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ACT American College Testing: Math Section Sample Questions:

1. For -π/2 ≤ θ ≤ π/2, |sin θ | ≥ 1 is true for all and only the values of θ in which of the following sets?

A) {-π/2, π/2}
B) {θ | -π/ 2 ≤θ≤π/2}
C) {θ | -π/ 2 < θ < π/2}
D) {π/2}
E) The empty set

2. In the diagram above, triangle ABC is a right triangle and the diameter of circle O is 2/3 the length of AB.

Which of the following is equal to the shaded area?

A) 24 - 16π square units
B) 24 - 4π square units
C) 48 - 16π square units
D) 48 - 4π square units
E) 20π square units

3. Which of the following has the greatest value when x = -1/4?

A) -3/8x
B) 16x
C) 1/81x
D) x -1
E) 4x + 3

4. When x = 4 and y = 6, by how much does the value of 3x 2 - 3y exceed the value of 2x 2 - 2y?

A) 10
B) 5
C) 15
D) 20

5. Wendy tutors math students after school every day for five days. Each day, she tutors twice as many students as she tutored the previous day.
If she tutors t students the first day, what is the average (arithmetic mean) number of students she tutors each day over the course of the week?

A)

B) 6t
C)

D) t
E) 5t

Solutions: