CLASS SECTION/SCHEDULE (FRI-AM, FRI-PM, SAT-AM, SAT-PM, SUN-AM, SUN-PM, ONLINE)

1.

A ladder 25 ft long is leaning against a vertical wall. If the bottom of the ladder is pulled horizontally away from the wall at 3 ft/sec, how fast is the top of the ladder sliding down the wall, when the bottom is 15 ft from the wall?

a) 1 ¼ ft/sec b) 2 ¼ ft/sec c) 3 ¼ ft/sec d) 4 ¼ ft/sec

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2.

A man 6 ft tall walks with a speed of 8 ft per second away from a street light atop an 18 foot pole. How fast is the tip of his shadow moving along the ground from the light pole?

a) 12 ft per second b) 13 ft per second c) 14 ft per second d) 15 ft per second

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3.

A ladder 10 feet long is resting against a wall. If the bottom of the ladder is sliding away from the wall at a rate of 1 foot per second, how fast is the top of the ladder moving down when the bottom of the ladder is 8 feet from the wall?

a) 2/3 feet per second b) 3/3 feet per second c) 4/3 feet per second d) 5/3 feet per second

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4.

Find how fast the volume of a balloon is changing when the radius is 6 inches and the diameter of the balloon is increasing at a rate of 3 inches per second.

a) 6.786 cubic inch per second b) 67.86 cubic inch per second c) 678.6 cubic inch per second d) 6786 cubic inch per second

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5.

Two cars leave an intersection at the same time. One car travels north at 35 mi/hr., the other travels east at 60 mi/hr. How fast is the distance between them changing after 2 hours?

a) 70 mph b) 75 mph c) 80 mph d) 85 mph

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6.

A model for newspaper circulation is C(t) = 83 – 9 ln t where C is newspaper circulation (in millions) and t is the number of years (t=0 corresponds to 1980). Estimate the circulation and find the rate of change of circulation in 2010 and explain the result.

a) 52.4 million, 0.2 million per year b) 52.4 million, 0.3 million per year c) 62.4 million, 0.2 million per year d) 62.4 million, 0.3 million per year

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7.

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8.

As the lead engineer, your specific task is to design the cable supporting the bridge deck. An initial analysis shows that the concrete tower is 150 meters above the road deck and that the support point for the main cable is 100 meters away from the concrete tower. How long does the cable have to be?

a) 178 meters b) 179 meters c) 180 meters d) 181 meters

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9.

As a hydraulic engineer, you are concerned with the amount and velocity of surface runoff resulting from the melting of snow in the springtime. Your consulting firm has asked you to find the grade (angle of inclination) in an area of a park. You know you can do this by using a surveyor’s level and casting a horizontal line of sight. You go to the site and pick two points in the park between which you can measure the length along the slope of the ground. You measure this length and find it to be 100 feet. Using your surveying skills, you then record the elevation at the same two points. It is 7.21 feet and 2.63 feet. What is the angle of inclination of the ground?

a) 2.62 degrees b) 3.62 degrees c) 4.62 degrees d) 5.62 degrees

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10.

You are an air traffic controller communicating with a plane in flight that will soon land. The pilot tells you he is flying at an altitude of 35,000 feet. You locate the airplane on your radar and tell the pilot that 100,000 feet separate him from the beginning of the runway (that imaginary straight line is the hypotenuse). What angle of descent must you tell the pilot he must take to land his plane at the beginning of the runway?

a) 19.5 degrees b) 20.5 degrees c) 21.5 degrees d) 22.5 degrees

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11.

You’re a ground crew operator preparing for the launch of a rocket carrying satellite equipment. You are working 1,200 feet from the launch pad. Your task is to measure the time it takes from lift-off till the rocket reaches an approximate height of 2000 feet. By doing this, you can get a good estimate of the velocity of the rocket by dividing the distance that it traveled by the amount of time that it took. From where you are standing what is the angle of inclination of your line of sight from the horizontal when the rocket reaches 2000 feet?

a) 56.04 degrees b) 57.04 degrees c) 58.04 degrees d) 59.04 degrees

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12.

