PLAN/ACT Problem Set #2

Sides AB and AC are the same length in △ABC, which has an exterior angle measuring 110°. What is the value of x?

• 80

• 70

• 60

• 55

• 40

Which of the following is the greatest?

For what value of x is the equation 6x - 15 = x + 85 true?

• 10

• 14

• 14 2/7

• 16 2/3

• 20

• 475 = 35w

• 475 = 35w + d

• (d - 475) = 35w

• d - 475 = w - 35

• d = 35w + 475

As shown below, 4 segments form 2 triangles. What is the measure of ∠BED?

• 130°

• 120°

• 110°

• 100°

• Cannot be determined from the given information

Given a figure similar to the one below, in which C is the midpoint of AB and CD is perpendicular to AB, which of the following statements is NOT necessarily true?

• AC = CD

• AC = BC

• AD = BD

• ∠ADC = ∠BCD

• ∠ADC = ∠BDC

While cruising on a lake, an old-fashioned steamship burns wood to create power. The ship's furnaces consume 1 cord of wood every 90 minutes. One cord of wood will fill a space in the shape of a rectangular prism 4 feet high, 8 feet long, and 4 feet wide.

Which of the following is closest to the number of cords of wood the steamship would burn during a 6-hour cruise?

• 1.5

• 2.7

• 4

• 5.4

• 6

While cruising on a lake, an old-fashioned steamship burns wood to create power. The ship's furnaces consume 1 cord of wood every 90 minutes. One cord of wood will fill a space in the shape of a rectangular prism 4 feet high, 8 feet long, and 4 feet wide. What is the minimum size, in cubic feet, that the storage area on the steamship must be to hold 3 cords of wood?

• 128

• 192

• 384

• 576

• 864

The graph below represents the steamship's travel for a particular cruise. The distance, in miles, that the steamship has traveled from its launch point is shown on the vertical axis and the time, in hours, that has elapsed since the steamship left its launch point is shown on the horizontal axis. Consider every possible line segment that has 2 distinct points on the curve as endpoints. Which of the following describe(s) the slope of at least one of these segments?

I. Positive

II. Negative

III. Zero

• II only

• III only

• I only

• I an II only

• I, II, and III

A survey of students was taken at Cactus Shadows Elementary School to decide whether gymnastics or computer skills should be offered as an after-school activity. Of the 47 students surveyed, 15 thought gymnastics should be offered, 24 thought computer skills should be offered, and 14 thought neither should be offered. How many of the 47 students thought both should be offered?

• 6

• 8

• 12

• 18

• 22