The amplitude of the trigonometric function shown below is defined as the average of the absolute values of the maximum value of f(x) and the minimum value of f(x). The trigonometric function graphed below can be described by the equation f(x) = a sin(bx + c), where a, b, and c are real numbers. Which of the following values describes the amplitude of this function?
(A) 1
(B) 2
(C) 3
(D) π
(E) 2π
If point A has a non-zero x-coordinate and a non-zero y-coordinate and at least one of these coordinate values is positive, then point A must be located in which of the 4 quadrants labeled below?
(A)I only (B) I or II only (C) II or IV only (D) II, III, or IV only (E) I, II, or IV only
Correct Answer: E
If a5 for a ≠ 0, which of the following statements must be true?
(F) x ≠ 0 and y ≠ 0 (G) x + y = 5 (H) x - y = 5 (J) xy = 5 (K) = 5
Correct Answer: H
If a(x) = b(x) + c(x), where b(x) = 3x2 - 8x + 113 and c(x) = - 3x2 + 18x + 7 and x is an integer, then a(x) is always divisible by which of the following?
(A) 6 (B) 7 (C) 10 (D) 12 (E) 15
Correct Answer: C
More ACT Math Exam Questions
- 1
For some x and y that satisfy the equation xy = -x2, which of the following is FALSE?
- 2When you multiply a number by 4 and then subtract 7, the result is the same as if you first subtracted 7 from the same number and then multiplied by 11. What is the number?
- 3At a banquet of 36 people, every person had a choice among beef stroganoff, chicken divan, and linguini primavera. If 25% chose beef stroganoff and 17 people chose chicken divan, how many people chose linguini primavera?
- 4
Given the equation |y2 - 11| - 2 = 0, which of the following is a solution but NOT a rational number?
- 5
RST is a right triangle with side lengths of r, s, and t, as shown below. What is the value of cos2 S + cos2 R?