The document contains 10 math problems from a Junior Varsity math competition held on Valentine's Day 2012. The problems cover a range of topics including probability, geometry, algebra, and word problems. Students were given 1-2 minutes to solve each problem and record their answer and work.

1. 2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 1
Jack and Jill want to play cards, but neither of them have a full deck. If Jack has all face cards excluding
diamonds and Jill has all number cards excluding spades, what is the probability of Jack, with the
combined deck, pulling out a king or club?
Student Number ____________
1min 2min
Answer:
P(A or B) = P(A)+P(B)-P(A&B)
P(A or B) = 3/39+13/39 - 1/39 = 15/39
2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 2
A square is inscribed in a sphere. If the diagonal of the square is equal to the diameter of the sphere,
what is the area of the square if the surface area of the sphere is equal to 400? (leave in terms of π)
Student Number ____________
1min 2min
Answer to #2:

2. = 100 since it is a cube a=b
r= units^2
d= 2 a=
2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 3
Given: f(x)= √x + 1/2x
g(x)= 1/3 + 2
z(x)=
Solve for f(z(g(x)))- z(x) when x = 3
Student Number ____________
1min 2min
Answer:
z(g(x))=
f(z(g(x)))=
plug in 3:
=
=
2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 4
In the figure, ∆ABC has a height of 12
units and an area of 60 units. If each
triangle within ∆ABC lies on the
previous triangle’s midpoints, what is
the area of the shaded region?

3. Student Number____________
1min 2min
Answer:
b=10
2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 5

4. B
70˚
D R
L 30˚
E
A
C
Student Number____________
1min 2min
Answer:
˚
Find
2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 6

5. B
15
1.75x + .5
30
A C
D
Solve for the area of ∆ABC.
Student Number____________
1min 2min
Answer:
30-60-90 ∆rules 1.75x + .5 = 7.5
1.75x = 7
Using or rules x=4
plug into
+6.5
2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 7

6. A
B R C
Student Number____________
1min 2min
Answer:
∆ABC is a right ∆ = Area = ½(product of legs)
∆ABC =
2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 8
Solve:

7. Student Number____________
1min 2min
Answer:
All relatively equal to .9 until .99 when multiplied together equals 9/100
2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 9
Josh starts driving at 20 mph and also starts accelerating by intervals of 4 mph. Bob starts driving fast at
100 mph and decelerates by intervals of 3 mph. They both start driving at 11:50 a.m. and
accelerate/decelerate 1 interval each minute. What time is it when Josh first reaches a speed that is
more than twice the speed Bob is at?
Student Number____________
1min 2min
Answer:
Let J(x)=Josh’s J(x)= 20+4x J(x)>2(B(x)) 20+4x > 2(100-3x) 18 is the minimum amount
Let B(x)=Bob’s B(x)= 100-3x 20+4x > 200-6x so add 18 to 11:50 a.m.
4x > 180-6x 12:08 p.m.
10x =180
x = 18
2012St. Valentine’s Day Mathacre
Junior Varsity Ciphering Question 10
Three congruent circles with radius 2 are drawn inside an equilateral triangle ∆ABC such that each circle
is tangent to the other two and to two sides of the triangle. Find the length of a side of ∆ABC.

8. Student Number____________
1min 2min
Answer:
Let the center of the two lower circles equal M and N and the point where the centers line up with the
base L and O. LMNO make a rectangle in which