothermic reactions release energy into the surrounding environment, endothermic reactions absorb thermal energy.
B Exothermic reactions release energy into the surroundings; in contrast, endothermic reactions absorb thermal energy.
C Because exothermic reactions release energy into the surrounding environment, endothermic reactions absorb thermal energy.
D Exothermic reactions release energy into the surrounding environment, but endothermic reactions absorbing thermal energy.
TSIA2 Writing Strand: Coordinating Clauses & Avoiding Splices Slide 15 of 20
DAY 09 Answer & Explanation
B
Exothermic reactions...; in contrast, endothermic reactions...
Avoid comma splices (Option A) and unparallel syntax fragments (Option D). Semicolons followed by transitional adverbs like "in contrast" link contrasting complete thoughts.
1. Option A is a comma splice because it joins two independent clauses with only a comma, which is a major error on the TSIA2.
2. Option C uses a causal transition ("Because"), which is scientifically inaccurate; endothermic absorption does not occur as a consequence of exothermic release.
3. Option B is perfect. The semicolon joins two complete, related thoughts, and "in contrast" matches the scientific opposition.
Key Skill: Correcting Run-Ons, Comma Splices, and Logical Mislinks Slide 16 of 20
DAY 10 TSIA2 Math Prep
Chemistry & Matter
A block of pure copper has a physical mass of exactly 178 grams. A laboratory cylinder measures the block's physical displacement volume at 20 cubic centimeters (\(\text{cm}^3\)).
What is the physical density of the copper block in grams per cubic centimeter (\(\text{g/cm}^3\))?
A 0.11 \(\text{g/cm}^3\)
B 4.45 \(\text{g/cm}^3\)
C 8.90 \(\text{g/cm}^3\)
D 3,560 \(\text{g/cm}^3\)
TSIA2 Diagnostic Standard: Quantitative Reasoning Slide 17 of 20
DAY 10 Answer & Explanation
C
8.9 \(\text{g/cm}^3\)
Density = Mass ÷ Volume
The unit itself tells you the exact formula to utilize: grams per cubic centimeter (\(\text{g} / \text{cm}^3\)). Divide the grams by the cubic centimeters.
1. Write down the core density equation:
\( \text{Density } (D) = \frac{\text{Mass } (m)}{\text{Volume } (V)} \).
2. Identify variables from the prompt:
- \( \text{Mass } m = 178 \text{ g} \)
- \( \text{Volume } V = 20 \text{ cm}^3 \).
3. Substitute these values into the ratio:
\( D = \frac{178 \text{ g}}{20 \text{ cm}^3} \).
4. Solve the fraction division:
\( D = \mathbf{8.9} \text{ g/cm}^3 \).
Key Skill: Solving Fractional Ratios in Density Applications Slide 18 of 20
DAY 10 TSIA2 ELAR Prep
Chemistry & Matter
Reading Passage
"Enzymes are specialized proteins that function as biological catalysts within cells. By lowering the activation energy barrier required for a chemical reaction to occur, they exponentially accelerate physiological processes without undergoing any permanent chemical alteration themselves."
A absorb thermal waste from reactions
B slow down unstable molecular processes
C speed up chemical reactions
D change their physical state permanently
TSIA2 Reading Strand: Vocabulary in Context Slide 19 of 20
DAY 10 Answer & Explanation
C
speed up chemical reactions
The sentence states: "...they exponentially accelerate physiological processes." "Accelerate" is the structural context clue for speed.
1. The text defines the catalysts' function in the second sentence: "By lowering the activation energy... they exponentially accelerate...".
2. The verb "accelerate" means to speed up or increase the velocity of something, which points directly to Option C.
3. The passage also notes they do so "without undergoing any permanent alteration themselves", which directly refutes Option D.
Key Skill: Decoding Technical Jargon using Explanatory Appositives Slide 20 of 20
The target claim focuses on how mass affects acceleration. Look for the sentence that links these two variables in a direct, numeric relationship.
1. Option A focuses on the relationship between net force and acceleration, rather than mass.
2. Option C gives a practical, real-world application of the law (heavy trucks), but doesn't mathematically isolate the link between mass and acceleration rate.
3. Option B provides direct mathematical proof: doubling the mass cuts acceleration in half. This serves as perfect, unambiguous evidence supporting the prompt's claim.
Key Skill: Isolating Claims and Matching Explicit Evidence Slide 4 of 20
DAY 12 TSIA2 Math Prep
Physics & Energy
According to physical laws, the net force \( F \) applied to an object varies directly with its acceleration \( a \).
