Sum = 4 or 10 3 ways each (\(\frac{1}{12}\))
Sum = 9 Pairs: \((3,6), (4,5), (5,4), (6,3) \rightarrow \frac{4}{36} = \mathbf{\frac{1}{9}}\).
• Total Pairings: \(\text{Size}(A) \times \text{Size}(B)\). (e.g., \(4 \times 5 = 20\) pairs).
• Negative Product Rule: Requires opposite signs:
• \((\text{Negative from A}) \times (\text{Positive from B})\)
• \((\text{Positive from A}) \times (\text{Negative from B})\)
• Positive Product Rule: Same signs: \((+) \times (+)\) OR \((-) \times (-)\).
• Zero Alert: \(0 \times \text{anything} = 0\). Zero is NOT negative and NOT positive. Never count zero pairs as favorable for signed products!
8. Mean & Probability Hybrid
To find \(P(\text{Random item } < \text{Mean})\):
1. Sum the list and divide by \(n\) to get exact Mean.
2. Count items strictly smaller than the Mean.
3. Divide count by \(n\). Convert fraction to decimal.
Top 3 TSIA2 Test-Day Speed Hacks Save 2+ Minutes Per Question
• Calculate Sums First: Don't set up complex fractional equations. Always multiply average by \(n\) right away.
• Order Before Median: TSIA2 lists are deliberately scrambled. Never pick the middle number without sorting first.
• Watch for Zero: When picking from sets with negative and positive numbers, remember \(0\) eliminates sign!
TSIA2 Mathematics Review • Companion Cheat Sheet Quick Reference Card
• Economy of Language: TSIA2 strictly penalizes redundancy. Eliminate words that repeat meaning (e.g., annual yearly \(\rightarrow\) annual; past history \(\rightarrow\) history).
TSIA2 ELAR Preparation • Sentence Revision & Editing Page 1 of 5
Section 1 • Sentence Boundaries & Punctuation
Name:
Date:
1. The severe winter storm knocked down power lines across the entire coastal region, consequently, emergency repair crews worked through the freezing night to restore electricity.
Select the best version of the underlined text:
A. region, consequently, emergency
B. region; consequently, emergency
C. region consequently emergency
D. region, and consequently emergency
2. Although the archaeological research team uncovered several ornate ceramic vessels and intact stone tools during their extensive excavation of the ancient settlement site.
Which revision best corrects the sentence fragment above?
A. Leave the sentence as it is written.
B. Although uncovering several ornate ceramic vessels and stone tools during excavation of the site.
C. Although the team uncovered ornate ceramic vessels and stone tools during the excavation, they could not determine the exact age of the settlement.
D. The team uncovered ornate ceramic vessels and stone tools; which provided new evidence.
3. The regional architectural firm specializes in three distinct styles of commercial design: modern industrial, sustainable green construction, and classical revival.
Select the best version of the underlined text:
A. design: modern industrial, sustainable green construction,
B. design; modern industrial, sustainable green construction,
C. design, which include: modern industrial, green construction,
D. design such as: modern industrial, sustainable construction,
4. The university opened an advanced artificial intelligence laboratory last fall enrollment in upper-level computer science courses surged by more than thirty-five percent.
Which option best repairs the run-on sentence?
A. fall enrollment in upper-level computer science courses surged
B. fall, enrollment in upper-level computer science courses surged
C. fall, and enrollment in upper-level computer science courses surged
D. fall but enrollment in upper-level computer science courses surged
5. The two clinical researchers published they're findings in an oncology journal, documenting the experimental vaccines impact on cell regeneration.
Select the version that correctly handles possessives and pronouns:
A. they're findings in an oncology journal, documenting the experimental vaccines
B. their findings in an oncology journal, documenting the experimental vaccine's
C. their findings in an oncology journal, documenting the experimental vaccines's
D. there findings in an oncology journal, documenting the experimental vaccine's
TSIA2 ELAR Preparation • Practice Part 1 Page 2 of 5
Section 2 • Agreement, Modifiers & Parallelism
Name:
Date:
6. The museum's acquisition of medieval illuminated manuscripts, bronze sculptures, and silver chalices were made possible by a generous endowment from a local foundation.
Select the correct verb phrase for subject-verb agreement:
A. were made possible by
B. was made possible by
C. have been made possible by
D. are being made possible by
7. Having thoroughly analyzed the quarterly revenue reports, several critical calculation errors were discovered by the senior forensic auditor before the tax audit commenced.
Which revision eliminates the dangling modifier?
A. several critical calculation errors were discovered by the senior forensic auditor
B. the senior forensic auditor discovered several critical calculation errors
C. the discovery of several critical calculation errors was made by the senior auditor
D. it became clear to the senior auditor that several calculation errors existed
8. Each of the forensic investigators must submit their final laboratory report to the presiding judge before the criminal trial opens next Monday.
