WorksheetsMathCounts Warmup/Workout 6
Total questions: 20
Worksheet time: 5hrs 0mins
If
A = 23−32+4(5+1) and B = 72−2(3 +1)2 What is the value of A−B ?
(a)
What is the ratio of the area of square ABCD to that of square BDEF in the figure shown?
1/3
1/2
1/4
1/5
2/3
What is the MEDIAN of the first ten prime numbers?
(a)
Let the value of a word equal the sum of the values of its letters. Suppose MATH has value M + A + T + H = 85 and M = 8, A = 3H, T = 73 and H = 1. If S = 3M - 15 and N = 2H + S, what is the value of SAMANTHA?
(a)
What is the reminder when the sum of 102−42 is divided by 8?
(a)
Hugo has a solid like the one shown, comprised of 32 unit cubes. He paints each face a solid red and then separates the solid into 32 individual unit cubes. What is the probability that a randomly selected unit cube has exactly one painted face?
1/20
7/10
3/16
5/14
9/21
If x equals twice its reciprocal, what is the value of x4?
(a)
A robotic vacuum cleaner vacuums one hotel room in 3/10 of an hour. At this rate, how many rooms of the same size will it vacuum in 3 hours?
(a)
Nya starts with an integer N and repeatedly subtracts 6. Mya starts with an integer M and repeatedly adds 8.
When Nya and Mya each have performed their respective repeated operation 13 times, both have a resulting value of 25. What is the value of N + M?
(a)
(1 + 21)(1 + 31)(1+41)...(1+191) ?
What is the value of:
(a)
The triangle with vertices A(0,4), B(3,0) and C(4,7) are dilated by a factor of 2 about the origin. What is the area of the dilated triangle?
(a)
A raffle has prizes valued at $1, $3, $15, $60, $120, $360 and $1800. If exactly $10,000 in prizes is to be awarded, what is the least number of prizes that can be awarded, assuming that there will be at least one prize of each value awarded?
(a)
The estimated weight of a salmon, in pounds, is the product of its length and the square of its girth, both in inches, divided by 775.
What is the estimated weight of a salmon with length 28.5 inches and girth 10.25 inches? Round to the nearest tenth.
(a)
Point Q is the reflection of P(a, 4) over the x-axis, and R is the reflection of Q over the y-axis. If the area of triangle PQR is 12 units2 and a>0, what is the value of a?
Round to the nearest tenth.
(a)
Trains pass through a rail yard of five separate tracks at five different frequencies: every 50 minutes, every hour, every 90 minutes, every 2 hours and every 3 hours.
If trains pass through on all five tracks at 9:00am, how many hours will elapse before trains next pass through on all five tracks at the same time?
(a)
Quadrilateral PSTU is inscribed in semicircle O, as shown, with PQ = 3 units, QR = 5 units and RS = 4 units. What is the area of quadrilateral PSTU?
Express your answer as a decimal rounded to the nearest tenth.
(a)
Points A, B, C, D and E are on a line positioned so that B is the midpoint of segment AD, D is 3/4 of the way from A to E, and C is 1/5 of the way from B to E. If AB = 6 units, what is the value of CE?
(a)
Vick pays $50 for 33 pounds of cashews, which he separates into smaller 3/8 pound bags. If Vick sells each bag for $0.79, what percent of this price is profit?
Express your answer to the nearest tenth of a percent.
(a)
To make bracelets, Alice bought 12 red beads and 10 white beads for $14, while Nevea bought 8 red beads and 15 white beads $13.50, What is the cost of a red bead?
(a)
8 −x2−y2−2xy = 0 for real numbers x and y, what is the value of ∣x+y∣ ?
2
5
32
22
52