If a net force of 15 Newtons (N) causes an acceleration of 3 \(\text{m/s}^2\), what net force in Newtons is required to cause an acceleration of 8 \(\text{m/s}^2\)?
A 24 N
B 30 N
C 40 N
D 120 N
TSIA2 Diagnostic Standard: Quantitative Reasoning Slide 5 of 20
DAY 12 Answer & Explanation
C
40 Newtons
Using variation constant k=5
"Varies directly" means \( F = ka \). Find the value of constant \( k \) using the first set of numbers, then solve for the second.
1. Write the direct variation equation: \( F = ka \).
2. Substitute the first set of values (\( F = 15 \), \( a = 3 \)) to calculate \( k \):
\( 15 = k(3) \implies k = \frac{15}{3} = 5 \). (This constant \( k \) represents mass).
3. Use the calculated constant \( k = 5 \) with the new target acceleration \( a = 8 \):
\( F = 5(8) \).
4. Solve: \( F = \mathbf{40} \text{ N} \).
Key Skill: Formulating and Solving Direct Proportions Slide 6 of 20
DAY 12 TSIA2 ELAR Prep
Physics & Energy
Resolve the Dangling Modifier
"Observing light refraction through a glass prism, a brilliant rainbow of colors was seen by the student."
A Observing light refraction, the student saw a brilliant rainbow of colors.
B Observing light refraction, a brilliant rainbow was seen.
C A brilliant rainbow of colors was seen by the student observing light.
D By observing light refraction, a brilliant rainbow of colors was seen.
TSIA2 Writing Strand: Dangling Modifiers Slide 7 of 20
DAY 12 Answer & Explanation
A
Observing light refraction..., the student saw...
The opening modifier is "Observing light...". Since the "rainbow" cannot perform the action of observing, the subject immediately after the comma must be the student.
1. A dangling modifier is an introductory phrase that does not logically modify the subject that immediately follows it.
2. The phrase "Observing light..." is a participle phrase describing an action. Placing "a brilliant rainbow" right after means the rainbow was doing the observing, which is illogical.
3. Restructuring the sentence so that "the student" is the main subject (Option A) links the modifier to its correct, logical actor.
Key Skill: Aligning Introductory Participles with Logical Subjects Slide 8 of 20
DAY 13 TSIA2 Math Prep
Physics & Energy
A research drone takes off and flies exactly 12 meters due East from its landing pad, and then turns and flies exactly 5 meters due North.
What is the straight-line displacement in meters of the research drone from its original landing pad?
A 7 meters
B 13 meters
C 17 meters
D 60 meters
TSIA2 Diagnostic Standard: Geometric & Spatial Reasoning Slide 9 of 20
DAY 13 Answer & Explanation
B
13 meters
Pythagorean Triple: 5-12-13
The flight path creates a right angle between East and North directions. Apply the Pythagorean theorem: \( a^2 + b^2 = c^2 \).
1. Due East and due North are perpendicular paths, creating a right-angled triangle.
2. The legs of this right triangle are \( a = 12 \text{ m} \) and \( b = 5 \text{ m} \).
3. The hypotenuse \( c \) represents the straight-line displacement vector:
\( c^2 = a^2 + b^2 \implies c^2 = 12^2 + 5^2 \).
4. Compute the sums: \( c^2 = 144 + 25 = 169 \).
5. Take the square root of both sides:
\( c = \sqrt{169} = \mathbf{13} \text{ meters} \).
Key Skill: Applying Pythagorean Theorem in Coordinate Space Slide 10 of 20
DAY 13 TSIA2 ELAR Prep
Physics & Energy
Passage 1 (Solar Photovoltaic) "Solar panels represent the cleanest source of localized power, extracting energy from sunlight with zero moving parts. Although highly sustainable, their intermittent generation patterns require battery storage to provide power after sunset."
Passage 2 (Kinetic Wind) "Wind turbines extract kinetic energy from moving air currents, offering an incredibly high footprint efficiency. However, wind speeds are highly erratic, which forces utility grids to maintain fossil-fuel-powered standby plants."
A They require expensive battery arrays to function at all.
B Their power generation is inconsistent and dependent on natural patterns.
C They occupy too much physical land space compared to fossil-fuel plants.
D They produce harmful chemical waste during active generation.
