Embed Size (px)
Citation preview
ALGEBRA 1GEOMETRYALGEBRA 2RELATED
TECHNICAL
2015 Vocational Math Meet: Round 1
100
200
300
100
200
300
100
200
300
100
200
300
Algebra 1100 points
The numbers 1, 2, 3, … 10 are written on ten index cards, one number per card. You shuffle the cards and, without looking at them, randomly select one card and throw it away.
If you randomly select a second card, what is the probability that it will have a prime number written on it?
Algebra 1 100 points Answer
The prime numbers are 2, 3, 5, and 7.
If no card was thrown away, the probability of a chosen card displaying a prime number would be 4/10. Each card in the deck has the same probability of being a prime number. Throwing away the first card has no effect.
2/5
Algebra 1 100 points
Algebra 1200 points
Nine numbers have a mean of k. If c is added to the nine numbers, the new mean is 2k. Express c in terms of k.
Algebra 1 200 points Answer
If the mean of nine numbers is k, their sum is 9k. The new mean, , equals 2k.
Algebra 1300 points
Simplify the expression
Algebra 1 300 points Answer
Factor the numerator to obtain
which simplifies to x.
x
Geometry100 points
A sphere and a hemisphere have the same volume. If the radius of the hemisphere is R and the radius of the sphere is r, find the value of
Geometry100 points Answer
The volume of the sphere is , and the volume of the hemisphere is The volumes are equal, so
We want so cube both sides.
8
Geometry200 points
The lengths of the sides of ∆ABC are AB = 20, BC = 24, and AC = 17. If AD = DE = EF = FC and , find IF.
Geometry200 points Answer
The parallel lines are equally spaced, so
Since ∆AFI ∆ACB, corresponding ∼sides of these triangles will be proportional.
Thus, = 18.
FI = 18
Geometry300 points
The circumference of a large circle is 2 cm greater than the circumference of a small circle. Exactly how much bigger is the radius of the large circle than the radius of the small circle?
Geometry300 points Answer
Small circle: radius = r, C = 2 r𝜋Large circle: radius = R, C = 2 R𝜋2 R = 2 r + 2𝜋 𝜋 = =
Hence, the larger radius is greater than the smaller radius.
Algebra 2100 points
If , find k.
Algebra 2 100 points Answer
Combine like terms to obtain 3(
Use the law of exponents to write
k = 18
Algebra 2200 points
If , find
Algebra 2 200 points Answer
27
Algebra 2300 points
Find the values of b if the equation has a double root:
Algebra 2 300 points Answer
If the equation has a double root, then the discriminant must equal zero.
Related Technical100 points
Most octopi have 8 arms. Each arm has 2 rows of suction cups, and each row contains between 100 and 125 suction cups. What is the difference between the maximum and minimum numbers of suction cups for an octopus?
Related Technical100 points Answer
The largest variation in the number of suction cups in one row is 25, and there are a total of 16 rows. Therefore, the largest variation would be 16 x 25.
400
Related Technical200 points
Sam makes $10.50 per hour. When he works a 40-hour week, his after-tax take home pay is $344.27. How large a raise, to the nearest percent, would Sam need so that his new take-home pay equals his current gross pay? (Assume that the tax rate does not change.)
Related Technical200 points Answer
new pay – old pay = percentage increase old pay
10.5(40)-344.27 = .22 344.27
22%
Related Technical300 points
A block of wood in the shape of a right rectangular prism has dimensions 1 ft. x 1ft. x 2 ft. If Tom saws it in half to create two blocks with dimensions 1 ft. x 1ft. x 1 ft., what is the percentage increase in the total surface area?
Related Technical300 points Answer
Original total surface area =4(1 • 2) + 2(1 • 1) = 10 ft2
After sawing, total surface area =
2 • 6(1 • 1) = 12 ft2
Since the original surface area was 10 ft2, the amount of increase was 2 ft2.
2/10 = 20% increase
20% increase
