March Regional Algebra 2 Individual Test
For all problems below, NOTA means “None Of The Above.”
1. The arithmetic mean (AM) of a set of 50 numbers is 32. The AM of a second set of 70 numbers is 53. Find the AM of all the numbers in both of the sets combined.
a) 44 b) 44.25 c) 44.5 d) 45 e) NOTA
2. Let Let be the simplified expression obtained by replacing in by . Let be the simplified expression obtained by replacing in by , and so forth. Find .
a) b) c) d) e) NOTA
3. The sum of 2 numbers, and with is 36. When is divided by 4 and is divided by 5, the sum of the quotients is 8. Find the numbers and
a) =16 & =20 b) =20 & =16 c) =26 & =10 d) No solution e) NOTA
4. On a fence are sparrows and pigeons. When 5 sparrows leave, there are 2 pigeons for every sparrow remaining. Then 25 pigeons leave, and now there are 3 sparrows remaining for every pigeon. Find the original number of sparrows.
a) 20 b) 25 c) 30 d) 35 e) NOTA
5. If = , then express in terms of .
a) f (x-1) +1 b) c) d) e) NOTA
6. If is true for all permissible values of then find the value of A + B.
a) 2 b) 3 c) 4 d) 5 e) NOTA
7. The perimeter of a sector of a circle is 12. Find the radius of that circle so that the area of the sector is a maximum.
a) 2 b) 3 c) 4 d) 6 e) NOTA
8. The sum of the squares of the first 20 positive integers is 2870. What is the sum of the squares of the first 19 positive integers?
a) 2350 b) 2361 c) 2470 d) 2850 e) NOTA
March Regional Algebra 2 Individual Test—p2
9. My dog was 100m from home and my cat was 80m from home. I called them, and they both ran directly home. If my dog ran twice as fast as my cat, how far from home was my cat when my dog reached home (in meters)?
a) 20m b) 30m c) 40m d) 50m e) NOTA
10. The capacity of an auditorium is 600. For a performance, with the auditorium not filled to capacity, the receipts were $330.00. Admission prices were $0.75 for adults and $0.25 for kids. If represents the number of adults at the performance, find the minimum value of .
a) 360 b) 361 c) 362 d) 363 e) NOTA
11. A watch is stopped for 15 minutes every hour on the hour. According to this watch, how many hours (in actual time) elapse during the interval the watch first displays 12 noon until the watch first displays 12 midnight?”
a) 13 b) 13.5 c) 14 d) 14.5 e) NOTA
12. An airplane flies round trip a distance of L miles each way. The velocity against a head wind is 160 mph, while the velocity with a tail wind is 240 mph. What is the average speed for the round trip?
a) 190 mph b) 192 mph c) 196 mph d) 200 mph e) NOTA
13. Simplify:
a) b) c) d) e) NOTA
14. For the equation one root is -5. Find the other root.
a) Cannot be determined b) 1 c) 2 d) 5 e) NOTA
15. Find for the parabola if the vertex of this parabola is (2, 4).
a) b) c) d) e) NOTA
March Regional Algebra 2 Individual Test—p3
16. When a marble rolls down an incline, its speed varies directly as the square root of the distance it has rolled. When it has rolled a quarter of the distance down the incline, its speed is 60 in/sec. What is the speed (in inches/sec) of the marble at the bottom of the incline?
a) 60 b) 90 c) 120 d) 150 e) NOTA
17. The first four terms of a series are 2, 5, 10 and 17. If the series is continued in the same way, then find the square root of the sum of the arithmetic and geometric means between the first and seventh terms.
a) 6 b) 7 c) 8 d) 9 e) NOTA
