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ACT American College Testing: Math Section Sample Questions:

1. The Smith family is planning to build a 3-room cabin which consists of 2 bedrooms (BR) and 1 living room (LR). Shown below are the rectangular floor plan (left figure) and a side view of the cabin (right figure). In the side view, the roof forms an isosceles triangle (Δ ABC ), the walls are perpendicular to the level floor (

),

, F is the midpoint of

, and

.

During the week the Smiths plan to roof the cabin, there is 20% chance of rain each day.
Mr. and Mrs. Smith plan to roof the cabin on 2 consecutive days.
Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?

A) 0.04
B) 0.08
C) 0.16
D) 0.20
E) 0.40

2. In the diagram above, ABCD is a square with an area of 100 cm 2 and lines BD and AC are the diagonals of ABCD.

If line EF is parallel to line BC and the length of line CF = 3√ 2 cm, which of the following is equal to the shaded area?

A) 25 cm2
B) 89 cm2
C) 39 cm2
D) 64 cm2
E) 78 cm2

3. When x= -3, the expression -2x 2 + 3x - 7 =:

A) -16
B) -34
C) 2
D) -10
E) -27

4. In a restaurant, the ratio of four-person booths to two-person booths is 3:5.
If 154 people can be seated in the restaurant, how many two-person booths are in the restaurant?

A) 57
B) 21
C) 35
D) 14
E) 70

5. The distribution of Jamal's high school grades by percentage of course credits is given in the circle graph below.

What is Jamal's grade point average if each A is worth 4 points; each B, 3 points; and each C, 2 points?

A) 3.0
B) 3.6
C) 3.7
D) Cannot be determined from the given information.
E) 3.4

Solutions: