Level 1
How many squares are in the following figure?
(See google doc)
(A) 16 (B) 17 (C) 29 (D) 30 (E) 31
(D) 30
If square ABCD has the same area as a circle of radius 4, what is the length of line segment AC? (A) 8pi (B) 4√2pi (C) 8√pi (D) √8pi (E) None
(B) 4√2pi
A circle with an area of 17pi has a sector with a central angle of 54 degrees. What is the exact area of the sector? (A) 27pi/17 (B) 17pi/7 (C) 34pi/13 (D) 13pi/20 (E) None
(E) None
Which of these has the closest value to 4√ 573?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7
(C) 5
The pages of a book are numbered consecutively, starting with page 1. It takes 258 digits to number all of the pages. What is the last page number? (A) 122 (B) 104 (C) 108 (D) 116 (E) None
I kept getting 123, probably wrong, so it's either(A) 122 or (E) None
Given the equation of a circle, x2+6x+y2−8y=11, find the distance between the center of the circle and the origin. (A) 25 (B) √ 5 (C) 6 (D) 5 (E) None
(D) 5
Which of the following describes the graph of the equation (x+y)2 = x2+y2 ? (A) two lines (B) a single point (C) the empty set (D) a circle (E) None
(A) two lines
Suppose 3 and 8 are the only individual scores that can be made in a certain game. Multiple turns are taken, and the scores from each turn are added to the sum. How many different scores are impossible for the person to obtain?
(A) 8 (B) 26 (C) 108 (D) Infinity (E) None
(B) 26
Recently, the WCU Math Club hosted a huge Pi Day Celebration at which anyone could come and enjoy a free slice of pie. The choices were apple pie, pecan pie or chocolate cream pie. They ordered an equal number of pecan and chocolate cream pies. They ordered 2 more apple pies than they did pecan pies. The total number of pies ordered was 17. Apple pies cost 9 dollars each while the other pies cost 8 dollars each. What was the total amount spent on pie by the Math Club? (A) $152 (B) $144 (C) $138 (D) $143 (E) None
(D) $143
The right triangle ABC has sides of the following lengths: AB=24, BC=7, AC=25
Let there exist a point D so that D is the midpoint of AB. What is the length of CD? (A) √139 (B) √193 (C) 12 (D) 16 (E) None
(B) √193
Alex has 12 coins in his pocket (a combination of nickels and dimes), worth a combined $0.80. Jack has 15 coins (another combination of nickels and dimes), worth a combined $1.15. If Tom has twice as many nickels as Alex, and half as many dimes as Jack, how much money is in his pocket? (A) $1.20 (B) $1.05 (C) $1.35 (D) $1.10 (E) None
(A) $1.20
The prime factorization of 36,000 is 253253. How many distinct integer divisors does 36,000 have?
(Hint: Jake talked about this last week, if you were paying attention!)
(A) 18 (B) 30 (C) 56 (D) 72 (E) None
(D) 72
One of Thom and Tom always lies on Tuesdays, Wednesdays and Thursdays, and always tells the truth on the other days of the week. The other always lies on Fridays, Saturdays and Sundays, and always tells the truth the other days of the week. At noon, the two had the following conversation:
Thom: I lie on Sundays.
Tom: I will lie tomorrow.
Thom: I lie on Mondays.
This conversation takes place on a (A) Monday (B) Tuesday (C) Wednesday (D) Thursday (E) Friday
(D) Thursday
Find the equation of the line that connects the vertex of the parabola y=x2−4x+8 with the center of the circle (x−5)2+(y+3)2=4. (A) y=4/3x + 32/3 (B) y=−1/2x − 13/2 (C) y=−7/3x + 26/3 (D) y=5/2x + 23/4 (E) None
(C) y=-7/3x + 26/3
A ball of putty is rolled into a perfect sphere, and then sliced into equal hemispheres, each of which has surface area measuring A square units, and volume measuring A cubic units. Find the radius of the original ball. (A) 2 units (B) 3 units (C) 4 units (D) 5 units (E) None
(E) None
Which of the following is equivalent to (1/√2+i/√2)46?
(A) -i (B) i/2 (C) -1/2 (D) 1/√2-i/√2 (E) None
(A) -i
How many integral values of x satisfy the inequality: x−4 ≤ 5x+3 ≤ x+30? (A) 5 (B) 6 (C) 7 (D) 8 (E) 9
(D) 8
For what value of k will the system of equations:
2x−3y=−4
−3x+ky=6
have an infinite number of solutions? (A) 9/2 (B) 2 (C) 4/3 (D) 1 (E) None
(A) 9/2
The cities of Robbinsville and Hickory are 160 miles apart. Car A leaves Robbinsville at 12:00pm driving toward Hickory at 45 mph. Car B leaves Hickory at 12:30pm driving along the same road toward Robbinsville at 60 mph. Both cars stop for lunch at 1:00 pm, with Car A back on the road at 1:15pm and Car B back on the road at 1:35pm, again driving 45 mph and 60 mph respectively. At what time do they meet? (A) 2:00pm (B) 2:05pm (C) 2:10pm (D) 2:15pm (E) None
(D) 2:15pm
How many times does f(x) = 3 sin(1/x) cross the x-axis in the interval [0.1,1]?
(A) 95 (B) 0 (C) 63 (D) 31 (E) None
(D) 31