1. Sample Problems 3 Gateway Calculus Bowl 2019
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 ( 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. Problem 11

13. Problem 12 If Ay’’+y’+y=0 ? ½ (d) 2 -1/2 (e) 3 1
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