Mathematics Quiz

A recursive formula for the sequence 81, 54, 36, ... is

• a_n = 81(0.67)^(n-1)

• a_1 = 81 a_n = a_{n-1} - 27

• a_n = 81 + (n-1)(-27)

• a_1 = 81 a_n = 0.67a_{n-1}

Given q(θ) = 2 cos(1/3 θ) on the interval -π < θ < π, the function q

• increases, then decreases

• decreases, then increases

• increases throughout the interval

• decreases throughout the interval

In a group of 50 trains, 30 have electric engines, 25 have diesel engines, and 10 have both diesel and electric engines. How many trains have neither electric nor diesel engines?

• 5

• 15

• 25

• 35

The weights of the 2500 students at Riverside High School are approximately normally distributed with a mean of 150 pounds and a standard deviation of 15 pounds. The number of students at Riverside who weigh between 135 and 165 pounds is closest to

• 1700

• 1800

• 1900

• 2000

A researcher wants to find out if listening to classical music helps people concentrate better. Which method of data collection is most appropriate?

• census

• survey

• observation study

• controlled experiment

A sequence is defined as b_n = b_{n-1} + log_{n+2}(n), where b_1 = 5. What is the value of b_3?

• 5

• 5.3

• 6.1

• 7

Given P(C) = 3/4 and P(D) = 2/5, where C and D are independent events, determine P(C ∩ D).

The scores on a collegiate mathematics readiness assessment are approximately normally distributed with a mean of 680 and a standard deviation of 120. Determine the percentage of scores between 650 and 850, to the nearest percent.

• A. 55%

• B. 60%

• C. 65%

• D. 70%

Mr. Bear wants to conduct a survey to see how students feel about changing the school mascot to a bear. Which plan is the best process for gathering an appropriate sample?

• A. Survey students in a random sample of senior homerooms.

• B. Survey every tenth student entering art classes in the school.

• C. Survey every fourth student entering the cafeteria during each lunch period.

• D. Survey all members of the school's varsity sports teams.

The depth of the water, d(t), in feet, on a given day at Ocean Bay, t hours after midnight is modeled by d(t) = 4 sin ((π/4) t) + 6. Which statement about the Ocean Bay tide is false?

• A. A low tide occurred at 3 am.

• B. The maximum depth of the water was 10 feet.

• C. The water depth at 6 am was approximately 8 feet.

• D. The difference in water depth between high tide and low tide is 8 feet.