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Multiple choice practice test
1.
(60 p.)
Let \( A_0=(0,0) \). Points \( A_1 \), \( A_2 \), \( \dots \) lie on the \( x \) axis and points \( B_1 \), \( B_2 \), \( \dots \) lie on the graph of \( y=\sqrt x \). Assume that for each \( k \) the triangle \( A_{k1}B_kA_k \) is equilateral. Find the minimal \( n \) such that \( A_0A_n\geq 100 \).
A
13
B
15
C
17
D
19
E
21
N
2.
(2 p.)
A basketball player made five successful shots during a game. Each shot was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player?
A
2
B
3
C
4
D
5
E
6
N
3.
(10 p.)
Points \( C \) and \( D \) are on the same side of diameter \( AB \) of circle \( k \). Assume that \( \angle AOC=30^{\circ} \) and \( \angle DOB=45^{\circ} \). Let \( \alpha_1 \) denote the area of the smaller sector \( COD \) of the circle, and let \( \alpha \) denote the area of the entire circle. Calculate the ratio \( \frac{\alpha_1}{\alpha} \).
A
\( \frac29 \)
B
\( \frac14 \)
C
\( \frac5{18} \)
D
\( \frac7{24} \)
E
\( \frac3{10} \)
N
4.
(12 p.)
There are two kinds of flowers in a shop. Roses cost 3 dollars each while carnations cost 2 dollars each. How many different kinds of bouquets can be bought with exactly 50 dollars?
A
1
B
7
C
9
D
16
E
17
N
5.
(15 p.)
A postman has a pedometer to count his steps. The pedometer records up to 99999 steps, then flips over to 000000 on the next step. The postman plans to determine his mileage for a year. On January 1 the postman sets the pedometer to 00000. During the year, the pedometer flips from 99999 to 00000 fortyfour times. On December 31 the pedometer reads 50000. The postman takes 1800 steps per mile. Which of the following is closest to the number of miles the postman has walked over the year?
A
2500
B
3000
C
3500
D
4000
E
4500
N
20052018
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