In the complex numbers, where 
, the conjugate of any value a + bi is a– bi.What is the result when you multiply 2 + 7i by its conjugate?
(A) 45
(B) –45
(C) 45i
(D) 53
(E) 53i
The figure below is a pentagon (5-sided figure). Suppose a second pentagon were overlaid on this pentagon. At most, the two figures could have how many points of intersection?
(A) 1 (B) 2 (C) 5 (D) 10 (E) Infinitely many
Correct Answer: E
What is the coefficient of x8 in the product of the polynomials below?
(–x4 + 3x3 - 5x2 + x - 5)(5x4 - 2x3 + x2 - 5x + 2)
（A）0 （B） 5 （C） 4 （D） -2 （E） -5
Correct Answer: E
If x is a real number and 3x = 81, then 3 × 2x =?
(A) 3 (B) 16 (C) 24 (D) 48 (E) 81
Correct Answer: D
More ACT Math Exam Questions
- 1
In the figure below, the circle with center O is tangent to
, 
, 
, and 
. The measure of angle 
BDE is 75° and the measure of DEA is 105°.
The lines in which of the following pairs of lines are necessarily parallel?
I.
and II.
and III.
and - 2A 25-foot ladder stands against a vertical wall at an angle of ndegrees with the ground. If , how far is the base of the ladder from the wall?
- 3
In a certain sequence of numbers, each term after the 1st term is the result of adding 2 to the previous term and multiplying that sum by 3. If the 4th term in the sequence is 186, what is the 2nd term?
- 4
The following figure shows the graph of
. Which of the answer choices are the correct amplitude and period of this function?
- 5
The points P, Q, R, and S lie in that order on a straight line. The midpoint of
is R and the midpoint of 
is Q. The length of 
is x feet and the length of 
is 4x - 16 feet. What is the length, in feet, of ?