TSIA2 Reading Strand: Informational Synthesis (Double Passage) Slide 11 of 20
DAY 13 Answer & Explanation
B
Their power generation is inconsistent and dependent on natural patterns.
Link the concepts of "intermittent" (from solar) and "erratic" (from wind) to find the shared synthesis conclusion.
1. Passage 1 explains that solar energy is "intermittent" (stopping and starting at intervals) due to sunset.
2. Passage 2 notes that wind energy is "erratic" (unpredictable) due to shifting weather speeds.
3. Synthesizing these details leads to the common point: both sources suffer from generation inconsistency based on natural factors (Option B).
Key Skill: Identifying Cross-Passage Synonyms & Parallel Themes Slide 12 of 20
DAY 14 TSIA2 Math Prep
Physics & Energy
An electric winch motor requires at least 120 Joules of energy per second to safely lift heavy physics laboratory equipment.
The motor consumes a base operating energy of 30 Joules per second when idling, plus an additional 15 Joules per second for every kilogram (\(w\)) of equipment lifted. Which inequality models the allowable weights?
A 15w + 30 \leq 120
B 15w + 30 \geq 120
C 30w + 15 \geq 120
D 15w \geq 120
TSIA2 Diagnostic Standard: Algebraic Reasoning Slide 13 of 20
DAY 14 Answer & Explanation
B
15w + 30 \geq 120
"At least" represents ≥
Translate the phrases systematically: "at least 120" indicates ≥ 120, and "15 Joules per kilogram \( w \) plus 30 base" translates to \( 15w + 30 \).
1. Formulate the consumption expression: The motor has a fixed base load of 30 Joules, and a variable rate of 15 Joules per kilogram \( w \).
\( \text{Total Consumed} = 15w + 30 \).
2. Map the requirement boundary: "at least" means the value can equal 120 or be greater than 120, but not less.
\( \text{Total Consumed} \ge 120 \).
3. Combine the expressions:
\( 15w + 30 \ge 120 \). (Option B).
Key Skill: Converting Text Constraints to Inequality Form Slide 14 of 20
DAY 14 TSIA2 ELAR Prep
Physics & Energy
Correcting Run-On Sentences
"Electromagnetism is one of the four fundamental forces of nature it governs the interactions between charged particles."
A forces of nature, it governs the interactions...
B forces of nature; it governs the interactions...
C forces of nature and governing the interactions...
D forces of nature, which governing the interactions...
TSIA2 Writing Strand: Correcting Run-On Sentences Slide 15 of 20
DAY 14 Answer & Explanation
B
forces of nature; it governs the interactions...
The sentence contains two independent clauses. Correcting them requires a period, a coordinating conjunction (FANBOYS), or a semicolon.
1. Clause 1 ("Electromagnetism is...") and Clause 2 ("it governs...") are both independent thoughts containing their own subjects and verbs.
2. Joining them with just a comma (Option A) creates a comma splice.
3. Placing a semicolon (Option B) perfectly connects these separate independent thoughts without causing grammatical errors.
Key Skill: Correcting Run-On Sentences using Punctuation Marks Slide 16 of 20
DAY 15 TSIA2 Math Prep
Physics & Energy
An engineering student plots the velocity of a test vehicle moving in a straight line.
At time \( t = 2 \text{ seconds} \), the velocity is \( 10 \text{ m/s} \). At time \( t = 6 \text{ seconds} \), the velocity is \( 34 \text{ m/s} \). What is the average acceleration (slope of velocity over time) in \(\text{m/s}^2\)?
A 4 \(\text{m/s}^2\)
B 6 \(\text{m/s}^2\)
C 8 \(\text{m/s}^2\)
D 12 \(\text{m/s}^2\)
TSIA2 Diagnostic Standard: Probabilistic & Statistical Reasoning Slide 17 of 20
DAY 15 Answer & Explanation
B
6 \(\text{m/s}^2\)
Rate of change (Slope)
Acceleration is calculated as change in velocity divided by change in time: \( a = \frac{v_2 - v_1}{t_2 - t_1} \).
1. Form coordinates from the prompt text:
- Point 1: \( (t_1, v_1) = (2, 10) \)
- Point 2: \( (t_2, v_2) = (6, 34) \).
2. Apply the linear slope equation:
\( \text{Slope } (m) = \frac{y_2 - y_1}{x_2 - x_1} \implies a = \frac{v_2 - v_1}{t_2 - t_1} \).