The boys ordered several pizzas for the weekend. When the first evening was over, the following amounts of pizza were left over: 1/4 of the pepperoni pizza, 1/2 of the cheese pizza, 3/4 of the mushroom pizza and 1/4 of the supreme pizza. The next morning, each boy ate the equivalent of 1/4 of a pizza for breakfast. If that finished the pizza, how many boys were there?

a) 7 b) 8 c) 9 d) 10

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13.

Dan read that an average snowfall of 10 inches yields 1 inch of water when melted. Very wet snow will measure 5 inches for one inch of water, and very dry snow may measure 20 inches for an inch of water. He made measurements for a storm that started with 5.3 inches of average snowfall. The precipitation changed to wet snow and dropped another 4.1 inches. The weather continued to warm up, and the storm finished with 1.5 inches of rain. What was the actual amount of water that fell during the storm? Round your answer to tenths.

a) 2.9 b) 3.0 c) 3.1 d) 3.2

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14.

Emily cut two circles from a sheet of colored paper measuring 8” by 12”. One circle had a radius of 3 inches and the other had a radius of 2.5 inches. How many square inches of paper are left over? Is it possible to cut another circle with a 3 inch radius from the paper?

a) 46 b) 47 c) 48 d) 49

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15.

Tom wants to buy items costing $25.35, $50.69, and $85.96. He earns $6.50 an hour doing odd jobs. If ten percent of his income is put aside for other purposes, how many hours must he work to earn the money he needs for his purchases? Round your answer to the nearest whole hour.

a) 26 b) 27 c) 28 d) 29

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16.

Three tenths of the wooden toys were painted blue and one fourth of them were painted green. Half of the remaining toys were painted red and half were painted yellow. If 300 toys are blue, how many are there of each of the other colors?

a) 220 b) 230 c) 240 d) 250

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17.

Assume that the number of hours Katie spent practicing soccer is represented by x. Michael practiced 4 hours more than 2 times the number of hours that Katie practiced. How long did Michael practice?

a) 2x + 4 b) 2x – 4 c) 2x + 8 d) 4x + 4

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18.

Patrick gets paid three dollars less than four times what Kevin gets paid. If the number of dollars that Kevin gets paid is represented by x, what does Patrick get paid?

a) 3 − 4x b) 3x − 4 c) 4x − 3 d) 4 − 3x

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19.

If the expression 9y − 5 represents a certain number, which of the following could NOT be the translation?

a) five less than nine times y b) five less than the sum of 9 and y c) the difference between 9y and 5 d) the product of nine and y, decreased by 5

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20.

Susan starts work at 4:00 and Dee starts at 5:00. They both finish at the same time. If Susan works x hours, how many hours does Dee work?

a) x + 1 b) x − 1 c) x d) 2x

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21.

If x and y are complementary angles, then:

a. sec x = csc y b. cos x = cos y c. tan x = tan y d. sin x = sin y

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22.

sin 2B = 2 sin B is true when B is equal to:

a. 0° b. 30° c. 60° d. 90°

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23.

If x = a cos 0 and y = b sin 0, then b^2 2x^22 + a^22 y^2 =

a. a²b² b. 2a²b² c. b² + a² d. ab

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24.

If sin A – cos A = 0, then the value of sin4 A + cos4 A is

a. 1 b. 2 c. 1/2 d. 1/3

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25.

Ratios of sides of a right triangle with respect to its acute angles are known as

a. Trigonometric ratios of the angles b. Trigonometry c. Trigonometric identities d. None of these

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26.

If sin 0 = √3 cos θ, 0° < θ < 90°, then θ is equal to

a. 60° b. 90° c. 45° d. 30°

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27.

Find the derivative of the function 2x2 + 8x + 9 with respect to x.

a. Df(x) = 4x – 8 b. Df(x) = 2x + 9 c. Df(x) = 2x + 8 d. Df(x) = 4x + 8

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28.

What is the first derivative dy/dx of the expression (xy)x = e?

a. – y(1 + ln xy) / x b. 0 c. – y(1 – ln xy) / x^2 d. y/x

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29.

Evaluate the differential of tan

a. ln sec θ dθ b. ln cos θ dθ c. sec θ tan θ dθ d. sec^2 θ dθ

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30.

Find the slope of the tangent to the curve y = x4 – 2x2 + 8 through point (2, 16).