Math Counts Warm-Up #3-4 2017-2018

If y is a number such that y² = (y + 2018)², what is the value of y? (a)  

Tags

CCSS.HSA-REI.B.4B

Maura is 5 years younger than her sister Cara. Seven years ago, Maura was half as old as her sister. How old is Maura now? (a)   years old

Tags

CCSS.8.EE.C.8C

A dartboard consists of three concentric circles with radii 10, 5 and 1, respectively,

measured in inches. The area between the largest and middle circles is colored green, the

area between the middle and smallest circles is colored yellow, and the area within the

smallest circle, the bull’s-eye, is colored red. If a thrown dart is guaranteed to hit the board, but its position on the board is uniformly random, what is the probability that it lands in the yellow portion of the board? Express your answer as a common fraction. (a)  

The 1990 and 2018 calendars are identical in the number of days in each month and the day of the week on which each day of each month occurs. In fact, the calendar repeats in these ways every 28 years until the year 2100. How many days are there in the 28 years preceding 2018? (a)   days

Tags

CCSS.3.MD.A.1

A right triangle has legs with lengths of 5 cm and 10 cm. What is the length of the altitude drawn to the hypotenuse of this triangle? Express your answer in simplest radical form. (Write the word "radical" where th radical sign would be used, such as 7 radical 3) (a)  

Min Zhang wrote down all of the two-digit multiples of 5. What is the probability that one of these numbers, chosen at random, has exactly two distinct primes that are factors? Express your answer as a common fraction. (a)  

Given a set of numbers with median m, the median of all the

numbers less than m is the called the lower quartile. The median

of all the numbers greater than m is called the upper quartile.

The absolute difference between the lower and upper quartiles is

called the interquartile range. What is the interquartile range for

the numbers in the stem-and-leaf plot shown? (a)  

Positive integers 1 to 36 are written in rows in a six-by-six array

as shown. Each prime number is crossed off, as well as all the

numbers in the diagonal extending up and to the right from that

prime. For example, 11 is prime and is crossed off along with the

6 above and to the right. What is the sum of the remaining values after all the primes and associated diagonals have been eliminated? (a)  

Tags

CCSS.7.NS.A.2C

What is the value of 1,000,000! ÷ 999,999!? (a)  

A cubic yard of topsoil is to be spread evenly in the garden at Prove It! Math Academy. The garden measures 10 feet by 8 feet. How many inches deep will the topsoil be? Express your answer as a mixed number (written so there is a space between the whole number and fraction, such as 1 2/5 or 7 3/8). (a)   inches

Tags

CCSS.5.MD.A.1