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Quiz: Science, Math, and Ideas

Test your understanding of Chapter 16. Choose the best answer, then click Show Answer to check.

Question 1

Who wrote the Brahmasphutasiddhanta in 628 CE, the first known text to give rules for zero as a number?

  1. Aryabhata
  2. Brahmagupta
  3. Al-Biruni
  4. Madhava of Sangamagrama
Show Answer

The correct answer is B. Brahmagupta wrote the Brahmasphutasiddhanta at Bhillamala in 628 CE. Aryabhata is a common wrong guess, but he lived earlier (476 to 550 CE) and is best known for the Aryabhatiya and his value of pi.

Concept Tested: Brahmagupta Bloom's Level: Remember

Question 2

The word "chaturanga," the name of the ancestor of chess, refers to which of these?

  1. The four seasons of the year
  2. The four directions on a compass
  3. The four corners of the board
  4. The four divisions of an old Indian army
Show Answer

The correct answer is D. Chaturanga means "four limbs," the elephants, chariots, cavalry and infantry of an old Indian army. The game was played on an 8-by-8 board, but the name is about the army, not the board's corners.

Concept Tested: Chaturanga Bloom's Level: Remember

Question 3

Panini, author of a famous grammar of Sanskrit, came from a town near Attock on the Indus River. In which present-day country is that?

  1. Pakistan
  2. Nepal
  3. Bangladesh
  4. Sri Lanka
Show Answer

The correct answer is A. Panini came from Shalatula, near Attock on the Indus, in present-day Pakistan. Many people assume all early Sanskrit scholars lived in today's India, but the Indus region was a major center of learning.

Concept Tested: Panini's Grammar Bloom's Level: Remember

Question 4

Why did the place value system need a symbol for zero, while Roman numerals did not?

  1. Roman numerals were only used for small numbers, so zero never came up.
  2. Place value uses fewer symbols, so it needed an extra one to reach ten.
  3. In place value a digit's worth depends on its position, so an empty position must be marked; Roman letters keep their value wherever they sit.
  4. The Romans had a zero symbol but chose not to write it on clocks.
Show Answer

The correct answer is C. In 507, the 0 keeps the 5 in the hundreds place; without it the number would read 57. Roman numerals add up fixed-value letters (DVII), so there is no empty position to hold. Option A is wrong because Romans wrote large numbers too, using letters like M and D.

Concept Tested: Place Value System Bloom's Level: Understand

Question 5

Why do historians use the name "Hindu-Arabic numerals" instead of "Arabic numerals"?

  1. Because the digits were invented in Arabia and later adopted in India
  2. Because the system began in South Asia and was developed and passed to Europe by scholars writing in Arabic
  3. Because Hindu and Muslim mathematicians invented the digits together on the same day
  4. Because the digits are only used in India and the Arab world today
Show Answer

The correct answer is B. The digits and place value began in South Asia, and scholars such as al-Khwarizmi spread them through the Arabic-speaking world to Europe. Option A reverses the direction of travel, which is the very mistake the double name is meant to correct.

Concept Tested: Hindu-Arabic Numerals Bloom's Level: Understand

Question 6

What is the best description of how the Kerala School's infinite series relate to European mathematics?

  1. Madhava found series for pi, sine and cosine centuries before European mathematicians rediscovered them independently.
  2. Madhava's notebooks were carried to England, where Newton copied them.
  3. The Kerala School invented the complete system of calculus, including derivatives and integrals.
  4. European mathematicians found the series first, and Kerala scholars learned them from traders.
Show Answer

The correct answer is A. Madhava (about 1350 to 1425) found these series, and Gregory and Newton found them again in the 1600s. Option B is a popular claim, but there is no solid evidence that the Kerala results reached Europe, so historians call the European work a rediscovery.

Concept Tested: Kerala School Bloom's Level: Analyze

Question 7

Why are Ayurveda, Unani medicine and yoga described in this chapter as "traditions" rather than proven treatments?

  1. Because they are no longer practiced anywhere
  2. Because they come from religious texts, and science cannot study them
  3. Because they were banned by governments in South Asia
  4. Because few well-designed studies support their health claims, and some products have even been unsafe
Show Answer

The correct answer is D. The US National Center for Complementary and Integrative Health reports limited scientific evidence for most Ayurvedic treatments and warns that some products contain lead, mercury or arsenic. Option A is wrong: these traditions are widely practiced today, and Unani is officially recognized in India and Pakistan. This is not medical advice.

Concept Tested: Ayurveda Bloom's Level: Understand

Question 8

Using the Zero and Place Value MicroSim, Ben builds the number 3,008 and ticks "Hide the zeros." What number does it appear to become?

  1. 308
  2. 3,800
  3. 38
  4. 3,008 (nothing changes)
Show Answer

The correct answer is C. Removing both zero symbols squeezes the 3 and the 8 together, so 3,008 looks like 38. Option A only removes one of the two zeros; both the hundreds and tens places are empty.

Concept Tested: Zero Bloom's Level: Apply

Question 9

Zara's Nanu writes a number on a recipe card in Bangla digits: ২০৫. Using what you learned about Bengali digits and place value, what number is it?

  1. 205
  2. 25
  3. 250
  4. 502
Show Answer

The correct answer is A. ২ is 2, ০ is 0 and ৫ is 5, and they are read left to right in the hundreds, tens and ones places, just like our digits. Option B forgets that the zero is holding the empty tens place.

Concept Tested: Brahmi Numerals Bloom's Level: Apply

Question 10

In 2017 the Bodleian Library announced that the Bakhshali manuscript might date to the 3rd or 4th century CE. In 2024, new radiocarbon results dated the tested leaves to roughly the late 700s to early 1000s CE. What is the best conclusion?

  1. Radiocarbon dating is useless, so the manuscript's age can never be known.
  2. Testing and re-testing corrected an early claim, which is how good science and history are supposed to work.
  3. The 2024 results prove that zero was invented in Europe.
  4. The manuscript must be a modern fake.
Show Answer

The correct answer is B. Experts questioned the 2017 result, the lab tested more leaves, and the date was revised. Option A goes too far: the method worked when applied carefully. The manuscript is still a genuine early text; it just isn't older than the Gwalior inscription of 876 CE.

Concept Tested: Zero Bloom's Level: Analyze