3. Substitute coordinates:
\( a = \frac{34 - 10}{6 - 2} \).
4. Solve the fraction:
\( a = \frac{24}{4} = \mathbf{6} \text{ m/s}^2 \). (Option B).
Key Skill: Calculating Linear Slopes from Word Problem Data Slide 18 of 20
DAY 15 TSIA2 ELAR Prep
Physics & Energy
Reading Passage
"In 1964, Arno Penzias and Robert Wilson detected a persistent, low-frequency hum using a highly sensitive antenna. After meticulously cleaning the telescope and eliminating all localized interference, they realized they had stumbled upon the Cosmic Microwave Background radiation—the thermal echo of the Big Bang. This serendipitous discovery revolutionized astrophysics, turning the theoretical Big Bang model into the dominant scientific paradigm."
A To detail the mechanical construction of early antennas.
B To explain how Penzias and Wilson eliminated antenna static.
C To describe the accidental discovery of the CMB and its impact.
D To argue that theoretical models are superior to laboratory observations.
TSIA2 Reading Strand: Determining Author's Main Purpose Slide 19 of 20
DAY 15 Answer & Explanation
C
To describe the accidental discovery of the CMB and its impact.
The passage contains terms such as "serendipitous discovery" and explains how it "revolutionized astrophysics". This signals both the accidental nature and historical significance.
1. Option A and B represent narrow, supporting details of how the scientists made their observations. They do not summarize the central objective.
2. Option D suggests an argumentative stance that is completely absent from this historical, informative passage.
3. Option C perfectly encapsulates the full paragraph, noting the "serendipitous" (accidental) nature of detecting the CMB, and concluding with its profound impact on scientific modeling.
Key Skill: Discerning Primary Purpose from Narrow Supporting Details Slide 20 of 20
The text explicitly states: "Over 90% of the world’s earthquakes... occur along these boundaries". This directly maps to a high concentration along boundaries.
1. An inference is a conclusion that can be logically drawn from the explicit facts inside the passage.
2. The fact that 90% of all global earthquakes occur at plate boundaries logically leads to the conclusion that plate boundaries are the main concentration zones for seismic events (Option B).
3. Options A, C, and D are unsupported by the text; the text does not mention atmospheric pressure, earthquake intensity comparisons, or movement away from the Pacific basin.
Key Skill: Inferring Main Concepts from Numeric Percentages Slide 4 of 20
DAY 17 TSIA2 Math Prep
Earth & Space Prep
A geologist models the exponential decay of Uranium-235 in a continental granite sample. The amount of Uranium remaining in micrograms after \( d \) decay cycles is represented by:
\( U(d) = 80 \left( \frac{1}{2} \right)^d \)
What is the remaining amount of Uranium in micrograms after exactly 4 decay cycles?
A 5 micrograms
B 10 micrograms
C 20 micrograms
D 40 micrograms
TSIA2 Diagnostic Standard: Algebraic Reasoning Slide 5 of 20
DAY 17 Answer & Explanation
A
5 micrograms
U(4) = 80 × (1/16)
The variable represents decay cycles. Substitute \( d = 4 \). Remember that \( \left( \frac{1}{2} \right)^4 \) equals \( \frac{1}{16} \) and solve.
1. Write down the exponential decay model: \( U(d) = 80 \left( \frac{1}{2} \right)^d \).
2. Identify that \( d = 4 \).
3. Substitute \( d = 4 \) into the equation:
\( U(4) = 80 \left( \frac{1}{2} \right)^4 \).
4. Evaluate the exponent first:
\( \left( \frac{1}{2} \right)^4 = \frac{1^4}{2^4} = \frac{1}{16} \).
5. Multiply: \( U(4) = \frac{80}{16} = 5 \) micrograms. (Option A).
Key Skill: Evaluating Non-Linear Exponential Models Slide 6 of 20
DAY 17 TSIA2 ELAR Prep
Earth & Space Prep
Resolve Parallel Structure Errors
"Geologists classify rocks into three distinct families: igneous rocks, which form from cooling magma; metamorphic rocks, which change under extreme heat and pressure; and sedimentary rocks are formed by layers of compressed sediment."
A Change "which form from cooling magma" to "forming from cooling magma"
B Change "sedimentary rocks are formed" to "sedimentary rocks, which form"
C Change "under extreme heat" to "under heat that is extreme"
D Change "distinct families" to "different families"
TSIA2 Writing Strand: Parallel Structure in Series Slide 7 of 20
DAY 17 Answer & Explanation
B
Change "sedimentary rocks are formed" to "sedimentary rocks, which form"
In any series, listed elements must share the same grammatical form. Check items 1 and 2: both use a comma followed by a "which" clause. Item 3 must match!
1. Parallel structure requires items in a list to use identical syntactic structures.
2. Item 1: "igneous rocks, which form from..."
Item 2: "metamorphic rocks, which change under..."
3. The original third item is a full passive clause: "sedimentary rocks are formed by...". This violates the established "noun + relative clause" parallel structure.
4. Rewriting as "sedimentary rocks, which form..." (Option B) resolves the structural error perfectly.
Key Skill: Matching Relative Clauses across Complex Lists Slide 8 of 20
DAY 18 TSIA2 Math Prep
Earth & Space Prep
An astronomer models the Earth as a perfect sphere with a radius of exactly \( R = 6,400 \text{ kilometers} \).
What is the approximate circumference of the Earth at the equator in kilometers? (Use the approximation \( \pi \approx 3.14 \)).
A 20,096 km
B 40,192 km
C 128,614,400 km
D 512,000,000 km
TSIA2 Diagnostic Standard: Geometric & Spatial Reasoning Slide 9 of 20
DAY 18 Answer & Explanation
B
40,192 km
C = 2πR
The formula for circumference is \( C = 2\pi R \), not the area formula \( A = \pi R^2 \). Make sure you don't square the radius!
1. Write down the equatorial circumference equation:
\( C = 2\pi R \).
2. Substitute the given values: \( R = 6,400 \) and \( \pi \approx 3.14 \).
\( C = 2 \times 3.14 \times 6,400 \).
3. Multiply the factors:
\( C = 6.28 \times 6,400 \).
4. Solve the final product:
\( C = \mathbf{40,192} \text{ kilometers} \). (Option B).
Key Skill: Solving Spherical Perimeter (Circumference) Equations Slide 10 of 20
DAY 18 TSIA2 ELAR Prep
Earth & Space Prep
Reading Passage
"The greenhouse effect on Earth is essential for maintaining liquid water and biological life, warming the surface by a moderate 33°C. In contrast, Venus possesses an ultra-dense carbon dioxide atmosphere that traps massive amounts of solar radiation. This extreme runaway greenhouse effect heats the Venusian surface to a scorching 460°C, hot enough to melt lead."
A Earth's greenhouse effect is more extreme than Venus.
B The Venusian atmosphere is completely devoid of carbon dioxide.
C Atmospheric composition directly influences surface temperature.
D Venus would support biological life if its atmosphere became denser.
TSIA2 Reading Strand: Drawing Conclusions from Comparisons Slide 11 of 20
DAY 18 Answer & Explanation
C
Atmospheric composition directly influences surface temperature.
Note the contrast in atmosphere and heat: Earth has a moderate greenhouse effect (+33°C), while Venus has an "ultra-dense carbon dioxide atmosphere" with extreme runaway heating (+460°C).
1. The passage contrasts the atmospheric densities and gas types of Earth and Venus alongside their resulting temperatures.
2. This data supports the conclusion that the composition and density of the atmosphere directly impacts a planet's surface heat retention (Option C).
3. Option A is factually inverted; Option B directly contradicts the text ("ultra-dense carbon dioxide atmosphere"); Option D represents an unsupported speculation.
Key Skill: Synthesizing Cause-and-Effect across Contrasting Datapoints Slide 12 of 20
DAY 19 TSIA2 Math Prep
Earth & Space Prep
A seismologist records the Richter scale magnitudes of 7 recent tremors in an active seismic fault zone:
2.1, 4.3, 3.5, 5.2, 3.8, 4.6, 2.9
What is the median magnitude of these recorded earthquakes?
A 3.5 magnitude
B 3.8 magnitude
C 4.1 magnitude
D 4.3 magnitude
TSIA2 Diagnostic Standard: Probabilistic & Statistical Reasoning Slide 13 of 20
DAY 19 Answer & Explanation
B
3.8 magnitude
Middle value of ordered data
"Median" indicates the physical middle value in a dataset. You MUST first arrange the numbers in numerical order from smallest to largest!
1. Retrieve raw data: 2.1, 4.3, 3.5, 5.2, 3.8, 4.6, 2.9. (Count \( N = 7 \)).
2. Re-arrange raw numbers from smallest to largest:
2.1, 2.9, 3.5, 3.8, 4.3, 4.6, 5.2.
