* I will post* seven new problems every weekend, one for each day of the week. The idea is that you work on your own during the week and I will post answers the following Saturday. For those of you who practiced with me last year, the process is similar.

* For instructions* on submitting weekly answers, click on the “Logistics” tab.

*posted problems, click on the “Archive” tab.*

**For previously****, click on the “News” tab.**

*For previous prizes*Week of Dec 9 – Dec 15, From the 2019 Mathcounts School Handboook.

Click GoogleForm to submit answers by Sat, Dec 15.

Dec 9: What is the probability that a sequence of five flips of a fair coin will not land heads up twice in a row? Express your answer as a common fraction.

Dec 10: Liz, Eva and Ace have played trivia as a team 33 times and won 24 times. What is the minimum number of games they must win to have an overall winning percentage of 80%?

Dec 11: A certain vending machine accepts nickels, dimes, quarters and dollar bills, and it provides change using nickels, dimes and quarters. If Sarah selects a healthful snack priced at $1.30 after inserting $2.00, in how many ways can the vending machine provide Sarah’s change?

Dec 12: What is the geometric mean of the median and mode of the set {23, 25, 3, 25, 20, 22, 21, 2, 1, 14, 12}? Express your answer in simplest radical form.

Dec 13: What is the mean of all three-digit positive integers whose digits are in the set {2, 0, 1, 9}?

Dec 14: If we define the binary operation as a b = ab + b for all numbers a and b, what positive value of x satisfies the equation x (4 x) = 550?

Dec 15: A circle with center P is inscribed in isosceles triangle ABC with apex angle A measuring 34 degrees. What is the degree measure of angle APC? Express your answer as a decimal to the nearest tenth.

Week of Dec 2 – Dec 8, * Transformations *(from the 2019 Mathcounts School Handboook)

Click GoogleForm to submit answers by Sat, Dec 8.

Dec 2: A point P(−3, 2) is translated right 4 units to its image P′. The point P′ is then translated up 3 units to its image P″. What is the distance from P to P″?

Answer: 5

Dec 3: A segment has endpoints A(0, 0) and B(−3, 4). Point C is the image of point B translated down 4 units and left 3 units. What is the perimeter of triangle ABC?

Answer: 16

Dec 4: A point Q(−3, 4) is reflected across the x-axis, and then the image Q′ is reflected across the line x = 2. What are the coordinates of the image Q″? Express your answer as an ordered pair.

Answer: (7,-4)

Dec 5: A point S(1, 6) is reflected across the line x − 2y = −6. What is the sum of the

coordinates of the image S′?

Answer: S'(3, 2). Sum of coordinates is 5.

Dec 6: What are the coordinates of the image of point D(−5, −3) when it is rotated 90 degrees clockwise about the origin? Express your answer as an ordered pair.

Answer: (-3, 5)

Dec 7: What are the coordinates of the image of the point E(3, −1) when it is rotated 90 degrees counterclockwise about the point F(5, 4)? Express your answer as an ordered pair.

Answer: (10,2)

Dec 8: A segment with endpoints G(−2, 3) and H(4, 7) is dilated by a scale factor of 2/3 with center of dilation (0, 0). What is the sum of all the coordinates of G′ and H′?

Answer: (-2+3+4+7)*2/3 = 8