Select the option that maintains formal standard pronoun-antecedent agreement:
A. must submit their final laboratory report to the presiding judge
B. must submit his or her final laboratory report to the presiding judge
C. have to submit their final laboratory report to the presiding judge
D. are required to submit their final laboratory report to the presiding judge
9. During her corporate legal internship, Maya was responsible for drafting trial briefs, conducting background interviews, and to summarize sworn deposition transcripts for senior partners.
Select the phrasing that maintains parallel structure:
A. to summarize sworn deposition transcripts
B. summarizing sworn deposition transcripts
C. she summarized sworn deposition transcripts
D. the summary of sworn deposition transcripts
10. The thermal insulation rating of modern fiberglass batting is significantly higher than traditional loose cellulose insulation.
Which option corrects the faulty comparison?
A. higher than traditional loose cellulose insulation.
B. higher than that of traditional loose cellulose insulation.
C. higher compared to traditional loose cellulose insulation.
D. higher than those of traditional loose cellulose insulation.
TSIA2 ELAR Preparation • Practice Part 2 Page 3 of 5
Section 3 • Sentence Completion & Conciseness
Name:
Date:
11. Solar energy production across the state has increased by over two hundred percent during the past decade. __________, battery storage technology remains a costly limiting factor during prolonged winter storms.
Which transitional word best completes the logical flow between the two sentences?
A. Furthermore
B. Consequently
C. However
D. Similarly
12. The metropolitan civic theater will hold an annual yearly audition each year in the month of September to select amateur actors for its holiday musical production.
Select the revision that expresses the idea most concisely and effectively without redundancy:
A. an annual yearly audition each year in the month of September
B. an annual audition in September
C. a yearly annual audition in the month of September
D. an audition held annually every year during September
13. The university board of regents voted unanimously to expand the merit grant program, emphasizing that financial resources should be accessible __________ every hardworking undergraduate applicant.
Select the correct idiomatic preposition to complete the sentence:
A. for
B. to
C. with
D. toward
14. The state conservation initiative aims not only to restore degraded coastal wetlands and also promoting sustainable ecotourism throughout the wildlife corridor.
Select the phrasing that correctly completes the correlative conjunction pair:
A. and also promoting sustainable ecotourism
B. but also to promote sustainable ecotourism
C. but it also aims at promoting sustainable ecotourism
D. as well as to promote sustainable ecotourism
15. __________ the municipal emergency agency deployed auxiliary flood barriers along the riverbank, numerous downtown storefronts suffered extensive water damage during the hurricane.
Which subordinating conjunction creates the most precise logical relationship?
A. Because
B. Even though
C. Since
D. When
TSIA2 ELAR Preparation • Practice Part 3 Page 4 of 5
Answer Explanations
100% TSIA2 Aligned
Boundaries & Punctuation
1. B: "Consequently" is a conjunctive adverb. Joining two independent clauses requires a semicolon before it and a comma after.
2. C: The original is a dependent fragment starting with "Although." Choice C attaches an independent clause to complete the thought.
3. A: A colon correctly follows the complete independent clause introducing the three styles. Semicolons and "such as:" are ungrammatical.
4. C: Joining two independent clauses requires comma + coordinating conjunction (FANBOYS: "and").
5. B: "Their" is possessive pronoun ("they're" = they are); "vaccine's" is singular possessive modifying "impact."
Grammar & Usage
6. B: The true subject is the singular noun "acquisition" (not the plural nouns in the prepositional phrase); requires singular "was made."
7. B: The auditor did the analyzing. The subject directly following the introductory phrase must be "the senior forensic auditor."
8. B: "Each" is formally a singular indefinite pronoun, requiring the singular pronoun phrase "his or her."
9. B: Parallel series of gerunds: "drafting...", "conducting...", and "summarizing...".
10. B: Compares the insulation rating to "that of" (the rating of) traditional cellulose, avoiding an illogical noun comparison.
Completion & Style
11. C: "However" establishes the contrast between production surge and battery storage limitations.
12. B: "An annual audition in September" eliminates the redundant repetitions of "yearly" and "each year."
13. B: Standard English idiom requires the adjective "accessible" to pair with preposition "to."
14. B: Correlative pair "not only [infinitive]... but also [infinitive]" ("to restore... to promote").
15. B: "Even though" expresses the concessive contrast between barrier deployment and storefront damage.
Quick Scoring Key
1: B
2: C
3: A
4: C
5: B
6: B
7: B
8: B
9: B
10: B
11: C
12: B
13: B
14: B
15: B
TSIA2 ELAR Preparation • Answer Key & Explanations Page 5 of 5