3. Since \( N = 7 \) is an odd number, the median is the exact middle term (the 4th value).
4. Identify the 4th term: 3.8. (Option B).
Key Skill: Ordering Datasets to Find Median Values Slide 14 of 20
DAY 19 TSIA2 ELAR Prep
Earth & Space Prep
Eliminate Wordiness & Redundancy
"In the present day and age of today, modern volcanologists can now predict volcanic eruptions by using advanced scientific measurements that are high-tech."
A Today, modern volcanologists can now predict eruptions using advanced scientific measurements.
B Modern volcanologists can predict eruptions using advanced measurements.
C Modern volcanologists can now currently predict eruptions by using high-tech, advanced measurements of science.
D In this day and age, volcanologists predict eruptions using advanced measurements.
TSIA2 Writing Strand: Eliminating Redundancy & Wordiness Slide 15 of 20
DAY 19 Answer & Explanation
B
Modern volcanologists can predict eruptions using advanced measurements.
"Volcanologists" are scientists, making "measurements of science" repetitive. "Modern" and "today" are redundant, as are "can" and "now".
1. The TSIA2 heavily tests conciseness. Writing should deliver the maximum amount of clarity with the minimum necessary words.
2. Option A is redundant: "Today" and "modern" and "now" all mean the same thing in this context.
3. Option B is clean, clear, and active, packing the entire meaning of the original 22-word sentence into just 9 words.
Key Skill: Trimming Over-written Prose to Active Declarative Clauses Slide 16 of 20
DAY 20 TSIA2 Math Prep
Earth & Space Prep
A space module can carry a maximum weight of 1,200 kg and a maximum volume of 10 m³.
Equipment crates (\(x\)) weigh 150 kg and occupy 1 m³. Survival crates (\(y\)) weigh 80 kg and occupy 2 m³. Which system represents these weight and volume boundaries?
A 150x + 80y \ge 1200 \\ x + 2y \ge 10
B 150x + 80y \leq 1200 \\ x + 2y \leq 10
C 80x + 150y \leq 1200 \\ 2x + y \leq 10
D 150x + 80y \leq 1200 \\ x + 2y \ge 10
TSIA2 Diagnostic Standard: Algebraic Reasoning Slide 17 of 20
DAY 20 Answer & Explanation
B
150x + 80y \leq 1200 \\ x + 2y \leq 10
"Maximum" represents ≤
The space module cannot exceed its boundaries. This makes the limit indicators "less than or equal to" (\(\le\)) for both weight and volume.
1. Form the weight inequality: Crate \( x \) is 150 kg and Crate \( y \) is 80 kg. Their total weight cannot exceed 1,200 kg:
\( 150x + 80y \leq 1,200 \).
2. Form the volume inequality: Crate \( x \) occupies 1 m³ and Crate \( y \) occupies 2 m³. Their total volume cannot exceed 10 m³:
\( 1x + 2y \leq 10 \implies x + 2y \leq 10 \).
3. Combining these bounds gives the system represented by Option B.
Key Skill: Writing Double Inequality Constrained Systems Slide 18 of 20
DAY 20 TSIA2 ELAR Prep
Earth & Space Prep
Reading Passage
"A stellar nebula is a colossal interstellar cloud of dust, hydrogen, and helium gas. Over millions of years, gravity pulls these elements closer together in pockets of increasing density until nuclear fusion ignites in the core, sparking the birth of a brand new luminous star."
A an exploding remnant of an old star
B a dense gravity well that traps light
C a massive interstellar cloud of dust and gas
D a nuclear reaction that creates helium
TSIA2 Reading Strand: Vocabulary in Context Slide 19 of 20
DAY 20 Answer & Explanation
C
a massive interstellar cloud of dust and gas
The sentence contains an explicit definition: "A stellar nebula is a colossal interstellar cloud of dust...". This appositive translates directly to the correct definition.
1. The text explicitly defines "nebula" in the very first sentence. "Colossal" means massive, and "interstellar cloud of dust, hydrogen, and helium gas" maps directly to Option C.
2. Identifying explicit appositive definitions is a core reading strategy for the TSIA2 reading section.
3. Option A describes a supernova remnant (different phase of stellar life), Option B describes a black hole, and Option D describes nuclear fusion. None match the explicit definition provided in the text.
Key Skill: Decoding Technical Vocabulary with Explicit Definitions Slide 20 of 20
