Gateway Calculus Bowl 2019

1. Gateway Calculus Bowl 2019 Sample Problems 3 Gateway High School/Colorado Youth Education Connection, 2012

2. Problem 1 Which of the following statements are substantially true? • Many of the mathematical concepts of the early Greeks were discovered independently, often earlier, in China. A book by Chang Tshang (200-142 BC) gives methods of arithmetic (including cube roots) and algebra, uses the decimal system with zero and negative numbers, and proves the Pythagorean Theorem. • Decimal numbers (sometimes called “Arabic Numerals”) do not come from Arabia, but were invented by early Chinese and Hindu people around 200 BC. • In Europe, the decimal number system was not generally accepted until around 1600 AD. • 1 only • 2 only • 1 and 2 only • 2 and 3 only • All of the above.

3. Problem 2

4. Problem 3 y f ′ f ′′

5. Problem 4 d. e. 0

6. Problem 5

7. Problem 6

8. Problem 7

9. Problem 8

10. Problem 9

11. Problem 10

12. Problem11

13. Problem 12 If what is the constant A for which y satisfies the equation Ay’’+y’+y=0 ? • ½ (d) 2 • -1/2 (e) 3 • 1

14. Problem 13 y x

15. Problem 14

16. Problem 15

17. Problem 16

18. Problem 17

19. Problem 18 • Regarding the “Elementary Functions”, they are (best answer): • Functions built up from any number of exponentials, logarithms, complex constants, and the variable x, through composition and combinations using +-*/. • Functions built up from any finite number of exponentials and complex constants, and the variable x, through composition and combinations using +-*/. • Exponential, logarithmic, trigonometric functions and polynomials. • Exponential, logarithmic, trigonometric functions, polynomials, and rational functions thereof. • All of the above are incorrect because they don’t include the inverse trigonometric functions.

20. Tie Breaker