SAT Rhetorical Synthesis Practice — Drill 7

The student wants to describe which group of children benefited most from the helmet program. Which choice most effectively uses relevant information from the notes to accomplish this goal?

1. A A city introduced free bike-helmet giveaways at elementary schools beginning in 2018.
2. B The bike-helmet program did not include any component addressing helmet use among teenagers.
3. C Helmet use among surveyed children rose from 34% to 71% within a year of the program's start.
4. D The increase in helmet use was largest among children from lower-income households, who had previously been least likely to own a helmet.

The student wants to explain the basic logical structure of a proof by contradiction. Which choice most effectively uses relevant information from the notes to accomplish this goal?

1. A The concept of a mathematical proof by contradiction was used by ancient Greek mathematicians.
2. B Some modern mathematicians have debated whether the method is equally rigorous as direct proof.
3. C Proof by contradiction remains widely used and accepted throughout most of mathematics today.
4. D A proof by contradiction assumes the opposite of what one wants to prove, then shows that this assumption leads to a logical impossibility.

The student wants to distinguish the early Chinese use of negative numbers from their reception in Europe. Which choice most effectively uses relevant information from the notes to accomplish this goal?

1. A Rafael Bombelli worked out consistent rules for negative numbers in the 16th century.
2. B Negative numbers were used for bookkeeping purposes by Chinese mathematicians as early as the Han dynasty.
3. C While Chinese mathematicians used negative numbers practically as early as the Han dynasty, European mathematicians largely rejected them as meaningless until the 17th century.
4. D Full acceptance of negative numbers in Europe did not occur until the 1800s.

The student wants to distinguish Brahmagupta's treatment of zero from its earlier uses. Which choice most effectively uses relevant information from the notes to accomplish this goal?

1. A Brahmagupta's work on zero was later transmitted to the Islamic world and eventually to Europe.
2. B While earlier cultures used zero only as a placeholder, Brahmagupta, in the 7th century CE, treated it as a number in its own right, defining rules for using it in arithmetic.
3. C The number zero as a placeholder was used by both ancient Babylonian and Mayan mathematicians.
4. D Indian mathematicians made numerous contributions to the field of mathematics over many centuries.

The student wants to distinguish Cantor's treatment of infinity from the earlier Greek approach. Which choice most effectively uses relevant information from the notes to accomplish this goal?

1. A Cantor showed that some infinite sets are larger than others, a result many found counterintuitive.
2. B Cantor's work initially faced strong resistance from several prominent mathematicians of his time.
3. C The concept of infinity was treated with suspicion by many ancient Greek mathematicians.
4. D While ancient Greek mathematicians largely avoided the concept of infinity, Cantor developed a rigorous framework for comparing different sizes of infinite sets.

The student wants to explain why students continue cramming despite evidence that spaced study is more effective. Which choice most effectively uses relevant information from the notes to accomplish this goal?

1. A This effect has been replicated across many types of material, from vocabulary words to scientific concepts.
2. B Surveys show that most students report cramming before exams rather than spacing out their study.
3. C The spacing effect refers to the finding that spread-out study sessions improve long-term retention.
4. D Researchers attribute the persistence of cramming partly to the fact that it feels more effective in the short term, even though it produces worse long-term retention.

The student wants to explain why students continue re-reading despite evidence that self-testing is more effective. Which choice most effectively uses relevant information from the notes to accomplish this goal?

1. A Researchers attribute the persistence of re-reading partly to the fact that it feels more effective in the moment, even though it produces worse long-term retention.
2. B Surveys show that most students report re-reading notes as their primary study method.
3. C This effect has been replicated across many types of material, from foreign vocabulary to historical dates.
4. D The testing effect refers to the finding that active recall improves long-term retention more than passive re-reading.

The student wants to explain the connection between Fibonacci numbers and patterns observed in nature. Which choice most effectively uses relevant information from the notes to accomplish this goal?

1. A Fibonacci numbers form a sequence in which each number is the sum of the two preceding numbers.
2. B As ratios between consecutive Fibonacci numbers approach the golden ratio, this same ratio has been observed in natural growth patterns like leaf arrangement and shell spirals.
3. C The sequence was first introduced to Western mathematics by Leonardo of Pisa in the 13th century.
4. D Similar sequences to the Fibonacci sequence appear earlier in Indian mathematics.

The student wants to explain why the base-60 system's influence persists in modern timekeeping despite base-10 being more common overall. Which choice most effectively uses relevant information from the notes to accomplish this goal?

1. A Base-10 systems likely originated from the practice of counting on ten fingers.
2. B Some computer scientists use base-2 systems because they align naturally with electronic on/off switches.
3. C Although most modern mathematics uses a base-10 system, the ancient Babylonian base-60 system's influence persists in how we divide hours into 60 minutes and circles into 360 degrees.
4. D Ancient Babylonian mathematicians used a base-60 number system for astronomical calculations as early as 2000 BCE.