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# M101-201330-practice2Exam

Department
Mathematics
Course Code
MATH101
Professor
All
Study Guide
Midterm

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Math 101 Practice Final Exam #2
1. Determine the third entry of the progression with ﬁrst entry 12 and second
entry 9 if the progression is...
(a) an arithmetic progression. (b) a geometric progression.
2. Determine the last digit of the number 912345?
3. If a meal consisting of steak, salad and potatoes costs \$30 where the steak
costs \$5 more than the potatoes and the potatoes cost twice as much as the
salad, then how much did each part of the meal cost?
4. Convert the number 20123into base-10.
5. Convert the number 364510 into Roman numerals.
6. Evaluate: (a)11010012+ 1011102; (b) 76585678; (c) 5A16 ×3116
7. Find all xsatisfying the following equations.
(a) 5x+ 4 = 6 mod 8
(b) 2x2= 4 mod 9
(c) 4x2= 0 mod 11
(d) x2+ 2x+ 1 = 0 mod 8
8. December 1, 2013 is a Sunday.
(a) What day of the week is December 1, 2153?
(b) What day of the week is December 1, 1953?
9. Find all Nbetween 0 and 1200 satisfying:
N2 mod 11
N3 mod 13
N4 mod 15
10. (a) Find the prime factorization of 8250 and 7700.
(b) How many divisors does 8250 have (i.e., what is d(8250))?
(c) What is gcd(8250,7700) and lcm(8250,7700)? You do not need to sim-
plify the prime factorization.
11. Use the Euclidean Algorithm, to calculate gcd(3964,5428).
12. If 2 chickens can lay 4 eggs in 6 days, then how many eggs will 8 chicken lay
in 12 days.